Go through the Spectrum Math Grade 6 Answer Key Chapter 1 Pretest and get the proper assistance needed during your homework.

Rewrite each expression using the Distributive Property.

Question 1.
a. 4 × (6 + 2) = ______
When solved 4 × (6 + 2), we get the answer 32.

Explanation:
4 × (6 + 2) = (4 × 6) + (4 × 2)
= 24 + 8
= 32.

b. (2 × 5) + (2 × 4) = ____
When solved (2 × 5) + (2 × 4), we get the answer 18.

Explanation:
(2 × 5) + (2 × 4) = 2 × (5 + 4)
= 2 × 9
= 18.

Question 2.
a. 4 × (2 + 6) = _______
When solved 4 × (2 + 6), we get the answer 32.

Explanation:
4 × (2 + 6) = (4 × 2) + (4 × 6)
= 8 + 24
= 32.

b. 6 × (5 – 1) = ____
When solved 6 × (5 – 1) , we get the answer 24.

Explanation:
6 × (5 – 1) = (6 × 5) – (6 × 1)
= 30 – 6
= 24.

Question 3.
a. (3 × 6) – (3 × 3) = ____
When solved (3 × 6) – (3 × 3) , we get the answer 9.

Explanation:
(3 × 6) – (3 × 3) = 3 × (6 – 3)
= 3 × 3
= 9.

b. 8 × (3 – 1) = ____
When solved 8 × (3 – 1), we get the answer 16.

Explanation:
8 × (3 – 1) = (8 × 3) – (8 × 1)
= 24 – 8
= 16.

Find the Greatest Common Factor of each set of numbers.

Question 4.
a. 5,20 ________
Greatest Common Factor of 5, 20: 5.

Explanation:
Factors of 5:                      Factors of 20:
1,5.                                     1,2,4,5,10,20.

b. 12,36 ________
Greatest Common Factor of 12, 36: 12.

Explanation:
Factors of 12:                      Factors of 36:
1,2,3,4,6,12.                          1,2,3,4,6,9.12,18,36.

c. 72,60 _____
Greatest Common Factor of 72, 60: 12.

Explanation:
Factors of 72:                                             Factors of 60:
1,2,3,4,6,8.9.12,18,24,36,72.                          1,2,3,5,6,10,12,20,30,60.

Question 5.
a. 65,39 ________
Greatest Common Factor of 65, 39: 3.

Explanation:
Factors of 65:                      Factors of 39:
1,5,3,65.                               1,3,13,39.

b. 95,76 ________
Greatest Common Factor of 95, 76: 19.

Explanation:
Factors of 95:                      Factors of 76:
1,5,19,95.                               1,2,4,19,38,76.

c. 96, 112 ____
Greatest Common Factor of 96, 112: 16.

Explanation:
Factors of 96:                                        Factors of 112:
1,2,3,4,6,8,12,16,24,32,48,96.                1,2,4,7, 8,14,16,28,56,112.

Find the Least Common Multiple of each set of numbers.

Question 6.
a. 12, 3 ________
Least Common Multiple of 12, 3: 12.

Explanation:
Multiples of 12:
12,  24, 36, 48, 60, 72, 84, 96, 108, 120.
Multiples of 3:
3,  6, 9, 12, 15, 18, 21, 24, 27, 30.

b. 15, 3, 2 ________
Least Common Multiple of 15, 3, 2: 30.

Explanation:
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40.

c. 4, 7 ____
Least Common Multiple of 4, 7: 28.

Explanation:
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Question 7.
a. 7, 10, 3 _____
Least Common Multiple of 7, 10, 3: 210.

Explanation:
Multiples of 7:
7,  14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210.
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147,150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210.

b. 12, 6 ____
Least Common Multiple of 12,6: 12.

Explanation:
Multiples of 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

c. 7, 3, 5 _____
Least Common Multiple of 7, 3, 5: 105.

Explanation:
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120.
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150.

Multiply or Divide.

Question 8.
a.

Explanation:
312 × 263 = ????
=> Multiplying 312 by 263, we get the product 82056.

b.

Explanation:
428 × 321 = ????
=> Multiplying 428 by 321, we get the product 1,37,388.

c.

Explanation:
2185 × 216 = ????
=> Multiplying 2185 by 216, we get the product 4,71,960.

d.

Explanation:
3372 × 351 = ????
=> Multiplying 3372 by 351, we get the product 11,83,572.

Question 9.
a.

Explanation:
6278 ÷ 73 = ???
=> Dividing 6278 by 73, we get 86 as quotient and 0 as remainder.

b.

Explanation:
8239 ÷ 54 = ????
=> Dividing 8239 by 54, we get 152 as quotient and 31 as remainder.

c.

Explanation:
54702 ÷ 27 = ????
=> Dividing 54702 by 27, we get 2026 as quotient and 0 as remainder.

d.

Explanation:
96542 ÷ 83 = ????
=> Dividing 96542 by 83, we get 1163 as quotient and 96 as remainder.

Question 10.
a.

Explanation:
2.86 × 0.3 = ???
=> Multiplying 2.86 by 0.3, we get the product 0.858.

b.

Explanation:
0.82 × 0.43 = ????
=> Multiplying 0.82 by 0.43, we get the product 0.3526.

c.

Explanation:
$78.53 × 16 =$????
=> Multiplying $78.53 by 16, we get the product$1256.48.

d.

Explanation:
3.21 × 8.72 = ????
=> Multiplying 3.21 by 8.72, we get the product 27.9912.

Question 11.
a.

Dividing 64 by 0.08, we get 800 as quotient and 0 as remainder.

Explanation:
64 ÷ 0.08 = ???
=> 64 ÷ 0.08 = (64 ÷ 0.08) × (100 ÷ 100)
=> 6400 ÷ 8
=> 800.

b.

Dividing 726 by 0.3, we get 2,420 as quotient and 0 as remainder.

Explanation:
726 ÷ 0.3 = ???
=> 726 ÷ 0.3 = (726 ÷ 0.3) × (10 ÷ 10)
=> 7260 ÷ 3
=> 2,420.

c.

Dividing 2.1995 by 0.83, we get 2.65 as quotient and 0 as remainder.

Explanation:
2.1995 ÷ 0.83 = ???
=> 2.1995 ÷ 0.83 = (2.1995 ÷ 0.83) × (100 ÷ 100)
=> 219.95 ÷ 83
=> 2.65.

d.

Dividing $7.70 by 14, we get$0.55 as quotient and 0 as remainder.

Explanation:
$7.70 ÷ 14 = ??? =>$7.70 ÷ 14 = $0.55. Solve each problem. Question 12. One bag of peanuts costs$ 1.52. How many bags can you buy with $34.96? You can buy ____ bags. Answer: Number of bags he can buy = 23. You can buy 23 bags. Explanation: Cost of one bag of peanuts =$ 1.52.
Total amount he has = $34.96. Number of bags he can buy = Total amount he has ÷ Cost of one bag of peanuts =$34.96 ÷ \$1.52
= 23.

Question 13.
A box containing 78.4 pounds of coffee will be divided into containers that hold 0.56 pounds each. How many containers can be filled?
_____ containers can be filled.