Spectrum Math

This handy Spectrum Math Grade 4 Answer Key Chapter 2 Lesson 2.4 Greater Than, Less Than, or Equal To provides detailed answers for the workbook questions.

Spectrum Math Grade 4 Chapter 2 Lesson 2.4 Greater Than, Less Than, or Equal To Answers Key

Inequalities are statements in which the numbers are not equal.
< means “is less than.” > means “is greater thon.”
= means “is equal to.”

Compare
35 and 42.
35 < 42
Compare the values.
Look at the tens.
3 tens is less than 4 tens.
35 is less than 42.
This is an inequality.

Compare
112 and 110.
112 > 110
Compare the values. Since the hundreds and tens are equal, look at the ones.
112 is greater than 110.
This is an inequality.

Compare 55 to 55.
55 = 55
These numbers are equal, so this is not an inequality.

Compare each pair of numbers. Write >, <, or =.

Question 1.
a. 105 _____ 120
Answer:
Here both the hundreds place is equal then look at the tens place.
The tens place of 105 is less than the tens place of 120,
So, 105 <120.
Therefore 105 less than 120. This is inequality.

b. 52 ____ 35
Answer:
Here tens place of 52 is greater than the tens place of 35.
So, 52 > 35.
Therefore 52 is greater than 35. This is inequality.

c. 10,362 ____ 10,562
Answer:
Here both the ten thousands and thousands place are equal then look at the hundreds place.
The hundreds place of 10,362 is less than the hundreds place of 10,562.
So, 10,362 < 10,562.
Therefore 10,362 less than 10,562. this is in equality.

Question 2.
a. 5,002 ____ 2,113
Answer:
Here thousands place of 1,002 is greater than the thousands place of 2,113.
So, 5,002 > 2,113.
Therefore 5,002 greater than 2,113. This is inequality.

b. 713 ____ 731
Answer:
Here the hundreds place of both numbers are same then look at the tens place.
The tens place of 713 is less than the tens place of 731.
So, 713 < 731.
Therefore 713 less than 731. This is inequality.

c. 12,317 ___ 11,713
Answer:
Here ten thousands place of both the numbers are same then look at the thousand place.
The thousands place of 12,317 is greater then the thousands place of 11,713.
So, 12,317 > 11,713.
Therefore 12,317 greater than 11,713. This is inequality.

Question 3.
a. 115,000 ____ 105,000
Answer:
Here lakhs place of both the numbers are same Then look at the ten thousands place.
The ten thousands place of 115,000 is greater than the 105,000.
So, 115,000 > 105,000.
Therefore 115,000 greater than the 105,000. this is inequality.

b. 23 ___ 32
Answer:
Here the tens place of 23 is less than the 32.
So, 23 < 32.
Therefore 23 less than 32. This is inequality.

c. 142 ___ 142
Answer:
Here ones, tens and hundreds place value of both the numbers are same.
So, 142 = 142.
Therefore 142 equal to 142. this is not a inequality.

Question 4.
a. 310 ____ 290
Answer:
Here hundreds place of 310 is greater than the hundreds place of 290.
So, 310 > 290.
Therefore 310 greater than 290. This is inequality.

b. 715 ___ 725
Answer:
Here both the hundreds place value is same. Then look at the tens place.
The tens place of 715 is less than the ten place of 725.
So, 715 < 725.
Therefore 715 less than 725. This is inequality.

c. 1,132,700 ____ 1,032,700
Answer:
The ten lakhs place of 1,132,700 is greater than the ten lakhs place of 1,032,700.
So, 1,132,700 > 1,032,700
Therefore 1,132,700 greater than 1,032,700. This is a inequality.

Question 5.
a. 616 ____ 106
Answer:
The hundreds place of 616 is greater than the hundreds place of 106.
So, 616 > 106.
Therefore 616 greater than 106. This is inequality.

b. 119,000 ___ 120,000
Answer:
Here the lakhs place of both the numbers are same. Then look at the ten thousands place.
The ten thousands place of 119,000 less than the ten thousands place of 120,000.
So, 119,000 < 120,000.
Therefore 119,000 less than 120,000. This is inequality.

c. 48,112 ___ 48,212
Answer:
Both the numbers have the same place value.
So, 48,112 = 48,212.
Therefore 48,112 is equal to the 48,212. This is equality.

Question 6.
a. 823 ____ 821
Answer:
Here both the hundreds and tens place are equal then look at the ones place.
The ones place of 823 is greater than the ones place of 821.
So, 823 > 821.
Therefore 823 greater than the 821. This is inequality.

b. 2,003,461 ___ 2,004,461
Answer:
The thousands place of 2,003,461 is less than the thousands place value of 2,004,461.
So, 2,003,461 < 2,004,461.
Therefore 2,003,461 is less than the 2,004,461. This is inequality.

c. 7,903 ___ 9,309
Answer:
The thousands place of 7,903 less than the thousand place value of 9,309.
So, 7,903 < 9,309.
Therefore 7,903 is less than 9,309. This is inequality.

Question 7.
a. 30 ____ 25
Answer:
The ten place of 30 is greater than the tens place of 25.
So, 30 > 25.
Therefore 30 greater than 25. This is inequality.

b. 47,999 ____ 45,999
Answer:
Here both the ten thousands place is equal. Then look at the thousands place.
The thousands place of 47,999 greater than the thousands place of 45,999.
So, 47,999 > 45,999.
Therefore 47,999 is greater than the  45,999. This is inequality.

c. 19,900 ____ 19,090
Answer:
Here ten thousands and thousands place are equal. then look at the hundreds place.
The hundreds place value of 19,900 is greater than the hundreds place value of 19,090.
So, 19,900 > 19,090.
Therefore 19,900 is greater than 19,090. This is inequality.

Question 8.
a. 111 ____ 111
Answer:
Both the place values of numbers are same.
So, 111 = 111.
Therefore 111 equal to 111. This is not a inequality.

b. 386,712 ____ 386,711
Answer:
Here lakhs, ten thousands, thousands, hundreds and tens place values are same.
The ones place of 386,712 greater than the 386,712.
So, 386,712 > 386,711.
Therefore 386,712 is greater than 386,711. This is inequality.

c. 615 ____ 614
Answer:
Here the hundreds and tens place is equal. Then look at the ones place.
The ones place of 625 is greater than the ones place of 614.
So, 615 > 614.
Therefore 615 greater than the 614. This is inequality.

Compare the numbers. Write <, >, or =.

Question 1.
a. 3,647 ____ 36,647
Answer:
The number 3,647 as 4 digits.
The number 36,647 as 5 digits.
So, 3,647 < 36,647.
Therefore 3,647 is less than 36,647. This is inequality.

b. 4,678 ___ 4,768
Answer:
Here both the thousands place value is same. Then look at the at the hundreds place value.
The hundreds place value of 4,678 is less than the hundreds place value of 4,768.
So, 4,678 < 4,768.
Therefore 4,678 is less than 4,768. This is inequality.

c. 68,035 ____ 68,025
Answer:
Here ten thousands, thousands and hundreds place value of both the numbers are same. The look at the tens place.
The tens place of 68,035 is greater than the tens place value of 68,025.
So, 68,035 > 68,025.
Therefore 68,035 is greater than 68,025. This is inequality.

Question 2.
a. 4,102,364 _____ 4,201,364
Answer:
The lakhs place of 4,102,364 is less than the lakhs place of 4,201,364.
So, 4,102,364 < 4,201,364
Therefore 4,102,364 is less than then the  4,201,364. This is inequality.

b. 56,703 ____ 56,702
Answer:
Here ten thousands, thousands, hundreds and tens place is of both the numbers are same. Then look at the ones place.
The ones place of 56,703 is less than the ones place of 56,702.
So, 56,703 > 56,702.
Therefore 56,703 is greater than the 56,702. This is inequality.

c. 125,125 ____ 125,150
Answer:
The tens place of 125,125 is less than the tens place of 125,150.
So, 125,125 < 125,150.
Therefore 125,125 less than 125,150. This is inequality.

Question 3.
a. 90,368 ____ 90,369
Answer:
here ten thousands, thousands, hundreds and tens place value of both the numbers are same. Then look at the ones place.
The ones place of 90,368 is less than the ones place of 90,369.
So, 90,368 < 90,369.
Therefore 90,368 less than 90,369. This is inequality.

b. 5,654,308 ___ 5,546,309
Answer:
The lakhs place of 5,654,308 is greater than the lakhs place of 5,546,309.
So, 5,654,308 > 5,546,309.
Therefore 5,654,308 is greater than the 5,546,309. This is inequality.

c. 65,003 ____ 65,013
Answer:
Here ten thousands, thousands, hundreds place value is same in both the numbers, then look at the ten place.
The tens place of 65,003 less than the tens place of 65,013.
So, 65,003 < 65,013.
Therefore 65,003 is less than the 65,013. This is inequality.

Question 4.
a. 4,567,801 ____ 456,780
Answer:
The number 4,567,801  as 7 digits.
The number 456,780 as 6 digits.
So, 4,567,801 > 456,780.
Therefore 4,567,801 is greater than the 456,780. This is inequality.

b. 7,621 ____ 7,261
Answer:
Here both the thousands place are same. Then look at the hundreds place.
The hundreds place of 7,621 is greater than the hundreds place of 7,261.
So, 7,621 > 7,261.
Therefore 7,621 greater than the 7,261. This is inequality.

c. 769,348 ____ 759,348
Answer:
Here both the lakhs place is same, Then look at the ten thousands place.
The ten thousands place of 769,348 is greater than the ten thousands place of 759,348.
So, 769,348 > 759,348.
Therefore 769,348 is greater than the 759,348. This is inequality.

Question 5.
a. 506,708 ___ 506,807
Answer:
The hundreds place of 506,708 is less than the hundreds place value of 506,807.
So, 506,708 < 506,807
Therefore 506,708 less than 506,807. This is inequality.

b. 1,365,333 ____ 1,365,333
Answer:
Her both the numbers are same.
So, 1,365,333 = 1,365,333
Therefore 1,365,333 is equal to 1,365,333. This is not a inequality.

c. 9,982 ____ 9,928
Answer:
Here thousands, hundreds is same. Then look at the tens place.
So, 9,982 < 9,928.
Therefore 9,982 greater than 9,928. This is inequality.

Question 6.
a. 224,364 ____ 234,364
Answer:
Both the numbers are same.
So, 224,364 = 234,364.
Therefore 224,364 is equal to  234,364. This is not inequality.

b. 32,506 ____ 23,605
Answer:
Here ten thousands place of 32,506 is greater than the ten thousands place of 23,605.
So, 32,506 > 23,605.
Therefore 32,506 is greater than 23,605. This is inequality.

c. 7,850 ____ 7,850
Answer:
Both the numbers are same.
So, 7,850 = 7,850
Therefore 7,850 is equal to 7,850. This is not a inequality.

Question 7.
a. 3,204,506 ____ 3,204,606
Answer:
The hundreds place of 3,204,506  is greater than the hundreds place of  3,204,606.
So, 3,204,506 > 3,204,606.
Therefore 3,204,506 is greater than 3,204,606. This is inequality

b. 9,851 ___ 9,850
Answer:
Here ones place of 9,851 is greater than the ones place of 9,850.
So, 9,851 > 9,850.
Therefore 9,851 is greater than 9,850. This is inequality.

c. 2,000,567 ____ 2,001,567
Answer:
Here thousands place of 2,000,567 is less than the thousands place of  2,001,567.
So, 2,000,567 < 2,001,567.
Therefore 2,000,567 less than 2,001,567. This is inequality.

Question 8.
a. 430,632 ____ 80,362
Answer:
The number 430,632 as 6 digits.
The number 80,362 as 5 digits.
So, 430,632 > 80,362.
Therefore 430,632 greater than 80,362. This is inequality.

b. 49,984 ____ 49,984
Answer:
Both the numbers are same.
So, 49,984 = 49,984
Therefore 49,984 is equal to 49,984. This is not inequality.

c. 5,640,002 ____ 5,639,992
Answer:
The ten thousands place 5,640,002 is greater than 5,639,992.
So, 5,640,002 > 5,639,992
Therefore 5,640,002 is greater than 5,639,992. This is inequality.

Question 9.
a. 172,302 ____ 173,302
Answer:
Here both the numbers are same.
So, 172,302 = 173,302.
Therefore 172,302 is equal to the 173,302. This is not a inequality.

b. 212,304 ____ 212,304
Answer:
Here both the numbers are same.
So, 212,304 = 212,304
Therefore 212,304 is equal to the 212,304. This is not a inequality.

c. 6,886 ___ 6,896
Answer:
Both the numbers same.
So, 6,886 = 6,896.
Therefore 6,886 is equal to 6,896. This is not a inequality.

This handy Spectrum Math Grade 4 Answer Key Chapter 2 Lesson 2.3 Rounding provides detailed answers for the workbook questions.

Spectrum Math Grade 4 Chapter 2 Lesson 2.3 Rounding Answers Key

Rounding

Round 783,538 to the nearest ten thousand.
Look at the thousands digit. 15,897

8 is greater than or equal to 5, so round 5 to 6 in the thousands place. Follow with zeros.
16,000

Round 234,034 to the nearest hundred. Look at the tens digit. 234,034
3 is less than 5, so 0 stays in the hundreds place. Follow with zeros.
234,000

Round to the nearest ten.

Question 1.
a. 6,421
________
Answer:
Given that the number is 6,421.
Here 1 is in ones place and 2 in tens place.
1 is less than 5. so, replace 1 with 0.
Therefore 6,421 rounded to the nearest ten is 6,420.

b. 5,882
________
Answer:
Given that the number is 5,882.
Here 2 is in ones place and 8 in tens place.
2 is less than 5. so, replace 2 with 0.
Therefore 5,882 rounded to the nearest ten is 5,880.

c. 45,288
________
Answer:
Given that the number is 45,288.
Here 8 is in ones place and 8 in tens place.
8 is greater than 5. so, replace 1 with 0 and add 1 to the tens place.
Therefore 45,288 rounded to the nearest ten is 45,288.

d. 975
________
Answer:
Given that the number is 975.
Here 5 is in ones place and 7 in tens place.
5 is greater than or equal to 5. so, replace 5 with 0 and add 1 to the tens place.
Therefore 975 rounded to the nearest ten is 980.

e. 13,936
________
Answer:
Given that the number is 13,936.
Here 6 is in ones place and 3 in tens place.
6 is greater than 5. so, replace 6 with 0 and add 1 to the tens place.
Therefore 13,936 rounded to the nearest ten is 13,936.

f. 842
________
Answer:
Given that the number is 842.
Here 2 is in ones place and 4 in tens place.
2 is less than 5. so, replace 2 with 0.
Therefore 842 rounded to the nearest ten is 840.

Question 2.
a. 9,855
________
Answer:
Given that the number is 9,855.
Here 5 is in ones place and 5 in tens place.
5 is greater than or equal to 5. so, replace 5 with 0 and 1 to the tens place.
Therefore 9,855 rounded to the nearest ten is 9,860.

b. 26,917
________
Answer:
Given that the number is 26,917.
Here 7 is in ones place and 1 in tens place.
7 is greater than 5. so, replace 7 with 0 and add 1 to the tens place.
Therefore 26.917 rounded to the nearest ten is 26,917.

c. 984
________
Answer:
Given that the number is 984.
Here 4 is in ones place and 8 in tens place.
4 is less than 5. so, replace 4 with 0.
Therefore 984 rounded to the nearest ten is 980.

d. 95,645
________
Answer:
Given that the number is 95,645.
Here 5 is in ones place and 4 in tens place.
5 is greater than or equal to 5. so, replace 5 with 0 and add 1 to the tens place.
Therefore 95,645 rounded to the nearest ten is 95,650.

e. 8,673
________
Answer:
Given that the number is 8,673.
Here 3 is in ones place and 7 in tens place.
3 is less than 5. so, replace 3 with 0.
Therefore 8,673 rounded to the nearest ten is 8,670.

f. 29,981
________
Answer:
Given that the number is 29,981.
Here 1 is in ones place and 8 in tens place.
1 is less than 5. so, replace 1 with 0.
Therefore 29,981 rounded to the nearest ten is 29,980.

Round to the nearest hundred.

Question 3.
a. 325, 793
________
Answer:
Given that the number is 325,793.
Here 9 in tens place and 7 in hundreds place.
90 is greater than 50. So replace 0 in ones and tens place, add 1 to the hundreds place.
Therefore 325,793 rounded to the nearest hundred is 325,700.

b. 49,832
________
Answer:
Given that the number is 49,832.
Here 3 in tens place and 8 in hundreds place.
80 is greater than 50. So replace 0 in ones and tens place, add 1 to the hundreds place.
Therefore 49,832 rounded to the nearest hundred is 49,800.

c. 123,652
________
Answer:
Given that the number is 123,652.
Here 5 in tens place and 6 in hundreds place.
00 is greater than or equal to 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 123,652 rounded to the nearest hundred is 123,600.

d. 24,635
________
Answer:
Given that the number is 24,635.
Here 3 in tens place and 6 in hundreds place.
30 is less than 50. So replace 0 in ones and tens place.
Therefore 24,635 rounded to the nearest hundred is 24,600.

e. 199,794
________
Answer:
Given that the number is 199,794.
Here 9 in tens place and 7 in hundreds place.
90 is greater than 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 199,794 rounded to the nearest hundred is 199,794.

f. 79,342
________
Answer:
Given that the number is 79,342.
Here 4 in tens place and 3 in hundreds place.
40 is less than 50. So replace 0 in ones and tens place.
Therefore 79,342 rounded to the nearest hundred is 79,300.

Question 4.
a.
798,759
________
Answer:
Given that the number is 798,759.
Here 5 in tens place and 7 in hundreds place.
50 is greater than or equal to 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 798,759 rounded to the nearest hundred is 798,700.

b. 58,345
________
Answer:
Given that the number is 58,345.
Here 4 in tens place and 3 in hundreds place.
40 is less than 50. So replace 0 in ones and tens place.
Therefore 58,345 rounded to the nearest hundred is 58,300.

c. 9,873
________
Answer:
Given that the number is 9,873.
Here 7 in tens place and 8 in hundreds place.
70 is greater than 50. So replace 0 in ones and tens place.
Therefore 9,873 rounded to the nearest hundred is 9,800.

d. 8,375
________
Answer:
Given that the number is 8,375.
Here 7 in tens place and 3 in hundreds place.
70 is greater than 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 8,375 rounded to the nearest hundred is 8,300.

e. 10,097
________
Answer:
Given that the number is 10,097.
Here 9 in tens place and 0 in hundreds place.
90 is greater than 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 10,097 rounded to the nearest hundred is 10,000.

f. 1,987,654
________
Answer:
Given that the number is 1,987,654.
Here 5 in tens place and 6 in hundreds place.
50 is greater than or equal to 50. So replace 0 in ones and tens place, 1 to the hundreds place.
Therefore 1,987,654 rounded to the nearest hundred is 1,987,600.

Round to the nearest thousand.

Question 6.
a. 567,523
________
Answer:
Given that the number is 567,523.
Here 5 is in hundreds place and 7 in thousands place.
500 is greater than or equal to 500. So, replace 0 in ones, tens and hundreds place and add 1 to the thousands place.
Therefore 567,523 rounded to the nearest thousand is 567,000.

b. 93,567
________
Answer:
Given that the number is 93,567.
Here 5 is in hundreds place and 3 in thousands place.
500 is greater than or equal to 500. So, replace 0 in ones, tens and hundreds place and add 1 to the thousands place.
Therefore 93,567 rounded to the nearest thousand is 93,000.

c. 4,378
________
Answer:
Given that the number is 4,378.
Here 3 is in hundreds place and 4 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 4,378 rounded to the nearest thousand is 4,000.

d. 12,499
________
Answer:
Given that the number is 12,499.
Here 4 is in hundreds place and 2 in thousands place.
400 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 12,499 rounded to the nearest thousand is 12,000.

e. 747,399
________
Answer:
Given that the number is 747,399.
Here 3 is in hundreds place and 7 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 747,399 rounded to the nearest thousand is 747,000.

f. 9,385
________
Answer:
Given that the number is 9,385.
Here 3 is in hundreds place and 9 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 9,385 rounded to the nearest thousand is 9,000.

Question 6.
a. 987,436
________
Answer:
Given that the number is 987,436.
Here 4 is in hundreds place and 7 in thousands place.
400 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 987,436 rounded to the nearest thousand is 987,000.

b. 346,345
________
Answer:
Given that the number is 346,345.
Here 3 is in hundreds place and 6 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 346,345 rounded to the nearest thousand is 346,000.

c. 98,345
________
Answer:
Given that the number is 98,345.
Here 3 is in hundreds place and 8 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 98,345 rounded to the nearest thousand is 98,000.

d. 8,564
________
Answer:
Given that the number is 8,564.
Here 5 is in hundreds place and 8 in thousands place.
500 is greater than or equal to 500. So, replace 0 in ones, tens and hundreds place and add 1 to the thousands place.
Therefore 8,564 rounded to the nearest thousand is 8,000.

e. 75,459
________
Answer:
Given that the number is 75,459.
Here 4 is in hundreds place and 5 in thousands place.
400 less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 75,459 rounded to the nearest thousand is 75,000.

f. 187,349
________
Answer:
Given that the number is 187,349.
Here 3 is in hundreds place and 7 in thousands place.
300 is less than 500. So, replace 0 in ones, tens and hundreds place.
Therefore 187,349 rounded to the nearest thousand is 187,000.

This handy Spectrum Math Grade 4 Answer Key Chapter 2 Lesson 2.2 Understanding Place Value (to hundred thousands) provides detailed answers for the workbook questions.

Spectrum Math Grade 4 Chapter 2 Lesson 2.2 Understanding Place Value (to hundred thousands) Answers Key

Write the number word.

Question 1.
152,731
___________
Answer:
Given that the number is 152,731.
The word form of 152,731 is one lakh fifty two thousand seven hundred and thirty one.

Question 2.
985,685
___________
Answer:
Given that the number is 985,685.
The word form of 985,685 is nine lakh eighty five thousand six hundred and eighty five.

Tell the digit in the place named.

Question 3.
a. 50,975
ten thousands
___________
Answer:
Given that the number is 50,975.
The digit in the ten thousands place of 50,975 is 50,000.

b. 986,580
hundred thousands
___________
Answer:
Given that the number is 986,580.
The digit in the hundred thousands place of 986,580 is 900,000.

Question 4.
a. 179,802
thousands
___________
Answer:
Given that the number is 179,802.
The digit in the thousands place of 179,802 is 9000.

b. 506,671
ten thousands
___________
Answer:
Given that the number is 506,671.
The digit in the ten thousands place of 506,671 is 06,671.

Question 5.
a. 865,003
ten thousands
___________
Answer:
Given that the number is 865,003.
The digit in the ten thousands place of 865,003 is 60,000.

b. 997,780
hundred thousands
___________
Answer:
Given that the number is 997,780.
The digit in the hundred thousands place of 997,780 is 900,000.

Write each number in expanded form.

Question 6.
a. 653,410
___________
Answer:
Given that the number is 653,410.
The expended form of the number is based on the place value of the number.
The expended form of 653,410 is 600,000 + 53000 + 400 + 10.
Here 653,410 is splits into 6 lakhs, 53 thousand, 4 hundred and 1 ten.

b. 76,982
___________
Answer:
Given that the number is 76,982.
The expended form of the number is based on the place value of the number.
The expended form of 76,982 is 70,000 + 6000 + 900 + 80 + 2.
Here 76,982 is splits into 7 lakhs, 6 thousand, 9 hundred, 8 tens and 2 ones.

Question 7.
a. sixty-two thousand five hundred twelve
___________
Answer:
Sixty-two thousand five hundred twelve in numeric form is 62,512.
The expended form of the number is based on the place value of the number.
The expended form of 62,512 is 62,000 + 500 + 10 + 2.
Here 76,982 is splits into 62 thousand, 5 hundred, 1 tens and 2 ones.

b. 103,254
___________
Answer:
Given that the number is 103,254.
The expended form of the number is based on the place value of the number.
The expended form of 103,254 is 1,00,000+ 3000 + 200 + 50 + 4.
Here 103,254 is splits into 1 lakhs, 3 thousand, 2 hundred, 5 tens and 4 ones.

Question 8.
a. 199,482
___________
Answer:
Given that the number is 199,482.
The expended form of the number is based on the place value of the number.
The expended form of 199,482 is 1,00,000 + 99000 + 400 + 80 + 2.
Here 199,482 is splits into 1 lakhs, 99 thousand, 4 hundred, 8 tens and 2 ones.

b. 32,451
___________
Answer:
Given that the number is 32,451.
The expended form of the number is based on the place value of the number.
The expended form of 32,451 is 32000 + 400 + 50 + 1.
Here 32,451 is splits into 32 thousand, 4 hundred, 5 tens and 1 ones.

This handy Spectrum Math Grade 4 Answer Key Chapter 2 Lesson 2.1 Adding Understanding Place Value (to hundreds) provides detailed answers for the workbook questions.

Spectrum Math Grade 4 Chapter 2 Lesson 2.1 Adding Understanding Place Value (to hundreds) Answers Key

Write each number in expanded form.

Question 1.
a. 54
50 + 4

b. 608
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 608 is 600 + 8.
Here 608 is splits into 6 hundreds and 8 ones.

c. 32
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 30 + 2
Here 32 is splits into 3 tens and 2 ones.

d. 421
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 421 is 400 + 20 + 1.
Here 421 is splits into 4 hundreds 2 tens and 1 ones.

Question 2.
a. 430
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 430 is 400 + 30.
Here 430 is splits into 4 hundreds 3 tens.

b. 549
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 549 is 500 + 40 + 9.
Here 549 is splits into 5 hundreds 4 tens and 9 ones.

c. 75
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 75 is 70 + 5.
Here 75 is splits into 7 tens and 5 ones.

d. 699
__________
Answer:
The expended form of the number is based on the place value of the number.
The expended form of 699 is 600 + 90 + 9.
Here 699 is splits into 6 hundreds 9 tens and 9 ones.

Question 3.
a. one hundred thirty-two
____________
Answer:
One hundred thirty-two in numeric form is 132
The expended form of the number is based on the place value of the number.
The expended form of 132 is 100 + 30 + 2.
Here 132 is splits into 1 hundreds 3 tens and 2 ones.

b. seven hundred twenty-one
____________
Answer:
Seven hundred twenty-one in numeric form is 721
The expended form of the number is based on the place value of the number.
The expended form of 721 is 700 + 20 + 1.
Here 721 is splits into 7 hundreds 2 tens and 1 ones.

c. thirty-nine
____________
Answer:
Thirty-nine in numeric form is 39.
The expended form of the number is based on the place value of the number.
The expended form of 39 is 30 + 9.
Here 39 is splits into 3 tens and 9 ones.

d. eighty-seven
____________
Answer:
Eighty-seven in numeric form is 87.
The expended form of the number is based on the place value of the number.
The expended form of 87 is 80 + 7.
Here 80 is splits into 8 tens and 7 ones.

Question 4.
a. nine hundred eleven
____________
Answer:
Nine hundred eleven in numeric form is 911.
The expended form of the number is based on the place value of the number.
The expended form of 911 is 900 + 10 + 1.
Here 911 is splits into 9 hundreds, 1 tens and 1 ones.

b. five hundred thirteen
____________
Answer:
Five hundred thirteen is numeric form is 513.
The expended form of the number is based on the place value of the number.
The expended form of 513 is 500 + 10 + 3.
Here 513 is splits into 5 hundreds, 1 tens and 3 ones.

c. one hundred ninety
____________
Answer:
One hundred ninety in numeric form is 190.
The expended form of the number is based on the place value of the number.
The expended form of 190 is 100 + 90.
Here 190 is splits into 1 hundred and 9 tens.

d. seventy
____________
Answer:
Seventy in numeric form is 70
The expended form of the number is based on the place value of the number.
The expended form of 70 is 70.
Here 70 is splits into 7 tens.

Write the numerical value of the digit in the place named.

Question 5.
a. 872
tens
70

b. 934
hundreds
__________
Answer:
Given that the number is 934.
The numeric value of hundreds place of 934 is 900.

c.
326
ones
__________
Answer:
Given that the number is 326.
The numeric value of ones place of 326 is 6.

d. 304
ones
__________
Answer:
Given that the number is 304.
The numeric value of ones place of 304 is 4.

Question 6.
a. 799
hundreds
__________
Answer:
Given that the number is 799.
The numeric value of hundreds place of 799 is 700.

b. 663
tens
__________
Answer:
Given that the number is 663.
The numeric value of tens place of 663 is 60.

c. 309
tens
__________
Answer:
Given that the number is 309.
The numeric value of tens place of 309 is 0..

d. 995
hundreds
__________
Answer:
Given that the number is 995.
The numeric value of hundreds place of 995 is 900.

Write the number word.

Question 7.
85,034
___________
Answer:
Given that the number is 85,034.
The word form of 85,034 is eighty five thousand thirty-four.

Question 8.
11,987
___________
Answer:
Given that the number is 11,987.
The word form of 11,987 is eleven thousand nine hundred and eighty seven.

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Pretest provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 1 Pretest Answers Key

Check What You Know

Adding and Subtracting Rational Numbers

Evaluate each expression.

Question 1.

a. opposite of 45 ______
Answer:  -45
opposite of 45 is -45
-45 and 45 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of -9 ______
Answer:  9
opposite of -9 is 9
-9 and 9 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of -10 ______
Answer:  10
opposite of -10 is 10
-10 and 10 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 2.
a. opposite of 21 ______
Answer:  -21
opposite of 21 is -21
-21 and 21 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of 6 ______
Answer:  -6
opposite of 6 is -6
-6 and 6 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of -10 ______
Answer:  10
opposite of -10 is 10
-10 and 10 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 3.
a. opposite of 52 ______
Answer:  -52
opposite of 52 is -52
-52 and 52 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of -89 ______
Answer:  89
opposite of -89 is 89
-89 and 89 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of 18 ______
Answer:  -18
opposite of 18 is -18
-18 and 18 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 4.
a. |7| ______
Answer: 7
|7| = 7
-7 and 7 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

b. |-34| ______
Answer: 34
|-34| = 34
-34 and 34 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

c. |58| ______
Answer: 58
|58| = 58
-58 and 58 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

Question 5.
a. -|35| ______
Answer: -35
-|35| = -35
-35 and 35 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

b. -|-56| ______
Answer: -56
-|-56| = -56
-56 and 56 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

c. |-39| ______
Answer: 39
|-39| = 39
-39 and 39 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

Identify the property of addition described as commutative, associative, or identity.

Question 6.
The sum of any number and zero is the original number. ___________
Answer: identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 7.
When two numbers are added, the sum is the same regardless of the order of addends. ___________
Answer: commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 8.
When three or more numbers are added, the sum is the same regardless of how the addends are grouped. _________
Answer: associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 9.
a. 7 + (1 + 9) = (7 + 1) + 9
___________
Answer: associative property
7 + (1 + 9) = (7 + 1) + 9 = associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 3 + 0 = 3
_________
Answer: identity property
3 + 0 = 3 = identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 10.
a. 9 + 5 = 5 + 9
_________
Answer: commutative property
9 + 5 = 5 + 9 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. 8 + 10 = 10 + 8
_________
Answer: commutative property
8 + 10 = 10 + 8 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 11.
a. 6 + (-6) = 0
_________
Answer: commutative property
6 + (-6) = 0 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (6 + 3) + 7 = 6 + (3 + 7)
____________
Answer: associative property
(6 + 3) + 7 = 6 + (3 + 7)= associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 12.
a. 15 + 0 = 15
_____________
Answer: identity property
15 + 0 = 15 = identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. 13 + 2 = 2 + 13
Answer: commutative property
13 + 2 = 2 + 13 = commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Add or subtract. Write fractions in simplest form.

Question 13.
a.

Answer: 4\(\frac{11}{12}\)
2\(\frac{1}{4}\) + 2\(\frac{2}{3}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 2) + \(\frac{1}{4}\) + \(\frac{2}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] + [\(\frac{2}{3}\)  x \(\frac{4}{4}\)]
= 4 + \(\frac{3}{12}\) + \(\frac{8}{12}\)
= 4 + \(\frac{3 + 8}{12}\)
After simplification,
= 4 + \(\frac{11}{12}\)
Therefore, the result is given by,
= 4\(\frac{11}{12}\)

b.

Answer: 5\(\frac{9}{14}\)
3\(\frac{1}{2}\) + 2\(\frac{1}{7}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 2) + \(\frac{1}{2}\) + \(\frac{1}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{2}\) x \(\frac{7}{7}\)] + [\(\frac{1}{7}\)  x \(\frac{2}{2}\)]
= 5 + \(\frac{7}{14}\) + \(\frac{2}{14}\)
= 5 + \(\frac{7 + 2}{14}\)
After simplification,
= 5 + \(\frac{9}{14}\)
Therefore, the result is given by,
= 5\(\frac{9}{14}\)

c.

Answer: 6\(\frac{19}{24}\)
2\(\frac{1}{8}\) + 4\(\frac{2}{3}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 4) + \(\frac{1}{8}\) + \(\frac{2}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{1}{8}\) x \(\frac{3}{3}\)] + [\(\frac{2}{3}\)  x \(\frac{8}{8}\)]
= 6 + \(\frac{3}{24}\) + \(\frac{16}{24}\)
= 6 + \(\frac{3 + 16}{24}\)
After simplification,
= 6 + \(\frac{19}{24}\)
Therefore, the result is given by,
= 6\(\frac{19}{24}\)

d.

Answer: 3\(\frac{53}{35}\)
1\(\frac{5}{7}\) + 2\(\frac{4}{5}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{5}{7}\) + \(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{5}{7}\) x \(\frac{5}{5}\)] + [\(\frac{4}{5}\)  x \(\frac{7}{7}\)]
= 3 + \(\frac{25}{35}\) + \(\frac{28}{35}\)
= 3 + \(\frac{25 + 28}{35}\)
After simplification,
= 3 + \(\frac{53}{35}\)
Therefore, the result is given by,
= 3\(\frac{53}{35}\)

Question 14.
a.

Answer: 4\(\frac{1}{12}\)
6\(\frac{1}{3}\) – 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (6 –  2) + \(\frac{1}{3}\) – \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{1}{3}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\)  x \(\frac{3}{3}\)]
= 4 + \(\frac{4}{12}\) – \(\frac{3}{12}\)
= 4 + \(\frac{4 – 3}{12}\)
After simplification,
=4 + \(\frac{1}{12}\)
Therefore, the result is given by,
= 4\(\frac{1}{12}\)

b.

Answer: \(\frac{1}{8}\)
\(\frac{3}{8}\) – \(\frac{1}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= \(\frac{3}{8}\) – \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{8}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\)  x \(\frac{8}{8}\)]
= \(\frac{12}{32}\) – \(\frac{8}{32}\)
= \(\frac{12 – 8}{32}\)
After simplification,
= \(\frac{4}{32}\)
Therefore, the result is given by,
= \(\frac{1}{8}\)

c.

Answer: 2\(\frac{1}{2}\)
5\(\frac{3}{10}\) – 2\(\frac{4}{5}\)
Partition the fractions and whole numbers to subtract them separately.
= (5 –  2) + \(\frac{3}{10}\) – \(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{3}{10}\) x \(\frac{5}{5}\)] – [\(\frac{4}{5}\)  x \(\frac{10}{10}\)]
= 3 + \(\frac{15}{50}\) – \(\frac{40}{50}\)
= 2 + \(\frac{65}{50}\) – \(\frac{40}{50}\)
= 2 + \(\frac{65 – 40}{50}\)
After simplification,
=2 + \(\frac{25}{50}\)
=2 + \(\frac{1}{2}\)
Therefore, the result is given by,
=2\(\frac{1}{2}\)

d.

Answer: 2\(\frac{3}{7}\)
3\(\frac{4}{7}\) – 1\(\frac{1}{2}\)
Partition the fractions and whole numbers to subtract them separately.
= (3 – 1) + \(\frac{4}{7}\) – \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{4}{7}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{7}{7}\)]
= 2 + \(\frac{8}{14}\) – \(\frac{2}{14}\)
= 2 + \(\frac{8 – 2}{14}\)
After simplification,
=2 + \(\frac{6}{14}\)
=2 + \(\frac{3}{7}\)
Therefore, the result is given by,
= 2\(\frac{3}{7}\)

Question 15.
a.
-3 + 2 = _____
Answer: -1
-3 + 2 = – 3 – (-2) = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b.
3 + (-2) = ____
Answer: 1
3 + (-2) = 3 – 2 = 1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c.
7 + (-4) = _____
Answer: 3
7 + (-4) = 7 – 4 = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 16.
a.
-8 + (-3) = ____
Answer: -11
-8 + (-3) = -8 – 3 = -11
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b.
-7 + 6 = ____
Answer: -1
-7 + 6 = -7 – (-6) = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c.
-4 + (-9) = _____
Answer: -13
-4 + (-9) = -4  – 9 = -13
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 17.
a.
6 – 12 = ____
Answer: -6
6 – 12 = 6 + (-12) = -6
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b.
3 – (-4) = ____
Answer: 7
3 – (-4) = 3 + 4 = 7
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c.
-2 – 4 = ____
Answer: -6
-2 – 4 = – 2 + (- 4 )= -6
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Solve each problem.

Question 18.
One box of cups weighs 4\(\frac{2}{3}\) ounces. Another box weighs 5\(\frac{3}{8}\) ounces. What is the total weight of the two boxes?
The total weights is _______ ounces.
Answer: 10\(\frac{1}{24}\)
The weight of one box of cups  =  4\(\frac{2}{3}\) ounces
The weight of second box of cups = 5\(\frac{3}{8}\) ounces
Therefore, the total weight of the cups = weight of first box + weight of second box
= 4\(\frac{2}{3}\) + 5\(\frac{3}{8}\)
4\(\frac{2}{3}\) + 5\(\frac{3}{8}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 5) + \(\frac{2}{3}\) + \(\frac{3}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 9 + [\(\frac{2}{3}\) x \(\frac{8}{8}\)] + [\(\frac{3}{8}\)  x \(\frac{3}{3}\)]
= 9 + \(\frac{16}{24}\) + \(\frac{9}{24}\)
= 9 + \(\frac{16 + 9 }{24}\)
After simplification,
=9 + \(\frac{25}{24}\)
= 9 + 1\(\frac{1}{24}\)
Therefore, the result is given by,
= 10\(\frac{1}{24}\)
Therefore The total weights is 10\(\frac{1}{24}\) ounces.

Question 19.
Luggage on a certain airline is limited to 2 pieces per person. Together, the 2 pieces can weigh no more than 58\(\frac{1}{2}\) pounds. If a passenger has one piece of luggage that weighs 32\(\frac{1}{3}\) pounds, what is the most the second piece can weigh?
The second piece can weigh ____ pounds.
Answer: 26\(\frac{5}{6}\)
Number of persons limited for the luggage on a certain airline = 2
Together, the 2 pieces can weigh = 58\(\frac{1}{2}\) pounds
passenger has one piece of luggage that weighs = 32\(\frac{1}{3}\) pounds
second piece  weigh = total weight – one piece
= 58\(\frac{1}{2}\) – 32\(\frac{1}{3}\)
58\(\frac{1}{2}\) – 32\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (58 – 32) + \(\frac{1}{2}\) – \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 26 + [\(\frac{1}{2}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{2}{2}\)]
= 26 + \(\frac{3}{6}\) – \(\frac{2}{6}\)
= 26 + \(\frac{3 + 2 }{6}\)
After simplification,
=25 + \(\frac{5}{6}\)
Therefore, the result is given by,
= 26\(\frac{5}{6}\)
Therefore, the second piece can weigh 26\(\frac{5}{6}\) pounds.

Question 20.
Mavis spends 1\(\frac{1}{4}\) hours on the bus every weekday (Monday through Friday). How many hours is she on the bus each week?
She is on the bus ____ hours each week.
Answer: 6\(\frac{1}{4}\)
Mavis spends 1\(\frac{1}{4}\) hours on the bus every weekday (Monday through Friday)
Number of hours is she on the bus each week = 5 x [1\(\frac{1}{4}\)] (As there are 5 days when we count from monday to friday)
By simplification,
5 x [1\(\frac{1}{4}\)] = 5\(\frac{5}{4}\) = 5 + 1\(\frac{1}{4}\) = 6\(\frac{1}{4}\)
Therefore, the result is 6\(\frac{1}{4}\)

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Posttest provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 1 Posttest Answers Key

Check What You Learned

Adding and Subtracting Rational Numbers

Evaluate each expression.

Question 1.
a. opposite of -54 _____
Answer:  54
opposite of -54 is 54
-54 and 54 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of 19 ____
Answer: -19
opposite of 19 is -19
-19 and 19 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of 31 ____
Answer: -31
opposite of 31 is -31
-31 and 31 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 2.
a. opposite of -6 ____
Answer:  6
opposite of -6 is 6
-6 and 6 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of 21 ____
Answer: -21
opposite of 21 is -21
-21 and 21 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of -10 ____
Answer: 10
opposite of -10 is 10
-10 and 10 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 3.
a. opposite of 54 ____
Answer: -54
opposite of 54 is -54
-54 and 54 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. opposite of -34 ___
Answer: 34
opposite of -34 is 34
-34 and 34 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

c. opposite of 86 ____
Answer: -86
opposite of 86 is -86
-86 and 86 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Question 4.
a. |-35| = ____
Answer: 35
|-35| = 35
-35 and 35 are absolute value because they are the same distance from zero on opposite sides of the number line.
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

b. -|-43| = ____
Answer: -43
-|-43| = -43
-43 and 43 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

c. |35| = ____
Answer: 35
|35| = 35
-35 and 35 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

Question 5.
a. -|75| = ___
Answer: -75
-|75| = -75
-75 and 75 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

b. -|83| = ___
Answer: -83
-|83| = -83
-83 and 83 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

c. -|99| = ____
Answer: -99
-|99| = -99
-99 and 99 are absolute value because they are the same distance from zero on opposite sides of the number line.
The absolute value of a number is a number that is the same distance from zero on a number line. The distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number.

Identify the property of addition described as commutative, associative, or identity.

Question 6.
When two numbers are added, the sum is the same regardless of the order of addends.
_________
Answer: commutative property
When two numbers are added, the sum is the same regardless of the order of addends =  commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 7.
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped.
______________
Answer: associative property
When three or more are grouped numbers are added, the sum is the same regardless of how the addends are grouped = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 8.
The sum of any number and zero is the original number.
___________
Answer: identity property
The sum of any number and zero is the original number. = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 9.
a. 4 + 1o = 10 + 4 ________________
Answer:  commutative property
4 + 10 = 10 + 4 = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. 1 + (-1) = 0 ____
Answer: commutative property
1 + (-1) = 0
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 10.
a. (1 + 8) + 2 = 1 + (8 + 2) _________
Answer:  associative property
(1 + 8) + 2 = 1 + (8 + 2) = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 3 + 5 = 5 + 3 _____
Answer: commutative property
3 + 5 = 5 + 3 = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 11.
a. 8 + 0 = 8 _____
Answer: identity property
8 + 0 = 8 = identity property
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. 2 + (6 + 4) = (2 + 6) + 4 _____
Answer: associative property
2 + (6 + 4) = (2 + 6) + 4 = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 12.
a. 12 + 9 = 9 + 12 _____
Answer: commutative property
12 + 9 = 9 + 12 = commutative property
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (8 + 5) + 3 = 8 + (5 + 3) ________
Answer: associative property
(8 + 5) + 3 = 8 + (5 + 3) = associative property
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Add or subtract. Write fractions in simplest form.

Question 13.
a.

Answer: 1\(\frac{61}{56}\)
\(\frac{3}{8}\) + 1\(\frac{5}{7}\)
Partition the fractions and whole numbers to add them separately.
= (0 + 1) + \(\frac{3}{8}\) + \(\frac{5}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{3}{8}\) x \(\frac{7}{7}\)] + [\(\frac{5}{7}\)  x \(\frac{8}{8}\)]
= 1 + \(\frac{21}{56}\) + \(\frac{40}{56}\)
= 1 + \(\frac{21 + 40}{56}\)
After simplification,
= 1 + \(\frac{61}{56}\)
Therefore, the result is given by,
= 1\(\frac{61}{56}\)

b.

Answer: 5\(\frac{7}{12}\)
2\(\frac{1}{4}\) + 3\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 3) + \(\frac{1}{4}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{4}{4}\)]
= 5 + \(\frac{3}{12}\) + \(\frac{4}{12}\)
= 5 + \(\frac{3 + 4}{12}\)
After simplification,
= 5 + \(\frac{7}{12}\)
Therefore, the result is given by,
= 5\(\frac{7}{12}\)

c.

Answer: 3\(\frac{41}{24}\)
1\(\frac{5}{6}\) + 2\(\frac{7}{8}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{5}{6}\) + \(\frac{7}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{5}{6}\) x \(\frac{8}{8}\)] + [\(\frac{7}{8}\)  x \(\frac{6}{6}\)]
= 3 + \(\frac{40}{48}\) + \(\frac{42}{48}\)
= 3 + \(\frac{40 + 42}{48}\)
After simplification,
= 3 + \(\frac{82}{48}\)
Therefore, the result is given by,
= 3\(\frac{41}{24}\)

d.

Answer: 6\(\frac{9}{8}\)
4\(\frac{3}{4}\) + 2\(\frac{3}{8}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 2) + \(\frac{3}{4}\) + \(\frac{3}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{3}{4}\) x \(\frac{8}{8}\)] + [\(\frac{3}{8}\)  x \(\frac{4}{4}\)]
= 6 + \(\frac{24}{32}\) + \(\frac{12}{32}\)
= 6 + \(\frac{24 + 12}{32}\)
After simplification,
= 6 + \(\frac{36}{32}\)
Therefore, the result is given by,
= 6\(\frac{9}{8}\)

Question 14.
a.

Answer: 3\(\frac{5}{12}\)
4\(\frac{2}{3}\) – 1\(\frac{1}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 1) + [\(\frac{2}{3}\) – \(\frac{1}{4}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{2}{3}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\)  x \(\frac{3}{3}\)]
= 3 + \(\frac{8}{12}\) – \(\frac{3}{12}\)
= 3 + \(\frac{8 – 3}{12}\)
After simplification,
= 3 + \(\frac{5}{12}\)
Therefore, the result is given by,
= 3\(\frac{5}{12}\)

b.

Answer: \(\frac{7}{16}\)
\(\frac{7}{8}\) – \(\frac{1}{2}\)
Partition the fractions and whole numbers to subtract them separately.
= \(\frac{7}{8}\) – \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{7}{8}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{8}{8}\)]
= \(\frac{14}{16}\) – \(\frac{7}{16}\)
= \(\frac{14 – 7}{16}\)
After simplification,
= \(\frac{7}{16}\)

c.

Answer: 2\(\frac{31}{70}\)
4\(\frac{3}{10}\) – 1\(\frac{6}{7}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 1) + [\(\frac{3}{10}\) – \(\frac{6}{7}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{3}{10}\) x \(\frac{7}{7}\)] – [\(\frac{6}{7}\)  x \(\frac{10}{10}\)]
= 3 + \(\frac{21}{70}\) – \(\frac{60}{70}\)
= 2 + \(\frac{91}{70}\) – \(\frac{60}{70}\)
= 2 + \(\frac{91 – 60}{70}\)
After simplification,
= 2 + \(\frac{31}{70}\)
Therefore, the result is given by,
= 2\(\frac{31}{70}\)

d.

Answer: 3\(\frac{13}{12}\)
5\(\frac{1}{4}\) – 2\(\frac{5}{6}\)
Partition the fractions and whole numbers to subtract them separately.
= (5 – 2 ) + \(\frac{1}{4}\) – \(\frac{5}{6}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{1}{4}\) x \(\frac{6}{6}\)] – [\(\frac{5}{6}\)  x \(\frac{4}{4}\)]
= 3 + \(\frac{6}{24}\) – \(\frac{20}{24}\)
= 3 + \(\frac{6 + 20}{24}\)
After simplification,
= 3 + \(\frac{26}{24}\)
Therefore, the result is given by,
= 3\(\frac{13}{12}\)

Question 15.
a. -6 + 4 = ____
Answer: -2
-6 + 4 = -6 – (-4) = -2
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 7 + (-3) = ____
Answer: 4
7 + (-3) = 7 – 3 = 4
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -5 + (-2) = ____
Answer: -7
-5 + (-2) = – 5 -2 = -7
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 16.
a. -9 + 12 = ___
Answer: 3
-9 + 12 = -9 – (-12) = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 8 + (-11) = ____
Answer: -3
8 + (-11) = 8 – 11 = -3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -4 + (-8) = ____
Answer: -12
-4 + (-8) = -4  – 8 = -12
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 17.
a. 13 – 16 = ____
Answer: -3
13 – 16 = 13 + (-16) = -3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 9 – (-8) = ___
Answer: 17
9 – (-8) = 9 + 8 = 17
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -3 – 7 = ____
Answer: -10
-3 – 7 = -3 + (-7) = -10
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Solve each problem.

Question 18.
A large patio brick weighs 4\(\frac{3}{8}\) pounds. A small patio brick weighs 2\(\frac{1}{3}\) pounds. How much more does the large brick weigh?
The large brick weighs ____ pounds more.
Answer: 2\(\frac{17}{24}\)
A large patio brick weighs 4\(\frac{3}{8}\) pounds
A small patio brick weighs 2\(\frac{1}{3}\) pounds
The more does the large brick weigh = large patio brick – small patio brick
= 4\(\frac{3}{8}\) – 2\(\frac{1}{3}\)
4\(\frac{3}{8}\) – 2\(\frac{1}{3}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 2) + \(\frac{3}{8}\) – \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{3}{8}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{8}{8}\)]
= 2 + \(\frac{9}{24}\) – \(\frac{8}{24}\)
= 2 + \(\frac{9 + 8 }{24}\)
After simplification,
=2 + \(\frac{17}{24}\)
Therefore, the result is given by,
= 2\(\frac{17}{24}\)
Therefore, the large brick weighs 2\(\frac{17}{24}\)pounds more.

Question 19.
A small bottle holds \(\frac{1}{3}\) of a liter. A large bottle holds 4\(\frac{1}{2}\) liters. How much more does the large bottle hold?
The large bottle holds ____ liters more.
Answer: 4\(\frac{1}{6}\)
A small bottle holds \(\frac{1}{3}\) of a liter
A large bottle holds 4\(\frac{1}{2}\) liters
The number of more does the large bottle hold = 4\(\frac{1}{2}\) – \(\frac{1}{3}\)
4\(\frac{1}{2}\) – \(\frac{1}{3}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 0) + \(\frac{1}{2}\) – \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{1}{2}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{2}{2}\)]
= 4 + \(\frac{3}{6}\) – \(\frac{2}{6}\)
= 4 + \(\frac{3 – 2 }{6}\)
After simplification,
=4 + \(\frac{1}{6}\)
Therefore, the result is given by,
= 4\(\frac{1}{6}\)
The large bottle holds  4\(\frac{1}{6}\) liters more.

Question 20.
The basketball team practiced 3\(\frac{1}{4}\) hours on Monday and 2\(\frac{1}{3}\) hours on Tuesday. How many hours has the team practiced so far this week?
The team has practiced ____ hours this week.
Answer: 5\(\frac{7}{24}\)
The basketball team practiced 3\(\frac{1}{4}\) hours on Monday and 2\(\frac{1}{3}\) hours on Tuesday. Therefore, total hours practiced by team so far this week = number of hours practiced on monday + number of hours practiced on tuesday
=  3\(\frac{1}{4}\) + 2\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 2) + \(\frac{1}{4}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{4}{4}\)]
= 5 + \(\frac{3}{24}\) + \(\frac{4}{24}\)
= 5 + \(\frac{3 + 4 }{24}\)
After simplification,
=5 + \(\frac{7}{24}\)
Therefore, the result is given by,
= 5\(\frac{7}{24}\)

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.9 Problem Solving provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 1 Lesson 1.9 Problem Solving Answers Key

Solve each problem.

Question 1.
At closing time, the bakery had 2\(\frac{1}{4}\) apple pies and 1\(\frac{1}{2}\) cherry pies left. How much more apple pie than cherry pie was left?
There was ___________ more of an apple pie than cherry.
Answer: 0\(\frac{3}{4}\)
Number of apple pies in the bakery at the closing time = 2\(\frac{1}{4}\)
Number of cherry pies in the bakery at the closing time = 1\(\frac{1}{2}\)
Therefore, number of more apple pie than cherry pie = 2\(\frac{1}{4}\) – 1\(\frac{1}{2}\)
Partition the fractions and whole numbers to subtract them separately.
= (2- 1) + [\(\frac{1}{4}\) – \(\frac{1}{2}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{1}{4}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{4}{4}\)]
= 1 + \(\frac{2}{8}\) – \(\frac{4}{8}\)
= 0 + \(\frac{10}{8}\) – \(\frac{4}{8}\)
= 0 + \(\frac{10 – 4}{8}\)
After simplification,
= 0 + \(\frac{6}{8}\)
= 0 + \(\frac{3}{4}\)
Therefore, the result is given by,
= 0\(\frac{3}{4}\)
There was 0\(\frac{3}{4}\) more of an apple pie than cherry

Question 2.
The hardware store sold 6\(\frac{3}{8}\) boxes of large nails and 7\(\frac{2}{5}\) boxes of small nails. In total, how many boxes of nails did the store sell?
The store sold ____________ boxes of nails.
Answer: 13\(\frac{31}{40}\)
number of boxes of large nails sold by hardware store = 6\(\frac{3}{8}\)
number of boxes of small nails sold by hardware store = 7\(\frac{2}{5}\)
Total number of boxes of nails sold by hardware store =  6\(\frac{3}{8}\) + 7\(\frac{2}{5}\)
Partition the fractions and whole numbers to add them separately.
= (6 + 7) + \(\frac{3}{8}\) + \(\frac{2}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 13 + [\(\frac{3}{8}\) x \(\frac{5}{5}\)] + [\(\frac{2}{5}\)  x \(\frac{8}{8}\)]
= 13 + \(\frac{15}{40}\) + \(\frac{16}{40}\)
= 13 + \(\frac{15 + 16}{40}\)
After simplification,
= 13 + \(\frac{31}{40}\)
Therefore, the result is given by,
= 13\(\frac{31}{40}\)
The store sold 13\(\frac{31}{40}\) boxes of nails.

Question 3.
Nita studied 4\(\frac{1}{3}\) hours on Saturday and 5\(\frac{1}{4}\) hours on Sunday. How many hours did she spend studying?
She spent ____________ hours studying.
Answer: 9\(\frac{7}{12}\)
Nita studied 4\(\frac{1}{3}\) hours on Saturday and 5\(\frac{1}{4}\) hours on Sunday.
Total hours did she spend on studying = 4\(\frac{1}{3}\) + 5\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 5) + \(\frac{1}{3}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 9 + [\(\frac{1}{3}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\)  x \(\frac{3}{3}\)]
= 9 + \(\frac{4}{12}\) + \(\frac{3}{12}\)
= 9 + \(\frac{4 + 3}{12}\)
After simplification,
= 9 + \(\frac{7}{12}\)
Therefore, the result is given by,
= 9\(\frac{7}{12}\)
She spent 9\(\frac{7}{12}\) hours studying.

Question 4.
Kwan is 5\(\frac{2}{3}\) feet tall. Mary is 4\(\frac{11}{12}\) feet tall. How much taller is Kwan?
Kwan is ___________ foot taller.
Answer: 0\(\frac{3}{4}\)
Kwan is 5\(\frac{2}{3}\) feet tall. Mary is 4\(\frac{11}{12}\) feet tall.
Kwan is taller than Mary = 5\(\frac{2}{3}\) – 4\(\frac{11}{12}\)
Partition the fractions and whole numbers to subtract them separately.
= (5- 4) + [\(\frac{2}{3}\) – \(\frac{11}{12}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{2}{3}\) x \(\frac{12}{12}\)] – [\(\frac{11}{12}\)  x \(\frac{3}{3}\)]
= 1 + \(\frac{24}{36}\) – \(\frac{33}{36}\)
= 0 + \(\frac{60}{36}\) – \(\frac{33}{36}\)
= 0 + \(\frac{60 – 33}{36}\)
After simplification,
= 0 + \(\frac{27}{36}\)
= 0 + \(\frac{3}{4}\)
Therefore, the result is given by,
= 0\(\frac{3}{4}\)
Kwan is 0\(\frac{3}{4}\) foot taller.

Question 5.
This week, Jim practiced the piano 1\(\frac{1}{8}\) hours on Monday and 2\(\frac{3}{7}\) hours on Tuesday. How many hours did he practice this week? How much longer did Jim practice on Tuesday than on Monday?
Jim practiced _____________ hours this week.
Jim practiced _______ hours longer on Tuesday.
Answer: i)3\(\frac{31}{56}\)
ii) 1\(\frac{17}{56}\)
Jim practiced the piano 1\(\frac{1}{8}\) hours on Monday and 2\(\frac{3}{7}\) hours on Tuesday.
Total number of hours practiced by Jim this week = 1\(\frac{1}{8}\) + 2\(\frac{3}{7}\)
Partition the fractions and whole numbers to add them separately.
= (1+ 2) + \(\frac{1}{8}\) + \(\frac{3}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{1}{8}\) x \(\frac{7}{7}\)] + [\(\frac{3}{7}\)  x \(\frac{8}{8}\)]
= 3 + \(\frac{7}{56}\) + \(\frac{24}{56}\)
= 3 + \(\frac{7 + 24}{56}\)
After simplification,
= 3 + \(\frac{31}{56}\)
Therefore, the result is given by,
= 3\(\frac{31}{56}\)
Jim practiced 3\(\frac{31}{56}\) hours this week.
Number of hours practiced by Jim on tuesday than monday = 2\(\frac{3}{7}\) – 1\(\frac{1}{8}\)
Partition the fractions and whole numbers to subtract them separately.
= (2- 1) + [\(\frac{3}{7}\) – \(\frac{1}{8}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{3}{7}\) x \(\frac{8}{8}\)] – [\(\frac{1}{8}\)  x \(\frac{7}{7}\)]
= 1 + \(\frac{24}{56}\) – \(\frac{7}{56}\)
= 1 + \(\frac{24 – 7}{56}\)
After simplification,
= 1 + \(\frac{17}{56}\)
Therefore, the result is given by,
= 1\(\frac{17}{56}\)
Jim practiced 1\(\frac{17}{56}\) hours longer on Tuesday.

Question 6.
Oscar caught a fish that weighed 4\(\frac{1}{6}\) pounds and then caught another that weighed 6\(\frac{5}{8}\) pounds. How much more did the second fish weigh?
The second fish weighed ____ pounds more.
Answer: 2\(\frac{11}{24}\)
Oscar caught a fish that weighed 4\(\frac{1}{6}\) pounds and then caught another that weighed 6\(\frac{5}{8}\) pounds.
The second fish weighed more pounds than first fish = 6\(\frac{5}{8}\) – 4\(\frac{1}{6}\)
Partition the fractions and whole numbers to subtract them separately.
= (6- 4) + [\(\frac{5}{8}\) – \(\frac{1}{6}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{5}{8}\) x \(\frac{6}{6}\)] – [\(\frac{1}{6}\)  x \(\frac{8}{8}\)]
= 2 + \(\frac{30}{48}\) – \(\frac{8}{48}\)
= 2 + \(\frac{30 – 8}{48}\)
After simplification,
= 2 + \(\frac{22}{48}\)
= 2 + \(\frac{11}{24}\)
Therefore, the result is given by,
= 2\(\frac{11}{24}\)
The second fish weighed 2\(\frac{11}{24}\) pounds more.

Solve each problem.

Question 1.
One cake recipe calls for \(\frac{2}{3}\) cup of sugar. Another recipe calls for 1\(\frac{1}{4}\) cups of sugar. How many cups of sugar are needed to make both cakes?
_____ cups of sugar are needed.
Answer: 1\(\frac{11}{12}\)
One cake recipe calls for \(\frac{2}{3}\) cup of sugar. Another recipe calls for 1\(\frac{1}{4}\) cups of sugar.
total cups of sugar that are needed to make both cakes = \(\frac{2}{3}\) + 1\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (0+ 1) + \(\frac{2}{3}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{2}{3}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\)  x \(\frac{3}{3}\)]
= 1 + \(\frac{8}{12}\) + \(\frac{3}{12}\)
= 1 + \(\frac{8 + 3}{12}\)
After simplification,
= 1 + \(\frac{11}{12}\)
Therefore, the result is given by,
= 1\(\frac{11}{12}\)
1\(\frac{11}{12}\) cups of sugar are needed.

Question 2.
Nicole and Daniel are splitting a pizza. Nicole eats \(\frac{1}{4}\) of a pizza and Daniel eats \(\frac{2}{3}\) of it. How much pizza is left?
____ of the pizza is left.
Answer: \(\frac{1}{12}\)
Nicole and Daniel are splitting a pizza. Nicole eats \(\frac{1}{4}\) of a pizza and Daniel eats \(\frac{2}{3}\) of it.
Piece of pizza ate by Nicole and Daniel = \(\frac{1}{4}\) + \(\frac{2}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{4}\) x \(\frac{3}{3}\)] + [\(\frac{2}{3}\)  x \(\frac{4}{4}\)]
= \(\frac{3}{12}\) + \(\frac{8}{12}\)
= \(\frac{3 + 8}{12}\)
After simplification, the result is given by,
= \(\frac{11}{12}\)
The piece of pizza left = 1 – \(\frac{11}{12}\) (consider whole pizza as 1 part, so subtract the completed piece of pizza from 1)
= \(\frac{12-11}{12}\)
= \(\frac{1}{12}\)
\(\frac{1}{12}\) of the pizza is left.

Question 3.
The Juarez family is making a cross-country trip. On Saturday, they traveled 450.8 miles. On Sunday, they traveled 604.6 miles. How many miles have they traveled so far?
They have travelled ____ miles.
Answer: 1055.4
On Saturday, they traveled 450.8 miles. On Sunday, they traveled 604.6 miles.
total miles they have traveled so far = 450.8 + 604.6 = 1055.4
They have travelled 1055.4 miles.

Question 4.
Kathy’s science book is 1\(\frac{1}{6}\) inches thick. Her reading book is 1\(\frac{3}{8}\) inches thick. How much thicker is her reading book than her science book?
It is ____ inches thicker.
Answer: 0\(\frac{5}{24}\)
Kathy’s science book is 1\(\frac{1}{6}\) inches thick. Her reading book is 1\(\frac{3}{8}\) inches thick
Kathy’s reading book is thicker than her science book by = 1\(\frac{3}{8}\) – 1\(\frac{1}{6}\)
Partition the fractions and whole numbers to subtract them separately.
= (1- 1) + [\(\frac{3}{8}\) – \(\frac{1}{6}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 0 + [\(\frac{3}{8}\) x \(\frac{6}{6}\)] – [\(\frac{1}{6}\)  x \(\frac{8}{8}\)]
= 0 + \(\frac{18}{48}\) – \(\frac{8}{48}\)
= 0 + \(\frac{18 – 8}{48}\)
After simplification,
= 0 + \(\frac{10}{48}\)
= 0 + \(\frac{5}{24}\)
Therefore, the result is given by,
= 0\(\frac{5}{24}\)
It is 0\(\frac{5}{24}\) inches thicker.

Question 5.
A large watermelon weighs 10.4 pounds. A smaller watermelon weighs 3.6 pounds. How much less does the smaller watermelon weigh?
It weighs ____ pounds less.
Answer: 6.8
A large watermelon weighs 10.4 pounds. A smaller watermelon weighs 3.6 pounds.
The smaller watermelon weighs less than the larger watermelon by = 10.4 – 3.6 = 6.8
It weighs 6.8 pounds less.

Question 6.
Terrance picked 115.2 pounds of apples on Monday. He picked 97.6 pounds of apples on Tuesday. How many pounds of apples did Terrance pick altogether?
Terrance picked ____ pounds of apples.
Answer: 212.8
Terrance picked 115.2 pounds of apples on Monday. He picked 97.6 pounds of apples on Tuesday.
total number of pounds of apples did Terrance pick altogether = 115.2 + 97.6 = 212.8
Terrance picked 212.8 pounds of apples.

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.8 Adding Using Mathematical Properties provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 1 Lesson 1.8 Adding Using Mathematical Properties Answers Key

The Commutative Property of Addition states: o + b = b + o
The Associative Property of Addition states: (a + b) + c = a + (b + c)
The Identity Property of Addition states: a + 0 = a

Rewrite each equation using your knowledge of addition properties.

Question 1.
a. 17 + n = ____
Answer:  n + 17
17 + n = n + 17
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. n + 0 = ____
Answer: n
n + 0 = n 
The above equation is an example of identity property.
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 2.
a. ____ = (x + y) + 2
Answer: x + (y + 2)
x + (y + 2) = (x + y) + 2
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. r + s = ____
Answer: s + r
r + s = s + r
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 3.
a. 0 + x = ____
Answer: x
0 + x = x
The above equation is an example of identity property.
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. (3 + g) + h = ____
Answer: 3 + (g + h)
(3 + g) + h = 3 + (g + h)
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 4.
a. (9 + r) + 5 = ____
Answer: 9 + (r + 5)
(9 + r) + 5 = 9 + (r + 5)
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. t + h = ____
Answer: h + t
t + h = h + t
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Solve each equation. Use the properties of addition to help.

Question 5.
a. 11 + 18 + 12 = ____
Answer: 41
11 + 18 + 12 = 41
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (5 + 3) + 0 = _______
Answer: 8
(5 + 3) + 0 = 5 + (3 + 0) = 8
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 6.
a. 14 + 15 + 16 = _____
Answer: 45
14 + 15 + 16 = 45
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (17 + 0) + 2 = _____
Answer: 19
(17 + 0) + 2 = 17 + (0 + 2) = 19
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 7.
a. 23 + 24 + 25 = ____
Answer:  72
23 + 24 + 25 = 72
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (4 + 5) + 0 = _____
Answer: 9
(4 + 5) + 0 = 4 + (5 + 0) = 9
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Question 8.
a. 54 + 43 + 19 = ____
Answer: 116
54 + 43 + 19 = 116
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. (8 + 0) + 10 = ____
Answer: 18
(8 + 0 ) + 10 = 8 + (0 + 10) = 18
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

Tell which property is used in each equation (commutative, associative, or identity).

Question 9.
a. 7 + (-7) = 0 _____
Answer: commutative property
7 + (-7) = 0 = commutative property
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

b. 4 + 6 = 6 + 4 _____
Answer: commutative property
4 + 6 = 6 + 4  = commutative property
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 10.
a. (11 + 2) + 8 = 11 + (2 + 8) ____
Answer: associative property
(11 + 2) + 8 = 11 + (2 + 8) = associative property
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 9 + 0 = 9 _____
Answer: identity property
9 + 0 = 9 = identity property
The above equation is an example of identity property.
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 11.
a. 6 + (4 + 3) = (6 + 4) + 3 _____
Answer: associative property
6 + (4 + 3) = (6 + 4) + 3 = associative property
The above equation is an example of associative property.
The associative property of addition is a mathematical statement that states that the arrangement of three or more integers does not change their sum. This means that no matter how the numbers are grouped, the sum of three or more integers remains the same.

b. 5 + 9 = 9 + 5 ______
Answer: commutative property
5 + 9 = 9 + 5 = commutative property
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

Question 12.
a. 15 + 0 = 15 ____
Answer: identity property
15 + 0 = 15 = identity property
The above equation is an example of identity property.
An identity in mathematics is a number, n, that results in the same number, n, when other numbers are added to it. The identity of the additive is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

b. 18 + 7 = 7 + 18 ______
Answer: commutative property
18 + 7 = 7 + 18 = commutative property
The above equation is an example for commutative property.
According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Therefore, the commutative property of addition, when we add two integers, the answer will remain unchanged even if the position of the numbers are changed.

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.7 Subtracting Fractions and Mixed Numbers provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 1 Lesson 1.7 Subtracting Fractions and Mixed Numbers Answers Key

To subtract fractions or mixed numbers when the denominators are different, rename the fractions so the denominators are the same.

Subtract. Write each answer in simplest form.

Question 1.
a.

Answer: \(\frac{7}{20}\)
\(\frac{3}{5}\) – \(\frac{1}{4}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{5}\) x \(\frac{4}{4}\)] – [\(\frac{1}{4}\)  x \(\frac{5}{5}\)]
= \(\frac{12}{20}\) – \(\frac{5}{20}\)
= \(\frac{12 – 5}{20}\)
After simplification, the result is given by,
= \(\frac{7}{20}\)

b.

Answer: \(\frac{1}{5}\)
\(\frac{1}{2}\) – \(\frac{3}{10}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{10}{10}\)] – [\(\frac{3}{10}\)  x \(\frac{2}{2}\)]
= \(\frac{10}{20}\) – \(\frac{6}{20}\)
= \(\frac{10 – 6}{20}\)
After simplification, the result is given by,
= \(\frac{4}{20}\)
= \(\frac{1}{5}\)

c.

Answer: \(\frac{3}{8}\)
\(\frac{7}{8}\) – \(\frac{1}{2}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{7}{8}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{8}{8}\)]
= \(\frac{14}{16}\) – \(\frac{8}{16}\)
= \(\frac{14 – 8}{16}\)
After simplification, the result is given by,
= \(\frac{6}{16}\)
= \(\frac{3}{8}\)

d.

Answer: \(\frac{7}{15}\)
\(\frac{4}{5}\) – \(\frac{1}{3}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{4}{5}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{5}{5}\)]
= \(\frac{12}{15}\) – \(\frac{5}{15}\)
= \(\frac{12 – 5}{15}\)
After simplification, the result is given by,
= \(\frac{7}{15}\)

Question 2.
a.

Answer: \(\frac{1}{2}\)
\(\frac{5}{6}\) – \(\frac{1}{3}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{5}{6}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{6}{6}\)]
= \(\frac{15}{18}\) – \(\frac{6}{18}\)
= \(\frac{15 – 6}{18}\)
After simplification, the result is given by,
= \(\frac{9}{18}\)
= \(\frac{1}{2}\)

b.

Answer: \(\frac{7}{15}\)
\(\frac{2}{3}\) – \(\frac{1}{5}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{3}\) x \(\frac{5}{5}\)] – [\(\frac{1}{5}\)  x \(\frac{3}{3}\)]
= \(\frac{10}{15}\) – \(\frac{3}{15}\)
= \(\frac{10 – 3}{15}\)
After simplification, the result is given by,
= \(\frac{7}{15}\)

c.

Answer: \(\frac{11}{24}\)
\(\frac{5}{8}\) – \(\frac{1}{6}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{5}{8}\) x \(\frac{6}{6}\)] – [\(\frac{1}{6}\)  x \(\frac{8}{8}\)]
= \(\frac{30}{48}\) – \(\frac{8}{48}\)
= \(\frac{30 – 8}{48}\)
After simplification, the result is given by,
= \(\frac{22}{48}\)
= \(\frac{11}{24}\)

d.

Answer: \(\frac{7}{20}\)
\(\frac{7}{10}\) – \(\frac{1}{2}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{7}{10}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{7}{10}\)]
= \(\frac{14}{20}\) – \(\frac{7}{20}\)
= \(\frac{14 – 7}{20}\)
After simplification, the result is given by,
= \(\frac{7}{20}\)

Question 3.
a.

Answer: \(\frac{1}{12}\)
\(\frac{3}{4}\) – \(\frac{2}{3}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{3}{3}\)] – [\(\frac{2}{3}\)  x \(\frac{4}{4}\)]
= \(\frac{9}{12}\) – \(\frac{8}{12}\)
= \(\frac{9 – 8}{12}\)
After simplification, the result is given by,
= \(\frac{1}{12}\)

b.

Answer: \(\frac{1}{18}\)
\(\frac{5}{9}\) – \(\frac{1}{2}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{5}{9}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{9}{9}\)]
= \(\frac{10}{18}\) – \(\frac{9}{18}\)
= \(\frac{10 – 9}{18}\)
After simplification, the result is given by,
= \(\frac{1}{18}\)

c.

Answer: \(\frac{1}{6}\)
\(\frac{1}{2}\) – \(\frac{1}{3}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{2}{2}\)]
= \(\frac{3}{6}\) – \(\frac{2}{6}\)
= \(\frac{3 – 2}{6}\)
After simplification, the result is given by,
= \(\frac{1}{6}\)

d.

Answer: \(\frac{41}{99}\)
\(\frac{7}{11}\) – \(\frac{2}{9}\)
To subtract fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{7}{11}\) x \(\frac{9}{9}\)] – [\(\frac{2}{9}\)  x \(\frac{11}{11}\)]
= \(\frac{63}{99}\) – \(\frac{22}{99}\)
= \(\frac{63 – 22}{99}\)
After simplification, the result is given by,
= \(\frac{41}{99}\)

Question 4.
a.

Answer: 1\(\frac{1}{8}\)
2\(\frac{3}{8}\) – 1\(\frac{2}{9}\)
Partition the fractions and whole numbers to subtract them separately.
= (2- 1) + [\(\frac{3}{8}\) – \(\frac{2}{9}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{3}{8}\) x \(\frac{9}{9}\)] – [\(\frac{2}{9}\)  x \(\frac{8}{8}\)]
= 1 + \(\frac{27}{72}\) – \(\frac{18}{72}\)
= 1 + \(\frac{27 – 18}{72}\)
After simplification,
= 1 + \(\frac{9}{72}\)
= 1 + \(\frac{1}{8}\)
Therefore, the result is given by,
= 1\(\frac{1}{8}\)

b.

Answer: 1\(\frac{11}{12}\)
3\(\frac{1}{4}\) – 1\(\frac{1}{3}\)
Partition the fractions and whole numbers to subtract them separately.
= (3- 1) + [\(\frac{1}{4}\) – \(\frac{1}{3}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{1}{4}\) x \(\frac{3}{3}\)] – [\(\frac{1}{3}\)  x \(\frac{4}{4}\)]
= 2 + \(\frac{3}{12}\) – \(\frac{4}{12}\)
= 1 + \(\frac{15}{12}\) – \(\frac{4}{12}\)
= 1 + \(\frac{15 – 4}{12}\)
After simplification,
= 1 + \(\frac{11}{12}\)
Therefore, the result is given by,
= 1\(\frac{11}{12}\)

c.

Answer: 0\(\frac{3}{4}\)
4\(\frac{1}{2}\) – 3\(\frac{3}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (4- 3) + [\(\frac{1}{2}\) – \(\frac{3}{4}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{1}{2}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\)  x \(\frac{2}{2}\)]
= 1 + \(\frac{4}{8}\) – \(\frac{6}{8}\)
= 0 + \(\frac{12}{8}\) – \(\frac{6}{8}\)
= 0 + \(\frac{12 – 6}{8}\)
After simplification,
= 0 + \(\frac{6}{8}\)
= 0 + \(\frac{3}{4}\)
Therefore, the result is given by,
= 0\(\frac{3}{4}\)

d.

Answer: 1\(\frac{43}{56}\)
6\(\frac{5}{8}\) – 4\(\frac{6}{7}\)
Partition the fractions and whole numbers to subtract them separately.
= (6 – 4) + [\(\frac{5}{8}\) – \(\frac{6}{7}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{5}{8}\) x \(\frac{7}{7}\)] – [\(\frac{6}{7}\)  x \(\frac{8}{8}\)]
= 2 + \(\frac{35}{56}\) – \(\frac{48}{56}\)
= 1 + \(\frac{91}{56}\) – \(\frac{48}{56}\)
= 1 + \(\frac{91 – 48}{56}\)
After simplification,
= 1 + \(\frac{43}{56}\)
Therefore, the result is given by,
= 1\(\frac{43}{56}\)

Question 5.
a.

Answer: 1\(\frac{49}{88}\)
3\(\frac{2}{11}\) – 1\(\frac{5}{8}\)
Partition the fractions and whole numbers to subtract them separately.
= (3 – 1) + [\(\frac{2}{11}\) – \(\frac{5}{8}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{2}{11}\) x \(\frac{8}{8}\)] – [\(\frac{5}{8}\)  x \(\frac{11}{11}\)]
= 2 + \(\frac{16}{88}\) – \(\frac{55}{88}\)
= 1 + \(\frac{104}{88}\) – \(\frac{55}{88}\)
= 1 + \(\frac{104 – 55}{88}\)
After simplification,
= 1 + \(\frac{49}{88}\)
Therefore, the result is given by,
= 1\(\frac{49}{88}\)

b.

Answer: 4\(\frac{4}{15}\)
7\(\frac{2}{3}\) – 3\(\frac{2}{5}\)
Partition the fractions and whole numbers to subtract them separately.
= (7 – 3) + [\(\frac{2}{3}\) – \(\frac{2}{5}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{2}{3}\) x \(\frac{5}{5}\)] – [\(\frac{2}{5}\)  x \(\frac{3}{3}\)]
= 4 + \(\frac{10}{15}\) – \(\frac{6}{15}\)
= 4 + \(\frac{10 – 6}{15}\)
After simplification,
= 4 + \(\frac{4}{15}\)
Therefore, the result is given by,
= 4\(\frac{4}{15}\)

c.

Answer: 2\(\frac{5}{6}\)
5\(\frac{1}{3}\) – 2\(\frac{1}{2}\)
Partition the fractions and whole numbers to subtract them separately.
= (5 – 2) + [\(\frac{1}{3}\) – \(\frac{1}{2}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{1}{3}\) x \(\frac{2}{2}\)] – [\(\frac{1}{2}\)  x \(\frac{3}{3}\)]
= 3 + \(\frac{2}{6}\) – \(\frac{3}{6}\)
= 2 + \(\frac{8}{6}\) – \(\frac{3}{6}\)
= 2 + \(\frac{8 – 3}{6}\)
After simplification,
= 2 + \(\frac{5}{6}\)
Therefore, the result is given by,
= 2\(\frac{5}{6}\)

d.

Answer: 1\(\frac{23}{42}\)
2\(\frac{5}{6}\) – 1\(\frac{2}{7}\)
Partition the fractions and whole numbers to subtract them separately.
= (2 – 1) + [\(\frac{5}{6}\) – \(\frac{2}{7}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 1 + [\(\frac{5}{6}\) x \(\frac{7}{7}\)] – [\(\frac{2}{7}\)  x \(\frac{6}{6}\)]
= 1 + \(\frac{35}{42}\) – \(\frac{12}{42}\)
= 1 + \(\frac{35 – 12}{42}\)
After simplification,
= 1 + \(\frac{23}{42}\)
Therefore, the result is given by,
= 1\(\frac{23}{42}\)

Question 6.
a.

Answer: 2\(\frac{5}{9}\)
4\(\frac{7}{9}\) – 2\(\frac{2}{3}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 2) + [\(\frac{7}{9}\) – \(\frac{2}{3}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{7}{9}\) x \(\frac{3}{3}\)] – [\(\frac{2}{3}\)  x \(\frac{9}{9}\)]
= 2 + \(\frac{21}{27}\) – \(\frac{6}{27}\)
= 2 + \(\frac{21 – 6}{27}\)
After simplification,
=  2+ \(\frac{15}{27}\)
=  2+ \(\frac{5}{9}\)
Therefore, the result is given by,
= 2\(\frac{5}{9}\)

b.

Answer: 1\(\frac{9}{20}\)
3\(\frac{1}{5}\) – 1\(\frac{3}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (3 – 1) + [\(\frac{1}{5}\) – \(\frac{3}{4}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{1}{5}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\)  x \(\frac{5}{5}\)]
= 2 + \(\frac{4}{20}\) – \(\frac{15}{20}\)
= 1 + \(\frac{24}{20}\) – \(\frac{15}{20}\)
= 1 + \(\frac{24 – 15}{20}\)
After simplification,
=  1+ \(\frac{9}{20}\)
Therefore, the result is given by,
= 1\(\frac{9}{20}\)

c.

Answer: 2\(\frac{17}{24}\)
4\(\frac{5}{6}\) – 2\(\frac{1}{8}\)
Partition the fractions and whole numbers to subtract them separately.
= (4 – 2) + [\(\frac{5}{6}\) – \(\frac{1}{8}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{5}{6}\) x \(\frac{8}{8}\)] – [\(\frac{1}{8}\)  x \(\frac{6}{6}\)]
= 2 + \(\frac{40}{48}\) – \(\frac{6}{48}\)
= 2 + \(\frac{40 – 6}{48}\)
After simplification,
= 2 + \(\frac{34}{48}\)
= 2 + \(\frac{17}{24}\)
Therefore, the result is given by,
= 2\(\frac{17}{24}\)

d.

Answer:1\(\frac{1}{4}\)
3\(\frac{1}{8}\) – 1\(\frac{3}{4}\)
Partition the fractions and whole numbers to subtract them separately.
= (3 – 1) + [\(\frac{1}{8}\) – \(\frac{3}{4}\)]
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{1}{8}\) x \(\frac{4}{4}\)] – [\(\frac{3}{4}\)  x \(\frac{8}{8}\)]
= 2 + \(\frac{4}{32}\) – \(\frac{24}{32}\)
= 1 + \(\frac{36}{32}\) – \(\frac{24}{32}\)
= 1 + \(\frac{36 – 24}{48}\)
After simplification,
= 1 + \(\frac{12}{48}\)
= 1 + \(\frac{1}{4}\)
Therefore, the result is given by,
= 1\(\frac{1}{4}\)

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.6 Subtracting Integers provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 1 Lesson 1.6 Subtracting Integers Answers Key

To subtract an integer, add its opposite (except in the case of 0).

Subtract.

Question 1.
a. 3 – 11 = ____
Answer: -8
3 – 11 = 3 + (-11) =  -8
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 5 – 2 = ____
Answer: 3
5 – 2 = 5 + (-2) = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -4 – 6 = ___
Answer: -10
-4 – 6 = -4 + (-6) = 10
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 2.
a. -12 – 3 = ____
Answer: -15
-12 – 3 = -12 + (-3) = -15
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -5 – (-6) = ____
Answer: 1
-5 – (-6) = -5 + 6 = 1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 14 – 19 = ____
Answer: -5
14 – 19 = 14 + (-19) = -5
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 3.
a. 4 – 19 = ____
Answer: -15
4 – 19 = 4 + (-19) = -15
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -11 – (-1) = ____
Answer: -10
-11 -(-1) = -11 + 1 = -10
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 16 – (-27) = ____
Answer: 43
16 – (-27) = 16 + 27 = 43
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 4.
a. -6 – (-6) = ____
Answer: 0
-6 – (-6) = -6 + 6 = 0
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -11 – 0 = ____
Answer: -11
-11 – 0 =-11 + (-0) = -11
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -2 – 2 = ____
Answer: -4
-2 – 2 = -2 + (-2) = -4
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 5.
a. 8 – 1 = ____
Answer: 7
8 – 1 = 8 + (-1) = 7
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 8 – (-1) = ____
Answer: 9
8 – (-1) = 8 + 1 = 9
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -13 – 3 = ____
Answer: -16
-13 – 3 = -13 + (-3) = -16
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 6.
a. 43 – 15 = ____
Answer: 28
43 – 15 = 43 + (-15) = 28
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -27 – (-39) = ____
Answer: 12
-27 – (-39) = -27 + 39 = 12
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -24 – (-38) = ____
Answer: 14
-24 – (-38) = -24 + 38 = 14
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 7.
a. -46 – (-31) = ____
Answer: -15
-46 – (-31) = -46 + 31 = -15
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -48 – (-47) = ____
Answer: -1
-48 – (-47) = -48 + 47 = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -38 – (-17) = ____
Answer: -21
-38 – (-17) = -38 + 17 = -21
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 8.
a. 9 – (-6) = ____
Answer: 15
9 – (-6) = 9 + 6 = 15
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 15 – (-1) = ____
Answer: 16
15 – (-1) = 15 + 1 = 16
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -19 – (-22) = ____
Answer: 3
-19 – (-22) = -19 + 22 = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 9.
a. (-3) – 24 = ____
Answer: -27
(-3) – 24 =-3 – 24 = -27
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -11 – 44 = ____
Answer: -55
-11 – 44 = -11 + (-44) = -55
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 42 – 45 = ____
Answer: -3
42 – 45 = 42 + (-45) = -3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 10.
a. -33 – 12 = ____
Answer: -45
-33 – 12 = -33 + (-12) = -45
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -37 – (-40) = ____
Answer: 3
-37 – (-40) = -37 + 40 = 3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 5 – (-32) = ___
Answer: 37
5 – (-32) = 5 + 32 = 37
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Subtract.

Question 1.
a. -32 – (-27) = ____
Answer: 5
-32 – (-27) = -32 + 27 = 5
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -26 – 3 = ____
Answer: -29
-26 – 3 = -26 + (-3) = -29
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 28 – (-20) = ____
Answer: 48
28 – (-20) = 28 + 20 = 48
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 2.
a. 7 – (-37) = ____
Answer: 44
7 – (-37) = 7 + 37 = 44
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -9 – 48 = ____
Answer: -57
-9 – 48 = -9 + (-48) = -57
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 28 – (-15) = ____
Answer: 43
28 – (-15) = 28 + 15 = 43
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 3.
a. 16 – (-1) = ___
Answer: 17
16 – (-1) = 16 + 1 = 17 
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 24 – (-49) = ____
Answer: 73
24 – (-49) = 24 + 49 = 73
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -30 – (-36) = ____
Answer: 6
-30 – (-36) = -30 + 36 = 6 
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 4.
a. -44 – 24 = ____
Answer: -68
-44 – 24 = – 44 + (-24) = -68
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -31 – 34 = ____
Answer: -65
-31 – 34 = -31 + (-34) = – 65
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -31 – (-13) = ____
Answer: -18
-31 – (-13) = -31 + 13 = -18
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 5.
a. -49 – (-46) = ____
Answer: -3
-49 – (-46) = -49 + 46 = -3
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -16 – 49 = ____
Answer: -65
-16 – 49 = -16 + (-49) = -65
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 18 – 28 = ____
Answer: -10
18 – 28 =18 + (-28) = -10
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 6.
a. -32 – (-50) = ___
Answer: 18
-32 – (-50) = -32 + 50 = 18
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -32 – (-21) = ___
Answer: -11
-32 – (-21) = -32 + 21 = -11
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -48 – (-47) = ____
Answer: -1
-48 – (-47) = – 48 + 47 = -1
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 7.
a. -5 – (-30) = ____
Answer: 25
-5 – (-30) = -5 + 30 = 25
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b.
14 – (-20) = ___
Answer: 34
14 – (-20) =14 + 20 = 34
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 9 – (-47) = ____
Answer: 56
9 – (-47) = 9 + 47 = 56
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 8.
a. -33 – 39 = ___
Answer: -72
-33 – 39 = -33 + (-39) = -78
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 4 – (-8) = ___
Answer: 12
4 – (-8) = 4 + 8 = 12 
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 1 – (-42) = ____
Answer: 43
1 – (-42) = 1 + 42 = 43
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 9.
a. 32 – (-41) = ___
Answer: 73
32 – (-41) = 32 + 41 = 73
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 40 – 44 = ___
Answer: -4
40 – 44 = 40 + (-44) = -4
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -13 – (-39) = ____
Answer: 26
-13 – (-39) = -13 + 39 = 26
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 10.
a. -50 – 19 = ____
Answer: -69
-50 – 19 = -50 + (-19) = -69
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 48 – (-32) = ____
Answer: 80
48 – (-32) = 48 + 32 = 80 
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -14 – (-39) = ____
Answer: 25
-14 – (-39) = -14 + 39 = 25 
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 11.
a. -18 – (-4) = ___
Answer: -14
-18 – (-4) = -18 + 4 = -14
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -45 – 13 = ___
Answer: -58
-45 – 13 = -45 + (-13) = -58
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 8 – (-67) = ____
Answer: 75
8 – (-67) = 8 + 67 =75
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 12.
a. 56 – (-21) = ____
Answer: 77
56 – (-21) = 56 + 21 = 77
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -11 – 34 = ____
Answer: -45
-11 – 34 = -11 + (-34) = -45
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. 24 – (-17) = ____
Answer: 41
24 – (-17) = 24 + 17 = 41
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 13.
a. 31 – (-31) = ____
Answer: 62
31 – (-31) = 31 + 31 = 62
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. 26 – (-9) = ____
Answer: 35
26 – (-9) = 26 + 9 = 35
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -83 – (-3) = ____
Answer: 80
-83 – (-3) = -83 + 3 = – 80
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

Question 14.
a. -87 – 6 = ____
Answer: -93
-87 – 6 = -87 + (-6) = -93
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

b. -90 – 12 = ___
Answer: -102
-90 – 12 = -90 + (-12) = -102
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

c. -46 – (-9) = ____
Answer: -37
-46 – (-9) = -46 + 9 = -37
Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number.

This handy Spectrum Math Grade 7 Answer Key Chapter 1 Lesson 1.4 Adding Fractions and Mixed Numbers provides detailed answers for the workbook questions.

Spectrum Math Grade 7 Chapter 1 Lesson 1.4 Adding Fractions and Mixed Numbers Answers Key

To add fractions or mixed numbers when the denominators are different, rename the fractions so the denominators are the same.

Add. Write each answer in simplest form.

Question 1.
a.

Answer: \(\frac{11}{8}\) = 1\(\frac{3}{8}\)
\(\frac{3}{4}\) +\(\frac{5}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{8}{8}\)] + [\(\frac{5}{8}\)  x \(\frac{4}{4}\)]
= \(\frac{24}{32}\) + \(\frac{20}{32}\)
= \(\frac{24 + 20}{32}\)
After simplification, the result is given by,
= \(\frac{44}{32}\) = \(\frac{11}{8}\) (by simplification)
= 1\(\frac{12}{32}\) = 1\(\frac{3}{8}\) (by simplification)

b.

Answer: \(\frac{5}{6}\) = 0\(\frac{5}{6}\)
\(\frac{1}{2}\) +\(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{2}{2}\)]
= \(\frac{3}{6}\) + \(\frac{2}{6}\)
= \(\frac{3 + 2}{6}\)
After simplification, the result is given by,
= \(\frac{5}{6}\)
= 0\(\frac{5}{6}\)

c.

Answer: \(\frac{23}{20}\) = 1\(\frac{3}{20}\)
\(\frac{3}{4}\) +\(\frac{2}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{5}{5}\)] + [\(\frac{2}{5}\)  x \(\frac{4}{4}\)]
= \(\frac{15}{20}\) + \(\frac{8}{20}\)
= \(\frac{15 + 8}{20}\)
After simplification, the result is given by,
= \(\frac{23}{20}\)
= 1\(\frac{3}{20}\)

d.

Answer: \(\frac{1}{2}\) = 0\(\frac{1}{2}\)
\(\frac{1}{6}\) +\(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{6}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{6}{6}\)]
= \(\frac{3}{18}\) + \(\frac{6}{18}\)
= \(\frac{3 + 6}{18}\)
After simplification, the result is given by,
= \(\frac{9}{18}\) = \(\frac{1}{2}\) (by simplification)
= 0\(\frac{9}{18}\) = 0\(\frac{1}{2}\) (by simplification)

Question 2.
a.

Answer: \(\frac{47}{40}\) = 1\(\frac{7}{40}\)
\(\frac{3}{8}\) +\(\frac{4}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{8}\) x \(\frac{5}{5}\)] + [\(\frac{4}{5}\)  x \(\frac{8}{8}\)]
= \(\frac{15}{40}\) + \(\frac{32}{40}\)
= \(\frac{15 + 32}{40}\)
After simplification, the result is given by,
= \(\frac{47}{40}\)
= 1\(\frac{7}{40}\)

b.

Answer: \(\frac{4}{5}\) = 0\(\frac{4}{5}\)
\(\frac{1}{2}\) +\(\frac{3}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{2}\) x \(\frac{10}{10}\)] + [\(\frac{3}{10}\)  x \(\frac{2}{2}\)]
= \(\frac{10}{20}\) + \(\frac{6}{20}\)
= \(\frac{10 + 6}{20}\)
After simplification, the result is given by,
= \(\frac{16}{20}\) = \(\frac{4}{5}\) (by simplification)
= 0\(\frac{16}{20}\) = 0\(\frac{4}{5}\) (by simplification)

c.

Answer: \(\frac{11}{12}\) = 0\(\frac{11}{12}\)
\(\frac{2}{3}\) +\(\frac{3}{12}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{3}\) x \(\frac{12}{12}\)] + [\(\frac{3}{12}\)  x \(\frac{3}{3}\)]
= \(\frac{24}{36}\) + \(\frac{9}{36}\)
= \(\frac{24 + 9}{36}\)
After simplification, the result is given by,
= \(\frac{33}{36}\) = \(\frac{11}{12}\) (by simplification)
= 0\(\frac{33}{36}\) = 0\(\frac{11}{12}\) (by simplification)

d.

Answer: \(\frac{29}{20}\) = 1\(\frac{9}{20}\)
\(\frac{3}{4}\) +\(\frac{7}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{3}{4}\) x \(\frac{10}{10}\)] + [\(\frac{7}{10}\)  x \(\frac{4}{4}\)]
= \(\frac{30}{40}\) + \(\frac{28}{40}\)
= \(\frac{30 + 28}{40}\)
After simplification, the result is given by,
= \(\frac{58}{40}\) = \(\frac{29}{20}\) (by simplification)
= 1\(\frac{18}{40}\) = 1\(\frac{9}{20}\) (by simplification)

Question 3.
a.

Answer: \(\frac{5}{8}\) = 0\(\frac{5}{8}\)
\(\frac{1}{4}\) +\(\frac{3}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{4}\) x \(\frac{8}{8}\)] + [\(\frac{3}{8}\)  x \(\frac{4}{4}\)]
= \(\frac{8}{32}\) + \(\frac{12}{32}\)
= \(\frac{8 + 12}{32}\)
After simplification, the result is given by,
= \(\frac{20}{32}\) = \(\frac{5}{8}\) (by simplification)
= 0\(\frac{20}{32}\) = 0\(\frac{5}{8}\) (by simplification)

b.

Answer: \(\frac{29}{35}\) = 0\(\frac{29}{35}\)
\(\frac{2}{5}\) +\(\frac{3}{7}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{5}\) x \(\frac{7}{7}\)] + [\(\frac{3}{7}\)  x \(\frac{5}{5}\)]
= \(\frac{14}{35}\) + \(\frac{15}{35}\)
= \(\frac{14 + 15}{35}\)
After simplification, the result is given by,
= \(\frac{29}{35}\)
= 0\(\frac{29}{35}\)
c.

Answer: \(\frac{57}{56}\) = 1\(\frac{1}{56}\)
\(\frac{1}{7}\) +\(\frac{7}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{1}{7}\) x \(\frac{8}{8}\)] + [\(\frac{7}{8}\)  x \(\frac{7}{7}\)]
= \(\frac{8}{56}\) + \(\frac{49}{56}\)
= \(\frac{8 + 49}{56}\)
After simplification, the result is given by,
= \(\frac{57}{56}\)
= 1\(\frac{1}{56}\)

d.

Answer: \(\frac{13}{15}\) = 0\(\frac{13}{15}\)
\(\frac{2}{3}\) +\(\frac{1}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= [\(\frac{2}{3}\) x \(\frac{5}{5}\)] + [\(\frac{1}{5}\)  x \(\frac{3}{3}\)]
= \(\frac{10}{15}\) + \(\frac{3}{15}\)
= \(\frac{10 + 3}{15}\)
After simplification, the result is given by,
= \(\frac{13}{15}\)
= 0\(\frac{13}{15}\)

Question 4.
a.

Answer: 3\(\frac{7}{12}\)
1\(\frac{1}{3}\) + 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{1}{3}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{1}{3}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\)  x \(\frac{3}{3}\)]
= 3 + \(\frac{4}{12}\) + \(\frac{3}{12}\)
= 3 + \(\frac{4 + 3}{12}\)
After simplification,
= 3 + \(\frac{7}{12}\)
Therefore, the result is given by,
= 3\(\frac{7}{12}\)

b.

Answer: 10\(\frac{7}{8}\)
3\(\frac{3}{8}\) + 7\(\frac{1}{2}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 7) + \(\frac{3}{8}\) + \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 10 + [\(\frac{3}{8}\) x \(\frac{2}{2}\)] + [\(\frac{1}{2}\)  x \(\frac{8}{8}\)]
= 10 + \(\frac{6}{16}\) + \(\frac{8}{16}\)
= 10 + \(\frac{6 + 8}{16}\)
After simplification,
= 10 + \(\frac{14}{16}\)
= 10 + \(\frac{7}{8}\) (by simplification)
Therefore, the result is given by,
= 10\(\frac{7}{8}\)

c.

Answer: 6\(\frac{13}{21}\)
4\(\frac{2}{7}\) + 2\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 2) + \(\frac{2}{7}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{2}{7}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{7}{7}\)]
= 6 + \(\frac{6}{21}\) + \(\frac{7}{21}\)
= 6 + \(\frac{6 + 7}{21}\)
After simplification,
= 6 + \(\frac{13}{21}\)
Therefore, the result is given by,
= 6\(\frac{13}{21}\)

d.

Answer: 4\(\frac{7}{10}\)
1\(\frac{2}{5}\) + 3\(\frac{3}{10}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 3) + \(\frac{2}{5}\) + \(\frac{3}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{2}{5}\) x \(\frac{10}{10}\)] + [\(\frac{3}{10}\)  x \(\frac{5}{5}\)]
= 4 + \(\frac{20}{50}\) + \(\frac{15}{50}\)
= 4 + \(\frac{20 + 15}{50}\)
After simplification,
= 4 + \(\frac{35}{50}\)
= 4 + \(\frac{7}{10}\) (by simplification)
Therefore, the result is given by,
= 4\(\frac{7}{10}\)

Question 5.
a.

Answer: 7\(\frac{7}{9}\)
4\(\frac{4}{9}\) + 3\(\frac{1}{3}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 3) + \(\frac{4}{9}\) + \(\frac{1}{3}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 7 + [\(\frac{4}{9}\) x \(\frac{3}{3}\)] + [\(\frac{1}{3}\)  x \(\frac{9}{9}\)]
= 7 + \(\frac{12}{27}\) + \(\frac{9}{27}\)
= 7 + \(\frac{12 + 9}{27}\)
After simplification,
= 7 + \(\frac{21}{27}\)
= 7 + \(\frac{7}{9}\) (by simplification)
Therefore, the result is given by,
= 7\(\frac{7}{9}\)

b.

Answer: 2\(\frac{33}{40}\)
1\(\frac{1}{8}\) + 1\(\frac{7}{10}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 1) + \(\frac{1}{8}\) + \(\frac{7}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 2 + [\(\frac{1}{8}\) x \(\frac{10}{10}\)] + [\(\frac{7}{10}\)  x \(\frac{8}{8}\)]
= 2 + \(\frac{10}{80}\) + \(\frac{56}{80}\)
= 2 + \(\frac{10 + 56}{80}\)
After simplification,
= 2 + \(\frac{66}{80}\)
= 2 + \(\frac{33}{40}\) (by simplification)
Therefore, the result is given by,
= 2\(\frac{33}{40}\)

c.

Answer: 5\(\frac{19}{24}\)
2\(\frac{1}{6}\) + 3\(\frac{5}{8}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 3) + \(\frac{1}{6}\) + \(\frac{5}{8}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{6}\) x \(\frac{8}{8}\)] + [\(\frac{5}{8}\)  x \(\frac{6}{6}\)]
= 5 + \(\frac{8}{48}\) + \(\frac{30}{48}\)
= 5 + \(\frac{8 + 30}{48}\)
After simplification,
= 5 + \(\frac{38}{48}\)
= 5 + \(\frac{19}{24}\) (by simplification)
Therefore, the result is given by,
= 5\(\frac{19}{24}\)

d.

Answer: 3\(\frac{22}{35}\)
1\(\frac{3}{7}\) + 2\(\frac{1}{5}\)
Partition the fractions and whole numbers to add them separately.
= (1 + 2) + \(\frac{3}{7}\) + \(\frac{1}{5}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{3}{7}\) x \(\frac{5}{5}\)] + [\(\frac{1}{5}\)  x \(\frac{7}{7}\)]
= 3 + \(\frac{15}{35}\) + \(\frac{7}{35}\)
= 3 + \(\frac{15 + 7}{35}\)
After simplification,
= 3 + \(\frac{22}{35}\)
Therefore, the result is given by,
= 3\(\frac{22}{35}\)

Question 6.
a.

Answer: 5\(\frac{3}{4}\)
3\(\frac{1}{2}\) + 2\(\frac{1}{4}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 2) + \(\frac{1}{2}\) + \(\frac{1}{4}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 5 + [\(\frac{1}{2}\) x \(\frac{4}{4}\)] + [\(\frac{1}{4}\)  x \(\frac{2}{2}\)]
= 5 + \(\frac{4}{8}\) + \(\frac{2}{8}\)
= 5 + \(\frac{4 + 2}{8}\)
After simplification,
= 5 + \(\frac{6}{8}\)
= 5 + \(\frac{3}{4}\) (by simplification)
Therefore, the result is given by,
= 5\(\frac{3}{4}\)

b.

Answer: 3\(\frac{25}{18}\)
2\(\frac{5}{6}\) + 1\(\frac{5}{9}\)
Partition the fractions and whole numbers to add them separately.
= (2 + 1) + \(\frac{5}{6}\) + \(\frac{5}{9}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 3 + [\(\frac{5}{6}\) x \(\frac{9}{9}\)] + [\(\frac{5}{9}\)  x \(\frac{6}{6}\)]
= 3 + \(\frac{45}{54}\) + \(\frac{30}{54}\)
= 3 + \(\frac{45 + 30}{54}\)
After simplification,
= 3 + \(\frac{75}{54}\)
= 3 + \(\frac{25}{18}\) (by simplification)
Therefore, the result is given by,
= 3\(\frac{25}{18}\)

c.

Answer: 4\(\frac{47}{70}\)
3\(\frac{4}{7}\) + 1\(\frac{1}{10}\)
Partition the fractions and whole numbers to add them separately.
= (3 + 1) + \(\frac{4}{7}\) + \(\frac{1}{10}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 4 + [\(\frac{4}{7}\) x \(\frac{10}{10}\)] + [\(\frac{1}{10}\)  x \(\frac{7}{7}\)]
= 4 + \(\frac{40}{70}\) + \(\frac{7}{70}\)
= 4 + \(\frac{40 + 7}{70}\)
After simplification,
= 4 + \(\frac{47}{70}\)
Therefore, the result is given by,
= 4\(\frac{47}{70}\)

d.

Answer: 6\(\frac{5}{6}\)
4\(\frac{1}{3}\) + 2\(\frac{1}{2}\)
Partition the fractions and whole numbers to add them separately.
= (4 + 2) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
To add fractions or mixed numbers when the denominators are different, rename the fractions in such a way by multiplying denominator of one fraction with another, to make the denominators same.
= 6 + [\(\frac{1}{3}\) x \(\frac{2}{2}\)] + [\(\frac{1}{2}\)  x \(\frac{3}{3}\)]
= 6 + \(\frac{2}{6}\) + \(\frac{3}{6}\)
= 6 + \(\frac{2 + 3}{6}\)
After simplification,
= 6 + \(\frac{5}{6}\)
Therefore, the result is given by,
= 6\(\frac{5}{6}\)