Our main aim is to provide a brief explanation of all the questions. We have provided the table of contents of chapter 7 Exponents in the below section. So, once go through the topics before you start your preparation. This will help you to know in which topic you are lagging. Hence make use of the resources provided on this page and try to score good marks in the exams. After your preparation we suggest the students to test your skills by solving the questions in the mid-chapter checkpoint and review test.

Lesson 1: Exponents

Lesson 2: Evaluate Expressions Involving Exponents

Lesson 3: Write Algebraic Expressions

Lesson 4: Identify Parts of Expressions

Lesson 5: Evaluate Algebraic Expressions and Formulas

Mid-Chapter Checkpoint

Lesson 6: Use Algebraic Expressions

Lesson 7: Problem Solving • Combine Like Terms

Lesson 8: Generate Equivalent Expressions

Lesson 9: Identify Equivalent Expressions

Chapter 7 Review/Test

### Share and Show – Page No. 359

Question 1.
Write 24 by using repeated multiplication. Then find the value of 24.
___________

Explanation:
The repeated factor is 2
The number 2 is repeated 4 times.
The repeated multiplication of 24 is 2 × 2 × 2 × 2 = 16
Thus the value of 24 is 16.

Use one or more exponents to write the expression.

Question 2.
7 × 7 × 7 × 7
Type below:
_____________

Explanation:
The repeated factor is 7.
7 is repeated four times.
The exponent of the repeated multiplication 7 × 7 × 7 × 7 is 74

Question 3.
5 × 5 × 5 × 5 × 5
Type below:
_____________

Explanation:
The repeated factor is 5. The number 5 is repeated five times.
The exponent of the repeated multiplication 5 × 5 × 5 × 5 × 5 is 55

Find the value.

Question 5.
202
______

Answer: 20 × 20 = 400

Explanation:
The repeated factor is 20
Write the factor 2 times.
20 × 20 = 400
The value of 202 = 400

Question 6.
821
______

Explanation:
The repeated factor is 82
Write the factor 1 time.
The value of 821 is 82

Complete the statement with the correct exponent.

Question 9.
5? = 125
______

Explanation:
The exponential form of 125 is 5 × 5 × 5 = 53
5? = 125
5? = 53
When bases are equal powers should be equated.
Thus the exponent is 3

Question 10.
16? = 16
______

Explanation:
The exponential form of 16 is 161
16? = 161
When bases are equal powers should be equated.
Thus the exponent is 1.

Question 13.
Select the expressions that are equivalent to 32. Mark all that apply.
Options:
a. 25
b. 84
c. 23 × 4
d. 2 × 4 × 4

Explanation:
The exponent of 32 by using the base 2 is 2 × 2 × 2 × 2 × 2  = 25
32 = 25
Thus the correct answer is option A.

### Bacterial Growth – Page No. 360

Bacteria are tiny, one-celled organisms that live almost everywhere on Earth. Although some bacteria cause disease, other bacteria are helpful to humans, other animals, and plants. For example, bacteria are needed to make yogurt and many types of cheese.

Under ideal conditions, a certain type of bacterium cell grows larger and then splits into 2 “daughter” cells. After 20 minutes, the daughter cells split, resulting in 4 cells. This splitting can happen again and again as long as conditions remain ideal.

Complete the table.

Extend the pattern in the table above to answer 14 and 15.

Question 14.
What power of 2 shows the number of cells after 3 hours? How many cells are there after 3 hours?
Type below:
_____________

Explanation:
So, each cell doubles every 20 mins. After 20 minutes, you have 1(2) = 2 cells. After 40 minutes, you have 2(2) = 4 cells, etc.
1 hour = 60 minutes
3 hours = 3 × 60 minutes = 180 minutes
180/20 = 9 divisions
Thus 29 cells are there after 3 hours.

Question 15.
How many minutes would it take to have a total of 4,096 cells?
_______ minutes

Explanation:
First, convert the cells into the exponential form.
The exponential form of 4096 is 2 × 2 × 2 × 2 × 2 × 2× 2 × 2× 2 × 2× 2 × 2 = 212
Multiply the power with 20
12 × 20 = 240
Thus it would take 240 minutes to have a total of 4,096 cells

### Exponents – Page No. 361

Use one or more exponents to write the expression.

Question 1.
6 × 6
Type below:
_____________

The number 6 is used as a repeated factor.
6 is used as a factor 2 times.
Now write the base and exponent for 6 × 6 = 62

Question 4.
64
_______

The repeated factor is 6.
Write the factor 4 times.
The value of 64 is 6 × 6 × 6 × 6 = 1296

Question 5.
16
_______

The repeated factor is 1.
Write the factor 6 times.
The value of 16 is 1 × 1 × 1 × 1 × 1 × 1 = 1

Question 6.
105
_______

The repeated factor is 10.
Write the factor 5 times.
The value of 105 is 10 × 10 × 10 × 10 × 10 = 1,00,000

Question 7.
Write 144 with an exponent by using 12 as the base.
Type below:
_____________

Answer: 12 × 12 = 122
The exponential form of 144 is 12 × 12 = 122

Question 8.
Write 343 with an exponent by using 7 as the base.
Type below:
_____________

Answer: The exponential form of 343 is 7 × 7 × 7 = 73

Question 11.
Explain what the expression 45 means and how to find its value.
Type below:
_____________

The repeated factor is 4.
Write the factor 5 times.
The value of 45 is 4 × 4 × 4 × 4 × 4 = 1024

### Lesson Check – Page No. 362

Question 1.
The number of games in the first round of a chess tournament is equal to 2 × 2 × 2 × 2 × 2 × 2. Write the number of games using an exponent.
Type below:
_____________

Explanation:

The number 2 is the repeated factor.
2 is repeated 6 times.
2 × 2 × 2 × 2 × 2 × 2 = 26

Spiral Review

Question 3.
The table shows the amounts of strawberry juice and lemonade needed to make different amounts of strawberry lemonade. Name another ratio of strawberry juice to lemonade that is equivalent to the ratios in the table.

Type below:
_____________

Explanation:
By using the above table we can find the ratio of strawberry juice to lemonade.
2 : 6 = 1 : 3
The ratio of strawberry juice to lemonade next to 4 : 12 is 5 : 15

Question 4.
Which percent is equivalent to the fraction $$\frac{37}{50}$$?
_______ %

Explanation:
$$\frac{37}{50}$$ × 100
0.74 × 100 = 74
Thus 74% is equivalent to the fraction $$\frac{37}{50}$$

Question 6.
Use the formula d = rt to find the distance traveled by car driving at an average speed of 50 miles per hour for 4.5 hours.
_______ miles

Explanation:
Given,
r = 50 miles/hour
t = 4.5 hours
Use the formula d = rt
d = 50 × 4.5 = 225 miles
Thus the distance traveled by car driving at an average speed of 50 miles per hour for 4.5 hours is 225 miles.

### Share and Show – Page No. 365

Question 1.
Evaluate the expression 9 + (52 − 10)
_______

Explanation:
First write the square for 52
52 is 25
Now simplify the expression 9 + (25 – 10)
9 + 15 = 24
So, 9 + (52 − 10) = 24

Evaluate the expression.

Question 4.
(8 + 92) − 4 × 10
_______

Explanation:
First multiply 9 × 9 = 81
(8 + 81) – (4 × 10)
Multiply 4 and 10.
4 × 10 = 40
(8 + 81) – (40)
89 – 40 = 49
(8 + 92) − 4 × 10 = 49

Evaluate the expression

Question 5.
10 + 62 × 2 ÷ 9
_______

Explanation:
10 + (62 × 2) ÷ 9
Multiply 6 × 6 = 36
10 + (36 × 2) ÷ 9
Multiply 36 and 2 and then divide by 9.
10 + (72 ÷ 9)
10 + 8 = 18
So, 10 + 62 × 2 ÷ 9 = 18

Question 6.
62 − (23 + 5)
_______

Explanation:

The value of 62 is 6 × 6 = 36
The value of 23 is 2 × 2 × 2 = 8
36 – (8 + 5)
36 – 13 = 23
Thus the answer for the expression for 62 − (23 + 5) is 23.

Question 7.
16 + 18 ÷ 9 + 34
_______

Explanation:
16 + (18 ÷ 9) + 34
First divide 18 by 9
16 + 2 + 34
18 + 34
The value of 34 is 3 × 3 × 3 × 3 = 81
18 + 81 = 99
Thus the answer for the expression 16 + (18 ÷ 9) + 34 is 99.

Place parentheses in the expression so that it equals the given value.

Question 8.
102 − 50 ÷ 5
value: 10
Type below:
_____________

Explanation:
102 − 50 ÷ 5
The factor of 102 is 10 × 10 = 100
(102 − 50) ÷ 5
50 ÷ 5 = 10
102 − 50 ÷ 5 = 10
The value of 102 − 50 ÷ 5 = 10

Question 9.
20 + 2 × 5 + 41
value: 38
Type below:
_____________

Explanation:
20 + 2 × 5 + 41
The value of 41 is 4.
20 + 2 × (5 + 4)
20 + 2 × 9
Now multiply 2 and 9.
20 + 18 = 38
The value of 20 + 2 × 5 + 41 = 38

Question 10.
28 ÷ 22 + 3
value: 4
Type below:
_____________

Explanation:
28 ÷ 22 + 3
28 ÷ (22 + 3)
The value of 22 is 4
28 ÷ (4 + 3)
28 ÷ 7 = 4
The value of 28 ÷ 22 + 3 is 4.

### Problem Solving + Applications – Page No. 366

Use the table for 11–13.

Question 11.
Write an Expression To find the cost of a window, multiply its area in square feet by the price per square foot. Write and evaluate an expression to find the cost of a knot window
$_______ Answer: 108 Explanation: To find the cost of the knot window multiply the area with the price per square foot. Area per square feet is 22 Price per square foot is$27
Cost = 22 × 27 = 4 × 27 = 108
Thus the cost of a knot window is $108 Question 13. DeShawn bought a tulip window. Emma bought a rose window. Write and evaluate an expression to determine how much more DeShawn paid for his window than Emma paid for hers.$ _______

Explanation:
Given that, DeShawn bought a tulip window.
DeShawn bought it for 42 × $33 = 16 ×$33 = 528
Emma bought a rose window
Emma bought it for 32 × 30 = 9 × 30 = 270
$528 –$270 = $258 DeShawn paid$258 for his window and Emma paid for hers.

Question 14.
What’s the Error? Darius wrote 17 − 22 = 225. Explain his error.
Type below:
_____________

Answer: 17 – 4 is actually 13 but not 225.

Question 15.
Ms. Hall wrote the expression 2 × (3 + 5)2÷ 4 on the board. Shyann said the first step is to evaluate 52. Explain Shyann’s mistake. Then evaluate the expression
_______

Explanation:
2 × (3 + 5)2÷ 4
2 × (8)2÷ 4
The square of 8 × 8 is 64.
2 × (64 ÷ 4) = 2 × 16 = 32

### Evaluate Expressions Involving Exponents – Page No. 367

Evaluate the expression.

Question 1.
5 + 17 − 102 ÷ 5
_______

Explanation:
5 + 17 – (100 ÷ 5)
Divide 100 by 5
(5 + 17) – 20
22 – 20 = 2
So, the value for the expression 5 + 17 − 102 ÷ 5 = 2

Question 2.
72 − 32 × 4
_______

Explanation:
72 − 32 × 4
72 − (32 × 4)
72 − (9 × 4)
49 – 36 = 13
Thus, 72 − 32 × 4 = 13

Question 3.
24 ÷ (7 − 5)
_______

Explanation:
24 ÷ (7 − 5)
24 ÷ 2
24 = 2 × 2 × 2 × 2 = 16
16 ÷ 2 = 8
24 ÷ (7 − 5) = 8

Question 6.
(12 − 8)3 − 24 × 2
_______

Explanation:
(12 − 8)3 − 24 × 2 = (4)3 − 24 × 2
64 – (24 × 2)
= 64 – 48 = 16
(12 − 8)3 − 24 × 2 = 16

Place parentheses in the expression so that it equals the given value.

Question 7.
12 × 2 + 23
value: 120
Type below:
_____________

12 × (2 + 23)
12 × (2 + 8)
12 × 10 = 120
12 × 2 + 23 = 120

Question 8.
72 + 1 − 5 × 3
value: 135
Type below:
_____________

(72 + 1 − 5) × 3
(49 + 1 – 5) × 3
(50 – 5) × 3
45 × 3 = 135
72 + 1 − 5 × 3 = 135

Problem Solving

Question 9.
Hugo is saving for a new baseball glove. He saves $10 the first week, and$6 each week for the next 6 weeks. The expression 10 + 62 represents the total amount in dollars he has saved. What is the total amount Hugo has saved?
$_______ Answer:$46

Explanation:
Hugo is saving for a new baseball glove.
He saves $10 the first week, and$6 each week for the next 6 weeks.
The expression 10 + 62 represents the total amount in dollars he has saved.
10 + 62 = 10 + 36 = 46
The total amount Hugo has saved is $46 Question 10. A scientist placed 5 fish eggs in a tank. Each day, twice the number of eggs from the previous day hatch. The expression 5 × 26 represents the number of eggs that hatch on the seventh day. How many eggs hatch on the seventh day? _______ eggs Answer: 320 eggs Explanation: A scientist placed 5 fish eggs in a tank. Each day, twice the number of eggs from the previous day hatch. The expression 5 × 26 represents the number of eggs that hatch on the seventh day. 5 × 26 = 5 × 64 = 320 eggs Therefore 320 eggs hatch on the seventh day. Question 11. Explain how you could determine whether a calculator correctly performs the order of operations. Type below: _____________ Answer: Create a problem that must use the order of operations and isn’t solved by just left to right. Solve it going left to right. Then solve it using the order of operations. Solve it on the calculator. Your answer on the calculator will match the one using the order of operations. ### Lesson Check – Page No. 368 Question 1. Ritchie wants to paint his bedroom ceiling and four walls. The ceiling and each of the walls are 8 feet by 8 feet. A gallon of paint covers 40 square feet. Write an expression that can be used to find the number of gallons of paint Ritchie needs to buy. Type below: _____________ Answer: Ritchie wants to paint his bedroom ceiling and four walls. The ceiling and each of the walls are 8 feet by 8 feet. A gallon of paint covers 40 square feet. 8 × 8 × (4 + 1) ÷ 40 82 (4 + 1) ÷ 40 Thus the expression that can be used to find the number of gallons of paint Ritchie needs to buy is 82 (4 + 1) ÷ 40 Question 2. A Chinese restaurant uses about 225 pairs of chopsticks each day. The manager wants to order a 30-day supply of chopsticks. The chopsticks come in boxes of 750 pairs. How many boxes should the manager order? _______ boxes Answer: 9 boxes Explanation: A Chinese restaurant uses about 225 pairs of chopsticks each day. The manager wants to order a 30-day supply of chopsticks. Multiply the number of pairs with the number of days 225 × 30 = 6750 The chopsticks come in boxes of 750 pairs. Now divide the number of chopsticks by the number of pairs. 6750 ÷ 750 = 9 boxes. Spiral Review Question 3. Annabelle spent$5 to buy 4 raffle tickets. How many tickets can she buy for $20? _______ tickets Answer: 16 tickets Explanation: Annabelle spent$5 to buy 4 raffle tickets.
To find the number of tickets she can buy for $20. ($20 ÷ $5) × 4 4 × 4 = 16 tickets That means she can buy 16 tickets for$20.

Question 5.
How many pounds are equivalent to 40 ounces?
_______ pounds

Explanation:
Convert from ounces to pounds.
1 pound = 16 ounces
1 ounce = 1/16 pound
40 ounces = 40 × 1/16 pound
40 ounces = 2.5 pounds
Thus, 2.5 pounds are equivalent to 40 ounces

Question 6.
List the expressions in order from least to greatest.
15 33 42 81
Type below:
_____________

15 33 42 81
15 = 1 × 1 × 1 × 1 × 1 = 1
33 = 3 × 3 × 3 = 27
42 = 4 × 4 = 16
81 = 8
Thus the order from least to greatest.
15 81 42 33

### Share and Show – Page No. 371

Question 1.
Write an algebraic expression for the product of 6 and p.
What operation does the word “product” indicate?
Type below:
_____________

Explanation:
The word product indicates multiplication.
Multiply 6 with p.
The algebraic expression for the product of 6 and p is 6 × p.

Write an algebraic expression for the word expression.

Question 2.
11 more than e
Type below:
_____________

Explanation:
The word more than indicates addition operation.
So, the algebraic expression is 11 + e

Question 3.
9 less than the quotient of n and 5
Type below:
_____________

Answer: 9 – (n ÷ 5)

Explanation:
The word “less than” indicates subtraction and the “quotient” indicates division.
So, the expression is 9 – (n ÷ 5)

Write an algebraic expression for the word expression.

Question 4.
20 divided by c
Type below:
_____________

Explanation:
Here we have to divide 20 by c.
The expression is 20 ÷ c

Question 5.
8 times the product of 5 and t
Type below:
_____________

Explanation:
The word times indicate multiplication and the product indicates multiplication.
Here we have to multiply 8 with 5 and t.
Thus the expression is 8 × 5 × t = 8 × 5t

Question 7.
A state park charges a $6.00 entry fee plus$7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights.
Type below:
_____________

Answer: $6.00 +$7.50 n

Explanation:
Given that, A state park charges a $6.00 entry fee plus$7.50 per night of camping.
Find the camping for n nights. The product of $7.50 camping for n nights.$7.50 × n
Now add park charges to the camping nights.
$6.00 +$7.50 n
Thus the algebraic expression for the cost in dollars of entering the park and camping for n nights is $6.00 +$7.50 n

Question 8.
Look for Structure At a bookstore, the expression 2c + 8g gives the cost in dollars of c comic books and g graphic novels. Next month, the store’s owner plans to increase the price of each graphic novel by $3. Write an expression that will give the cost of c comic books and g graphic novels next month. Type below: _____________ Answer: 2c + 11g Explanation: Look for Structure At a bookstore, the expression 2c + 8g gives the cost in dollars of c comic books and g graphic novels. Next month, the store’s owner plans to increase the price of each graphic novel by$3.
Here we have to add $3 to 8 g = 3g + 8g = 11g Sum of cost of c comic books and g graphic novels Thus the expression is 2c + 11g ### Unlock the Problem – Page No. 372 Question 9. Martina signs up for the cell phone plan described at the right. Write an expression that gives the total cost of the plan in dollars if Martina uses it for m months. a. What information do you know about the cell phone plan? Type below: _____________ Answer: Pay a low monthly fee of$50. Receive $10 off your first month’s fee. Question 9. b. Write an expression for the monthly fee in dollars for m months. Type below: _____________ Answer: M is the number of months. 50 × m Given that$10 off on first-month fee.
50m + (50-10)
50m + $40 Question 9. c. What operation can you use to show the discount of$10 for the first month?
Type below:
_____________

Answer: We have to use subtraction operations to show a discount of $10 for the first month. Question 9. d. Write an expression for the total cost of the plan in dollars for m months Type below: _____________ Answer: 50m + 40 Question 10. A group of n friends evenly share the cost of dinner. The dinner costs$74. After dinner, each friend pays $11 for a movie. Write an expression to represent what each friend paid for dinner and the movie. Type below: _____________ Answer: 74 ÷ n + 11n Explanation: Given, A group of n friends evenly share the cost of dinner. The dinner costs$74. After dinner, each friend pays $11 for a movie. The word share represents the division operation. That means we have to divide 74 by n. 74 ÷ n After that n friends paid$11 for the movie
Multiply 11 with n.
Thus the expression to represent what each friend paid for dinner and the movie is 74 ÷ n + 11n

Question 11.
A cell phone company charges $40 per month plus$0.05 for each text message sent. Select the expressions that represent the cost in dollars for one month of cell phone usage and sending m text messages. Mark all that apply.
Options:
a. 40m + 0.05
b. 40 + 0.05m
c. 40 more than the product of 0.05 and m
d. the product of 40 and m plus 0.05

Explanation:
A cell phone company charges $40 per month plus$0.05 for each text message sent.
Let m represent the messages sent.
40m + 0.05m
Thus the answer is option B.

### Write Algebraic Expressions – Page No. 373

Write an algebraic expression for the word expression.

Question 1.
13 less than p
Type below:
_____________

Explanation:
Less than is nothing but subtraction.
So the expression for 13 less than p is 13 – p

Question 3.
6 more than the difference between b and 5
Type below:
_____________

Answer: 6 + (b – 5)

Explanation:
More than is nothing but addition and difference mean subtraction.
The expression for 6 more than the difference of b and 5 is 6 + (b – 5)

Question 4.
the sum of 15 and the product of 5 and v
Type below:
_____________

Explanation:
Product is nothing but multiplication and sum is nothing but an addition.
So, the expression for the sum of 15 and the product of 5 and v is 15 + 5 × v

Question 5.
the difference of 2 and the product of 3 and k
Type below:
_____________

Explanation:
The difference means subtraction and Product are nothing but the multiplication
So, the difference between 2 and the product of 3 and k is 2 – 3 × k
2 – 3k

Question 7.
the quotient of m and 7
Type below:
_____________

Explanation:
Given the quotient of m and 7
That means we have to divide m by 7.
Thus the answer is m ÷ 7

Question 8.
9 more than 2 multiplied by f
Type below:
_____________

Explanation:
9 more than 2 multiplied by f
We have to add 9 to 2 × f
So, the expression is 9 + 2f

Question 9.
6 minus the difference between x and 3
Type below:
_____________

Answer: 6 – (x – 3)

Explanation:
First, subtract 3 from x
The expression for 6 minus the difference of x and 3 is 6 – (x – 3)

Question 10.
10 less than the quotient of g and 3
Type below:
_____________

Answer: 10 – (g ÷ 3)

Explanation:
The quotient of g and 3 is nothing but dividing g by 3
g ÷ 3
Now subtract g ÷ 3 from 10.
So, the expression for 10 less than the quotient of g and 3 is 10 – (g ÷ 3)

Question 11.
the sum of 4 multiplied by a and 5 multiplied by b
Type below:
_____________

Explanation:
First, multiply 4 with a and then multiply 5 with b
4a + 5b
So, the sum of 4 multiplied by a and 5 multiplied by b is 4a + 5b

Question 12.
14 more than the difference between r and s
Type below:
_____________

Answer: 14 + (r – s)

Explanation:
Subtract r and s
And then add 14 to that r -s
14 + (r – s)

Problem Solving

Question 13.
Let h represent Mark’s height in inches. Suzanne is 7 inches shorter than Mark. Write an algebraic expression that represents Suzanne’s height in inches.
Type below:
_____________

Explanation:
Let h represent Mark’s height in inches. Suzanne is 7 inches shorter than Mark.
That means we have to subtract 7 from h.
i.e., h – 7
Thus Suzanne’s height is h – 7 inches.

Question 14.
A company rents bicycles for a fee of $10 plus$4 per hour of use. Write an algebraic expression for the total cost in dollars for renting a bicycle for h hours.
Type below:
_____________

Explanation:
A company rents bicycles for a fee of $10 plus$4 per hour of use.
Multiply 4 with hours
And then 10 to 4h
10 + 4h
Thus the total cost in dollars for renting a bicycle for h hours is 10 + 4h

Question 15.
Give an example of a real-world situation involving two unknown quantities. Then write an algebraic expression to represent the situation.
Type below:
_____________

Cooper bikes so many miles per day and does it for 7 months.
The expression for the question is 6m × 7

### Lesson Check – Page No. 374

Question 1.
The female lion at a zoo weighs 190 pounds more than the female cheetah. Let c represent the weight in pounds of the cheetah. Write an expression that gives the weight in pounds of the lion.
Type below:
_____________

Explanation:
Given that, The female lion at a zoo weighs 190 pounds more than the female cheetah.
Let c represent the weight in pounds of the cheetah.
We have to add 190 to the weight in pounds of the cheetah.
That means c + 190
Thus the expression that gives the weight in pounds of the lion is c + 190.

Question 2.
Tickets to a play cost $8 each. Write an expression that gives the ticket cost in dollars for a group of g girls and b-boys. Type below: _____________ Answer: 8 × (g + b) Explanation: First add girls group and boys group. g + b And then multiply 8 with the group of girls and boys. 8 × (g + b) So, the expression that gives the ticket cost in dollars for a group of g girls and b-boys is 8 × (g + b). Spiral Review Question 4. There are 32 peanuts in a bag. Elliott takes 25% of the peanuts from the bag. Then Zaire takes 50% of the remaining peanuts. How many peanuts are left in the bag? _______ peanuts Answer: 12 Explanation: First, we have to find 25% of 32. 25% of 32 its 0.25 × 32=8 Now we have to subtract 32 and 8 32 – 8=24 Now we have to find 50% of 24 50% of 24 = 12 24-12=12. Thus 12 peanuts are left in the bag. Question 6. Write an expression using exponents that represent the area of the figure in square centimeters Type below: _____________ Answer: 72 – 22 Explanation: The area of the square is 7 cm × 7 cm = 72 The area of the square is 2 cm × 2 cm = 22 Now subtract a small square from the large square. The expression that represents the area of the figure is 72 – 22 ### Share and Show – Page No. 377 Identify the parts of the expression. Then, write a word expression for the numerical or algebraic expression. Question 1. 7 × (9 ÷ 3) Type below: _____________ Answer: The quotient of 9 and 3 and then multiply by 7. Word expression: Product of 7 with the quotient of 9 and 3. On Your Own Practice: Copy and Solve Identify the parts of the expression. Then write a word expression for the numerical or algebraic expression. Question 3. 8 + (10 − 7) Type below: _____________ Answer: Subtraction is the difference between 10 and 7. Addition to the subtraction of 10 and 7. Word expression: Add 8 to the difference between 10 and 7. Question 4. 1.5 × 6 + 8.3 Type below: _____________ Answer: The addition is the sum of 6 and 8.3 and then multiply the sum to 1.5. Word expression: 1.5 times the sum of 6 and 8.3 Question 5. b + 12x Type below: _____________ Answer: Product of 12 and x. Add b to the product of 12 and x. Word expression: Sum of b to the product of 12 and x. Question 6. 4a ÷ 6 Type below: _____________ Answer: The division is the quotient of 4a and 6. Multiply 4 and a. The expression is the product of 4 and divided by 6. Word expression: The quotient of the products 4 and a and 6. Identify the terms of the expression. Then, give the coefficient of each term. Question 7. k − $$\frac{1}{3}$$d Type below: _____________ Answer: The terms of the expression are k and $$\frac{1}{3}$$d Coefficients – 1 and $$\frac{1}{3}$$ Question 8. 0.5x + 2.5y Type below: _____________ Answer: The terms of the expression are 0.5x and 2.5y Coefficients – 0.5 and 2.5 Question 9. Connect Symbols and Words Ava said she wrote an expression with three terms. She said the first term has a coefficient 7, the second term has a coefficient 1, and the third term has a coefficient 0.1. Each term involves a different variable. Write an expression that could be the expression Ava wrote Type below: _____________ Answer: Connect Symbols and Words Ava said she wrote an expression with three terms. She said the first term has the coefficient 7, the second term has a coefficient 1, and the third term has a coefficient 0.1. The expression for the first term is 7x The expression for the second term is 1y The expression for the third term is 0.1z 7x + y + 0.1z ### Problem Solving + Applications – Page No. 378 Use the table for 10–12. Question 10. A football team scored 2 touchdowns and 2 extra points. Their opponent scored 1 touchdown and 2 field goals. Write a numerical expression for the points scored in the game. Type below: _____________ Answer: A football team scored 2 touchdowns and 2 extra points. 2 touchdowns = 2 × 6 2 extra points = 2 × 1 Their opponent scored 1 touchdown and 2 field goals. 1 touchdown = 1 × 6 2 field goals = 2 × 3 Thue the numerical expression is 12 + 2 + 6 + 6 14 + 12 The numerical expression for the points scored in the game is 14 + 12. Question 11. Write an algebraic expression for the number of points scored by a football team that makes t touchdowns, f field goals, and e extra points Type below: _____________ Answer: 6t + 3f + e Explanation: The number of points scored by a football team that makes t touchdowns, f field goals, and e extra points. The table shows that touchdown has 6 points, field goal has 3 points and extra point has 1 point. So we need to add all the points to make the expressions That means 6t + 3f + e Question 12. Identify the parts of the expression you wrote in Exercise 11. Type below: _____________ Question 13. Give an example of an expression involving multiplication in which one of the factors is a sum. Explain why you do or do not need parentheses in your expression Type below: _____________ Answer: 6 × 2 + 3 In this expression, there is no need for parentheses because there are no exponents or multiple operations. Question 14. Kennedy bought a pounds of almonds at$5 per pound and p pounds of peanuts at $2 per pound. Write an algebraic expression for the cost of Kennedy’s purchase. Type below: _____________ Answer: 5 + 2p = x Explanation: Kennedy bought a pounds of almonds at$5 per pound and p pounds of peanuts at $2 per pound. We have to multiply p with$2 per pound.
The algebraic expression for the cost of Kennedy’s purchase is the sum of 5 and the product of p and 2
Thus the expression is 5 + 2p = x

### Identify Parts of Expressions – Page No. 379

Identify the parts of the expression. Then write a word expression for the numerical or algebraic expression.

Question 1.
(16 − 7) ÷ 3
Type below:
_____________

Subtraction is the difference between 16 and 7. The division is the quotient of the difference and 3
Word expression: the quotient of the difference 16 and 7 and 3.

Identify the terms of the expression. Then give the coefficient of each term.

Question 3.
11r + 7s
Type below:
_____________

The terms of the expression are 11r and 7s
The coefficient of each term is 11 and 7.

Question 4.
6g − h
Type below:
_____________

The terms of the expression are 6g and h
The coefficient of each term is 6 and 1.

Problem Solving

Question 5.
Adam bought granola bars at the store. The expression 6p + 5n gives the number of bars in p boxes of plain granola bars and n boxes of granola bars with nuts. What are the terms of the expression?
Type below:
_____________

Adam bought granola bars at the store.
The expression 6p + 5n gives the number of bars in p boxes of plain granola bars and n boxes of granola bars with nuts.
The terms of the expression are 6p and 5n.

Question 6.
In the sixth grade, each student will get 4 new books. There is one class of 15 students and one class of 20 students. The expression 4 × (15 + 20) gives the total number of new books. Write a word expression for the numerical expression.
Type below:
_____________

In the sixth grade, each student will get 4 new books.
There is one class of 15 students and one class of 20 students.
The expression 4 × (15 + 20) gives the total number of new books.
The product of 4 the sum of 15 and 20.

Question 7.
Explain how knowing the order of operations helps you write a word expression for a numerical or algebraic expression.
Type below:
_____________

Answer: Because if you don’t know and use the order of operations you can get an entirely different answer.

### Lesson Check – Page No. 380

Question 1.
A fabric store sells pieces of material for $5 each. Ali bought 2 white pieces and 8 blue pieces. She also bought a pack of buttons for$3. The expression 5 × (2 + 8) + 3 gives the cost in dollars of Ali’s purchase. How can you describe the term (2 + 8) in words?
Type below:
_____________

Answer: the sum of 2 and 8

Explanation:
A fabric store sells pieces of material for $5 each. Ali bought 2 white pieces and 8 blue pieces. She also bought a pack of buttons for$3.
The expression 5 × (2 + 8) + 3 gives the cost in dollars of Ali’s purchase.
The word expression for the term 2 + 8 is the sum of 2 and 8.

Question 2.
A hotel offers two different types of rooms. The expression k + 2f gives the number of beds in the hotel where k is the number of rooms with a king-size bed and f is the number of rooms with 2 full-size beds. What are the terms of the expression?
Type below:
_____________

Explanation:
The terms for the expression k + 2f is k and 2f.

Spiral Review

Question 3.
Meg paid $9 for 2 tuna sandwiches. At the same rate, how much does Meg pay for 8 tuna sandwiches?$ _______

Explanation:
Meg paid $9 for 2 tuna sandwiches. To find how much does Meg pay for 8 tuna sandwiches 2 –$9
8 -?
$9 × 8/2 = 72/2 = 36 Thus Meg pays$36 for 8 tuna sandwiches.

Question 5.
It took Eduardo 8 hours to drive from Buffalo, NY, to New York City, a distance of about 400 miles. Find his average speed.
_______ miles per hour

Explanation:
Given,
It took Eduardo 8 hours to drive from Buffalo, NY, to New York City, a distance of about 400 miles.
We can use the formula d = rt
r = d/t
r = 400 miles/8 hours
r = 50 miles per hour

Question 6.
Write an expression that represents the value, in cents, of n nickels.
Type below:
_____________

Explanation:
An expression does not have an equal sign.
Since the value of a nickel is 5 cents and you want to find out the value of n nickels (which means if you had any number of nickels) the expression would be
.05n

### Share and Show – Page No. 383

Question 1.
Evaluate 5k + 6 for k = 4.
_______

Explanation:
The expression is 5k + 6
Substitute the value k = 4
5(4) + 6 = 20 + 6 = 26
5k + 6 = 26

Evaluate the expression for the given value of the variable.

Question 2.
m − 9 for m = 13
_______

Explanation:
m – 9
Substitute the value of m in the expression
13 – 9 = 4
Thus m – 9 = 4

Question 5.
The formula A = lw gives the area A of a rectangle with length l and width w. What is the area in square feet of a United States flag with a length of 12 feet and a width of 8 feet?
_______ square feet

Explanation:
Use the formula A = lw
Length = 12 feet
Width = 8 feet
A = lw
A = 12 feet × 8 feet = 96 square feet
Thus the area of the United States flag is 96 square feet.

Practice: Copy and Solve Evaluate the expression for the given value of the variable.

Question 6.
7s + 5 for s = 3
_______

Explanation:
Given the expression 7s + 5
Substitute  the value of S in the above expression
7(3) + 5 = 21 + 5 = 26

Question 7.
21 − 4d for d = 5
_______

Explanation:
Given the expression 21 – 4d
Substitute  the value d = 5 in the above expression
21 – 4(5) = 21 – 20 = 1

Question 9.
6 × (2v − 3) for v = 5
_______

Explanation:
Given the expression 6 × (2v – 3)
Substitute the value of v in the above expression.
6 × (2v – 3) = 6 × (2 × 5 – 3)
6 × (10 – 3)
6 × 7 = 42
Thus the value of 6 × (2v – 3) = 42

Question 12.
The formula P = 4s gives the perimeter P of a square with side length s. How much greater is the perimeter of a square with a side length of 5 $$\frac{1}{2}$$ inches than a square with a side length of 5 inches?
_______ inches

Explanation:
We have to use the formula P = 4s to find the perimeter of the square.
4 × 5 $$\frac{1}{2}$$
Convert the mixed fraction to the improper fraction.
4 × 11/2 = 2 × 11 = 22 inches
4 × 5 inches = 20 inches
To find which has the greater  perimeter  we have to subtract 20 inches from 22 inches
22 inches – 20 inches = 2 inches
Thus the perimeter of a square with 5 $$\frac{1}{2}$$ inches is 2 inches greater than a square with a side length of 5 inches.

### Problem Solving + Applications – Page No. 384

The table shows how much a company charges for skateboard wheels. Each pack of 8 wheels costs $50. Shipping costs$7 for any order. Use the table for 13−15.

Question 13.
Complete the table.
Type below:
_____________

Question 14.
A skateboard club has $200 to spend on new wheels this year. What is the greatest number of packs of wheels the club can order? _______ packs Answer: 3 packs Explanation: A skateboard club has$200 to spend on new wheels this year.
From the above table, we can say that the club can order 3 packs of wheels.

Question 15.
Make Sense of Problems A sporting goods store placed an order for 12 packs of wheels on the first day of each month last year. How much did the sporting goods store spend on these orders last year?
$_______ Answer: 7284 Explanation: Make Sense of Problems A sporting goods store placed an order for 12 packs of wheels on the first day of each month last year. Substitute n = 7 in the expression 50 × n + 7 We get, 50 × 12 + 7 600 + 7 = 607 Now multiply 607 with 12 607 × 12 = 7284 Therefore the sporting goods store spent$7284 on these orders last year.

Question 16.
What’s the Error? Bob used these steps to evaluate 3m − 3 ÷ 3 for m = 8. Explain his error.
3 × 8 − 3 ÷ 3 = 24 − 3 ÷ 3
= 21 ÷ 3
= 7
Type below:
_____________

First, he has to subtract 8 and 3. But he first multiplied and then subtracted 24 and 3.
3 × 8 − 3 ÷ 3 = 3 × (8 − 3) ÷ 3
3 × 5 ÷ 3
15 ÷ 3 = 5

Question 17.
The surface area of a cube can be found by using the formula 6s2, where s represents the length of the side of the cube.
The surface area of a cube that has a side length of 3 meters is _____ meters squared.
The surface area of a cube that has a side length                       meters
of 3 meters is _____________ squared

Explanation:
The surface area of a cube can be found by using the formula 6s2
he surface area of a cube that has a side length of 3 meters
s2 = 32 = 9
6 × 9 = 54 square meters

### Evaluate Algebraic Expressions and Formulas – Page No. 385

Evaluate the expression for the given values of the variables.

Question 1.
w + 6 for w = 11
_______

Explanation:
Given the expression w + 6
Substitute the value w = 6 in the expression
w + 6 = 11 + 6 = 17

Question 3.
b2 − 4 for b = 5
_______

Explanation:
Substitute the value b = 5 in the expression
b2 − 4 = 52 − 4 = 25 – 4 = 21
Thus the value for the expression b2 − 4 is 21.

Question 4.
(h − 3)2 for h = 5
_______

Explanation:
We have to substitute the value h = 5
(h − 3)2 = (5 − 3)2
= (2)2 = 4
Therefore the value of (h − 3)2 is 4.

Question 6.
4 × (21 − 3h) for h = 5
_______

Explanation:
Substitute h = 5 in the given expression.
4 × (21 – 3h) = 4 × (21 – 3(5))
4 × (21 – 15) = 4 × 6 = 24
Therefore the value for 4 × (21 – 3h) is 24.

Question 7.
7m − 9n for m = 7 and n = 5
_______

Explanation:
Substitute the values m = 7 and n = 5 in the above expression.
7m – 9n = 7 × 7 – 9 × 5
= 49 – 45 = 4
Thus 7m – 9n = 4.

Question 8.
d2 − 9k + 3 for d = 10 and k = 9
_______

Explanation:
Given the expression d2 − 9k + 3
Now substitute d = 10 and k = 9 in the expression.
d2 − 9k + 3 = 102 − 9(9) + 3
100 – 81 + 3 = 22
Thus the value for the expression d2 − 9k + 3 is 22.

Question 9.
3x + 4y ÷ 2 for x = 7 and y = 10
_______

Explanation:
Substitute the values x = 7 and y = 10 in the expression.
3x + 4y ÷ 2 = 3(7) + 4(10) ÷ 2
21 + 40 ÷ 2 = 21 + 20 = 41
Thus the value for 3x + 4y ÷ 2 is 41.

Problem Solving

Question 10.
The formula P = 2l + 2w gives the perimeter P of a rectangular room with length l and width w. A rectangular living room is 26 feet long and 21 feet wide. What is the perimeter of the room?
_______ feet

Explanation:
Use the formula  of the perimeter  of a rectangle P = 2l + 2w
L = 26 feet
W = 21 feet
P = 2(26) + 2(21)
P = 52 feet + 42 feet
P = 94 feet
Therefore the perimeter of a room is 94 feet.

Question 12.
Explain how the terms variable, algebraic expression, and evaluate are related.
Type below:
_____________

Answer: To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. If we know the variables, we can replace the variables with their values and then evaluate the expression.

### Lesson Check – Page No. 386

Question 1.
When Debbie babysits, she charges $5 to go to the house plus$8 for every hour she is there. The expression 5 + 8h gives the amount in dollars she charges. How much will she charge to baby-sit for 5 hours?
$_______ Answer: 45 Explanation: When Debbie baby-sits, she charges$5 to go to the house plus $8 for every hour she is there. The expression 5 + 8h gives the amount in dollars she charges. If h = 5 hours Substitute the value h in the above expression. 5 + 8h = 5 + 8(5) = 5 + 40 = 45 Thus she charges$45 to baby-sit for 5 hours.

Question 2.
The formula to find the cost C in dollars of a square sheet of glass is C = 25s2 where s represents the length of a side in feet. How much will Ricardo pay for a square sheet of glass that is 3 feet on each side?
$_______ Answer:$225

Explanation:
Use the formula C = 25s2
s represents the length of a side in feet.
s = 3 feet
Substitute the value s in the above formula.
C = 25s2
C = 25(32)
C = 25(9) = 225
Ricardo pays $225 for a square sheet of glass that is 3 feet on each side. Spiral Review Question 3. Evaluate using the order of operations. $$\frac{3}{4}+\frac{5}{6} \div \frac{2}{3}$$ _______ Answer: 2 Explanation: $$\frac{3}{4}$$ + [/latex]\frac{5}{6}[/latex] ÷ [/latex]\frac{2}{3}[/latex] [/latex]\frac{5}{6}[/latex] ÷ [/latex]\frac{2}{3}[/latex] = [/latex]\frac{5}{6}[/latex] × [/latex]\frac{3}{2}[/latex] = [/latex]\frac{15}{12}[/latex] = [/latex]\frac{5}{4}[/latex] Now convert the improper fraction to the mixed fraction. [/latex]\frac{5}{4}[/latex] = 1 [/latex]\frac{1}{4}[/latex] 1 [/latex]\frac{1}{4}[/latex] + $$\frac{3}{4}$$ 1 + [/latex]\frac{1}{4}[/latex] + $$\frac{3}{4}$$ = 1 + 1 = 2 $$\frac{3}{4}+\frac{5}{6} \div \frac{2}{3}$$ = 2 Question 4. Patricia scored 80% on a math test. She missed 4 problems. How many problems were on the test? _______ problems Answer: 20 Explanation: Patricia scored 80% on a math test. She missed 4 problems. 4 ÷ 80% 4 × [/latex]\frac{100}{80}[/latex] = 4 × 5 = 20 Therefore there are 20 questions in the test. Question 5. What is the value of 73? _______ Answer: 343 Explanation: 73 = 7 × 7 × 7 = 49 × 7 = 343 Thus the value of 73 is 343. Question 6. James and his friends ordered b hamburgers that cost$4 each and f fruit cups that cost $3 each. Write an algebraic expression for the total cost in dollars of their purchases. Type below: _____________ Answer: 4b + 3f Explanation: Given that, James and his friends ordered b hamburgers that cost$4 each and f fruit cups that cost $3 each. Multiply b with$4 and multiply $3 with f Add 4b and 3f Thus the expression is 4b + 3f. ### Vocabulary – Page No. 387 Choose the best term from the box to complete the sentence. Question 1. A(n) _____ tells how many times a base is used as a factor. Type below: _____________ Answer: Exponent An Exponent tells how many times a base is used as a factor. Question 2. The mathematical phrase 5+2×18 is an example of a(n) _____. Type below: _____________ Answer: Numerical expression The mathematical phrase 5+2×18 is an example of a Numerical expression. Concepts and Skills Find the value. Question 3. 54 ________ Answer: 5 × 5 × 5 × 5 = 625 Explanation: The number 5 is the repeated factor. 5 is used 4 times. Multiply 5 four times. 5 × 5 × 5 × 5 = 625 Question 4. 212 ________ Answer: 21 × 21 = 441 Explanation: The number 21 is the repeated factor. 21 is used 2 times. Multiply 21 two times. 21 × 21 = 441 Question 5. 83 ________ Answer: 8 × 8 × 8 = 512 Explanation: The number 8 is the repeated factor. 8 is used 3 times. 8 × 8 × 8 = 512 Evaluate the expression. Question 8. 30 − (33 − 8) ________ Answer: 11 Explanation: 33 = 3 × 3 × 3 = 27 30 − (33 − 8) = 30 – (27 – 8) = 30 – 19 = 11 30 − (33 − 8) = 11 So, 30 − (33 − 8) is 11. Write an algebraic expression for the word expression. Question 9. the quotient of c and 8 Type below: _____________ Answer: c ÷ 8 The quotient is nothing but the division of c by 8. So, the expression is c ÷ 8. Question 10. 16 more than the product of 5 and p Type below: _____________ Answer: 16 + 5p Explanation: The operation for more than is addition. Here we have to add 16 to the product of 5 and p. The product is the operation for multiplication. Multiply 5 and p and then add 16 to it. The expression of the word is 16 + 5p. Evaluate the expression for the given value of the variable. Question 12. 5 × (h + 3) for h = 7 ________ Answer: 50 Explanation: Given expression is 5 × (h + 3) Substitute h = 7 in the above expression. 5 × (h + 3) = 5 × (7 + 3) 5 × 10 = 50 5 × (h + 3) = 50 Question 13. 2 × (c2 − 5) for c = 4 ________ Answer: 22 Explanation: Given 2 × (c2 − 5) Substitute c = 4 in the expression 2 × (c2 − 5) = 2 × (42 − 5) = 2 × (16 – 5) = 2 × 11 = 22 2 × (c2 − 5) = 22 Question 14. 7a − 4a for a = 8 ________ Answer: 24 Explanation: Given, 7a − 4a Subtract the like terms 7a − 4a = 3a Now substitute the value a = 8 in the above expression 3a = 3 × 8 = 24 7a − 4a = 24 ### Page No. 388 Question 16. A clothing store is raising the price of all its sweaters by$3.00. Write an expression that could be used to find the new price of a sweater that originally cost d dollars.
Type below:
_____________

Explanation:
A clothing store is raising the price of all its sweaters by $3.00. The cost of the sweater is d dollars. The store is going to add$3.
So, the new price of a sweater is the sum of d dollars and $3. The expression is d + 3. Question 17. Kendra bought a magazine for$3 and 4 paperback books for $5 each. The expression 3 + 4 × 5 represents the total cost in dollars of her purchases. What are the terms in this expression? Type below: _____________ Answer: 3 and 4 × 5 Explanation: Kendra bought a magazine for$3 and 4 paperback books for $5 each. The expression 3 + 4 × 5 represents the total cost in dollars of her purchases. The terms in the expression are 3, 4, and 5. Question 18. The expression 5c + 7m gives the number of people who can ride in c cars and m minivans. What are the coefficients in this expression? Type below: _____________ Answer: The coefficients in the expression 5c + 7m are 5 and 7. Question 19. The formula P = a + b + c gives the perimeter P of a triangle with side lengths a, b, and c. How much greater is the perimeter of a triangular field with sides that measure 33 yards, 56 yards, and 65 yards than the perimeter of a triangular field with sides that measure 26 yards, 49 yards, and 38 yards? ________ yards Answer: 41 yards Explanation: First, we have to calculate the perimeter of the 1st triangle. Given: a = 33 yards b = 56 yards c = 65 yards P1 = a + b + c P1 = 33 + 56 + 65 = 154 yards Now we have to calculate the perimeter of 2nd triangle. Given: a = 26 yards b = 49 yards c = 38 yards P2 = a + b + c P2 = 26 + 49 + 38 = 113 yards Now we have to calculate which triangle has greater perimeter and how much greater. P1 – P2 = 154 yards – 113 yards = 41 yards Therefore, 41 yards greater is the perimeter of the 1st triangular field than the perimeter of the 2nd triangular field. ### Share and Show – Page No. 391 Louisa read that the highest elevation of Mount Everest is 8,848 meters. She wants to know how much higher Mount Everest is than Mount Rainier. Use this information for 1–2. Question 1. Write an expression to represent the difference in the heights of the two mountains. Tell what the variable in your expression represents. Type below: _____________ Answer: 8848 – h, where h represents the height of the Mount Rainier Explanation: Given that, the height of Mount Everest is 8848 meters Let the height of Mount Rainier is h The difference in height of Mount Everest and height of Mount Rainier is 8848 – h. Question 2. Louisa researches the highest elevation of Mount Rainier and finds that it is 4,392 meters. Use your expression to find the difference in the mountains’ heights. ________ meters Answer: 4456 meters Explanation: The height of the Mount Rainier = 4392 meters Replace the value of the height of the Mount Rainier in the above expression. 8848 – h = 8848 meters – 4392 meters = 4456 meters Thus the difference between the height of the two mountains is 4456 meters. On Your Own A muffin recipe calls for 3 times as much flour as sugar. Use this information for 3–5. Question 3. Write an expression that can be used to find the amount of flour needed for a given amount of sugar. Tell what the variable in your expression represents. Type below: _____________ Answer: Let the amount of sugar used to represent the variable s. The expression to find the amount of flour needed for a given amount of sugar is 3 × m i.e., 3m Question 5. Reason Quantitatively Is the value of the variable in your expression restricted to a particular set of numbers? Explain. Type below: _____________ Answer: The values that make the denominator equal to zero for a rational expression are known as restricted values. The solutions are restricted values since they result in a denominator of zero when replaced for the variable(s). Practice: Copy and Solve Write an algebraic expression for each word expression. Then evaluate the expression for these values of the variable: $$\frac{1}{2}$$, 4, and 6.5. Question 6. the quotient of p and 4 Type below: _____________ Answer: p ÷ 4 Explanation: The expression is p ÷ 4 p = $$\frac{1}{2}$$ $$\frac{1}{2}$$ ÷ 4 $$\frac{1}{2}$$/4 = $$\frac{1}{8}$$ p ÷ 4 when p = $$\frac{1}{2}$$ is $$\frac{1}{8}$$ p = 4 4 ÷ 4 = 1 p = 6.5 6.5 ÷ 4 = 1.625 ### Problem Solving + Applications – Page No. 392 Use the graph for 8–10. Question 8. Write expressions for the distance in feet that each animal could run at top speed in a given amount of time. Tell what the variable in your expressions represents. Type below: _____________ Answer: The expression for distance in feet for Elephant = 22t The expression for distance in feet for Cheetah = 103t The expression for distance in feet for Giraffe = 51t The expression for distance in feet for hippopotamus = 21t Where t represents the time. Question 9. How much farther could a cheetah run in 20 seconds at top speed than a hippopotamus could? ______ feet Answer: 1640 feet Explanation: The expression for distance in feet for Cheetah = 103t where t = 20 sec 103t = 103 × 20 sec = 2060 feet The expression for distance in feet for hippopotamus = 21t where t = 20 sec 21t = 21 × 20 = 420 feet Now we have to find How much farther could a cheetah run in 20 seconds at top speed than a hippopotamus could 2060 feet – 420 feet = 1640 feet Question 10. A giraffe runs at top speed toward a tree that is 400 feet away. Write an expression that represents the giraffe’s distance in feet from the tree after s seconds. Type below: _____________ Answer: The expression representing the giraffe’s distance from tree after s seconds, if the rate is 51 ft per second. 7 43/60 seconds in all Question 11. A carnival charges$7 for admission and $2 for each ride. An expression for the total cost of going to the carnival and riding n rides is 7 + 2n. Complete the table by finding the total cost of going to the carnival and riding n rides. Type below: _____________ Answer: ### Use Algebraic Expressions – Page No. 393 Jeff sold the pumpkins he grew for$7 each at the farmer’s market.

Question 1.
Write an expression to represent the amount of money in dollars Jeff made selling the pumpkins. Tell what the variable in your expression represents
Type below:
_____________

Answer: 7p, where p is the number of pumpkins

Question 2.
If Jeff sold 30 pumpkins, how much money did he make?
$________ Answer: 210 Explanation: The expression is 7p p = 30 pumpkins 7 × 30 = 210 Thus Jeff sold 30 pumpkins for$210.

An architect is designing a building. Each floor will be 12 feet tall.

Question 3.
Write an expression for the number of floors the building can have for a given building height. Tell what the variable in your expression represents.
Type below:
_____________

Answer: The expression for the number of floors is h/12, where h is the height of the building.

Question 4.
If the architect is designing a building that is 132 feet tall, how many floors can be built?
________ floors

Explanation:
Given the height of the building is 132 feet
Substitute h in the above expression
h/12 = 132/12 = 11 floors
Thus 11 floors can be built.

Write an algebraic expression for each word expression. Then evaluate the expression for these values of the variable: 1, 6, 13.5.

Question 6.
13 more than the product of m and 5
Type below:
_____________

Explanation:
For m = 1
13 + 5m = 13 + 5(1) = 13 + 6 = 19
For m = 6
13 + 5m = 13 + 5(6) = 13 + 30 = 43
For m = 13.5
13 + 5m = 13 + 5(13.5) = 13 + 67.5 = 80.5

Problem Solving

Question 7.
In the town of Pleasant Hill, there is an average of 16 sunny days each month. Write an expression to represent the approximate number of sunny days for any number of months. Tell what the variable represents.
Type below:
_____________

Explanation:
In the town of Pleasant Hill, there is an average of 16 sunny days each month. Write an expression to represent the approximate number of sunny days for any number of months.
we have to multiply the number of months with 16
The expression will be 16 times m = 16m

Question 8.
How many sunny days can a resident of Pleasant Hill expect to have in 9 months?
________ days

Explanation:
The expression to represent the approximate number of sunny days for any number of months is 16m
m = 9
Substitute the value of m in the expression.
16m = 16 × 9 = 144 days

Question 9.
Describe a situation in which a variable could be used to represent any whole number greater than 0.
Type below:
_____________

Answer: To represent the number of people any answer can be accepted.

### Lesson Check – Page No. 394

Question 1.
Oliver drives 45 miles per hour. Write an expression that represents the distance in miles he will travel for h hours driven.
Type below:
_____________

Explanation:
It is given that Oliver drives 45 miles per hour. Let the number of hours he drove be h. Distance is the product of speed and time. The distance traveled by Oliver is defined by the expression as 45h.

Question 2.
Socks cost $5 per pair. The expression 5p represents the cost in dollars of p pairs of socks. Why must p be a whole number? Type below: _____________ Answer: p must be a whole number because in almost 100% of all stores it is not allowed to buy a single sock, you must always buy a pair of socks. Spiral Review Question 3. Sterling silver consists of 92.5% silver and 7.5% copper. What decimal represents the portion of the silver in sterling silver? ________ Answer: 0.925 Explanation: If Sterling silver is 92.5% silver, that means it has 92.5/100 * 100% silver The fraction 92.5/100 can be simplified by just moving the decimal 2 places to the left: 92.5/100 = .925 Question 4. How many pints are equivalent to 3 gallons? ________ pints Answer: 24 Explanation: Convert from gallons to pints. 1 gallon = 8 pints 3 gallons = 3 × 8 pints = 24 pints 24 pints are equivalent to 3 gallons. Question 5. Which operation should be done first to evaluate 10 + (66 – 62)? Type below: _____________ Answer: Square 6 ### Share and Show – Page No. 397 Question 1. Museum admission costs$7, and tickets to the mammoth exhibit cost $5. The expression 7p + 5p represents the cost in dollars for p people to visit the museum and attend the exhibit. Simplify the expression by combining like terms. Type below: _____________ Answer: 12p Explanation: 7p+5p When you combine like terms, you just add all the terms that have the same variable so you get 7p + 5p = 12p Question 2. What if the cost of tickets to the exhibit was reduced to$3? Write an expression for the new cost in dollars for p people to visit the museum and attend the exhibit. Then, simplify the expression by combining like terms.
Type below:
_____________

Explanation:
Museum admission costs $7, and tickets to the mammoth exhibit cost$5.
The expression 7p + 5p represents the cost in dollars for p people to visit the museum and attend the exhibit.
The cost of tickets to the mammoth exhibit is $5. If it is reduced to$3 then the cost will be $5 –$2 = $3 12p – 2p = 10p Question 3. A store receives tomatoes in boxes of 40 tomatoes each. About 4 tomatoes per box cannot be sold due to damage. The expression 40b − 4b gives the number of tomatoes that the store can sell from a shipment of b boxes. Simplify the expression by combining like terms. Type below: _____________ Answer: 36b Explanation: Given, A store receives tomatoes in boxes of 40 tomatoes each. About 4 tomatoes per box cannot be sold due to damage. The expression 40b − 4b gives the number of tomatoes that the store can sell from a shipment of b boxes. Subtract 40b and 4b 40b – 4b = 36b Question 4. Each cheerleading uniform includes a shirt and a skirt. The shirts cost$12 each, and the skirts cost $18 each. The expression 12u + 18u represents the cost in dollars of buying u uniforms. Simplify the expression by combining like terms. Type below: _____________ Answer: 30u Explanation: The expression 12u + 18u represents the cost in dollars of buying u uniforms. 12u and 18u are the like terms. So add the two terms 12u + 18u = 30u Question 5. A shop sells vases holding 9 red roses and 6 white roses. The expression 9v + 6v represents the total number of roses needed for v vases. Simplify the expression by combining like terms. Type below: _____________ Answer: 15v Explanation: A shop sells vases holding 9 red roses and 6 white roses. The expression 9v + 6v represents the total number of roses needed for v vases. The like terms are 9v and 6v 9v + 6v = 15v ### On Your Own – Page No. 398 Question 6. Marco received a gift card. He used it to buy 2 bike lights for$10.50 each. Then he bought a handlebar bag for $18.25. After these purchases, he had$0.75 left on the card. How much money was on the gift card when Marco received it?
$_______ Answer: Marco received a gift card. He used it to buy 2 bike lights for$10.50 each.
Then he bought a handlebar bag for $18.25. After these purchases, he had$0.75 left on the card.
Add total amount = 2 × $10.50 +$18.25 + $0.75$21 + $19 =$40
$40 was on the gift card when Marco received it. Question 7. Lydia collects shells. She has 24 sea snail shells, 16 conch shells, and 32 scallop shells. She wants to display the shells in equal rows, with only one type of shell in each row. What is the greatest number of shells Lydia can put in each row? _______ shells Answer: 8 shells Explanation: Lydia collects shells. She has 24 sea snail shells, 16 conch shells, and 32 scallop shells. She wants to display the shells in equal rows, with only one type of shell in each row. The possible shells in equal rows are 8 because 16, 24, and 32 are multiples of 8. Thus the greatest number of shells Lydia can put in each row is 8. Question 9. Verify the Reasoning of Others Karina states that you can simplify the expression 20x + 4 by combining like terms to get 24x. Does Karina’s statement make sense? Explain. Type below: _____________ Answer: Karina’s statement doesn’t make sense. Because 20x + 4 are not the like terms. We can add only the like terms. 20x + 4 ≠ 24x Question 10. Vincent is ordering accessories for his surfboard. A set of fins costs$24 each and a leash costs $15. The shipping cost is$4 per order. The expression 24b + 15b + 4 can be used to find the cost in dollars of buying b fins and b leashes plus the cost of shipping.
For numbers, 10a–10c, select True or False for each statement.
10a. The terms are 24b, 15b, and 4.
10b. The like terms are 24b and 15b.
10c. The simplified expression is 43b.
10a. _____________
10b. _____________
10c. _____________

10a. True
10b. True
10c. False

Explanation:
a. The terms of the expression 24b + 15b + 4 area 24b, 15b, 4.
b. The terms are said to be like if they have a common variable. So, the common terms are 24b, 15b.
c. Combine the like terms 24b and 15b
24b + 15b = 39b
Thus the statement is false.

### Problem Solving Combine Like Terms – Page No. 399

Question 1.
A box of pens costs $3 and a box of markers costs$5. The expression 3p + 5p represents the cost in dollars to make p packages that include 1 box of pens and 1 box of markers. Simplify the expression by combining like terms.
Type below:
_____________

Answer: 3p + 5p = 8p

Explanation:
A box of pens costs $3 and a box of markers costs$5.
The expression 3p + 5p represents the cost in dollars to make p packages that include 1 box of pens and 1 box of markers.
Adding the like terms 3p + 5p is 8p.

Question 2.
Riley’s parents got a cell phone plan that has a $40 monthly fee for the first phone. For each extra phone, there is a$15 phone service charge and a $10 text service charge. The expression 40 + 15e + 10e represents the total phone bill in dollars, where e is the number of extra phones. Simplify the expression by combining like terms. Type below: _____________ Answer: 25e + 40 Explanation: Given that, Riley’s parents got a cell phone plan that has a$40 monthly fee for the first phone.
For each extra phone, there is a $15 phone service charge and a$10 text service charge.
The expression 40 + 15e + 10e represents the total phone bill in dollars,
We have to combine the like terms here
The like terms in the expression are 15e and 10e.
That means 40 + 15e + 10e = 25e + 40

Question 3.
A radio show lasts for h hours. For every 60 minutes of air time during the show, there are 8 minutes of commercials. The expression 60h – 8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms.
Type below:
_____________

Explanation:
A radio show lasts for h hours. For every 60 minutes of air time during the show, there are 8 minutes of commercials.
The expression 60h – 8h represents the air time in minutes available for talk and music.
Now we have to Subtract the like terms 60h – 8h = 52h

Question 5.
Explain how combining like terms is similar to adding and subtracting whole numbers. How are they different?
Type below:
_____________

Answer: It’s the same because you are adding or subtracting numbers but it’s different because they can only be added or subtracted if the variable attached is the same. There are no variables when adding/subtracting regular whole numbers.

### Lesson Check – Page No. 400

Question 1.
For each gym class, a school has 10 soccer balls and 6 volleyballs. All of the classes share 15 basketballs. The expression 10c + 6c + 15 represents the total number of balls the school has for c classes. What is a simpler form of the expression?
Type below:
_____________

Explanation:
For each gym class, a school has 10 soccer balls and 6 volleyballs.
All of the classes share 15 basketballs.
c represents classes.
The expression is 10c + 6c + 15
Combine the like terms 10c and 6c
Now add common terms 10c + 6c + 15 = 16c + 15

Spiral Review

Question 3.
A bag has 8 bagels. Three of the bagels are cranberry. What percent of the bagels are cranberry?
________ %

Explanation:
[/latex]\frac{3}{8}[/latex] = 0.375
0.375 × 100 = 37.5 %
37.5% of the bagels are cranberry.

Question 4.
How many kilograms are equivalent to 3,200 grams?
________ kilograms

Explanation:
Convert from grams into kilograms
1000 grams = 1kg
3200 grams = 3200 × 1/1000 kg = 3.2 kg
3.2 kilograms are equivalent to 3,200 grams.

Question 5.
Toni earns $200 per week plus$5 for every magazine subscription that she sells. Write an expression that represents how much she will earn in dollars in a week in which she sells s subscriptions.
Type below:
_____________

Explanation:
Toni earns $200 per week plus$5 for every magazine subscription that she sells.
s represents subscriptions.
200 + 5 × s
Thus the expression that represents how much she will earn in dollars in a week is 200 + 5s

Question 6.
At a snack stand, drinks cost $1.50. Write an expression that could be used to find the total cost in dollars of d drinks. Type below: _____________ Answer: 1.5d Explanation: At a snack stand, drinks cost$1.50.
To find the total cost in dollars of d drinks we have to multiply 1.50 by d.
1.50 × d
Thus the expression that could be used to find the total cost in dollars of d drinks is 1.5d

### Share and Show – Page No. 403

Use properties of operations to write an equivalent expression by combining like terms.

Question 1.
$$3 \frac{7}{10} r-1 \frac{1}{5} r$$
Type below:
_____________

Answer: 2 $$frac{5}{10}$$r

Explanation:
3 $$frac{7}{10}$$r – 1 $$frac{1}{5}$$r
3 + $$frac{7}{10}$$r – 1 – $$frac{1}{5}$$r
3 – 1 = 2
$$frac{7}{10}$$r – $$frac{1}{5}$$r
$$frac{7}{10}$$r – $$frac{2}{10}$$r = $$frac{5}{10}$$r
$$3 \frac{7}{10} r-1 \frac{1}{5} r$$ = 2 $$frac{5}{10}$$r

Question 2.
20a + 18 + 16a
Type below:
_____________

Explanation:
Combine  the like terms first
16a and 20a are like terms in the given expression.
16a + 20a +18 = 36a + 18

Use the Distributive Property to write an equivalent expression.

Question 4.
8(h + 1.5)
Type below:
_____________

Explanation:
Here we have to use the distributive property for the above expression.
8(h + 1.5) = 8 × h + 1.5 × 8
= 8h + 12
Thus 8(h + 1.5) is 8h + 12.

Question 5.
4m + 4p
Type below:
_____________

Explanation:
Here we have to take 4 as a common factor from the expression.
4m + 4p = 4 × m + 4 × p
That implies 4 × (m + p)

Question 6.
3a + 9b
Type below:
_____________

Explanation:
Let us take 4 as a common factor from the expression.
3a + 9b = 3 × a + 9 × b
3(a + 3b)
3a + 9b = 3(a + 3b)

Practice: Copy and Solve Use the Distributive Property to write an equivalent expression.

Question 7.
3.5(w + 7)
Type below:
_____________

Explanation:
Use the distributive property.
Multiply within the parentheses.
3.5(w + 7) = 3.5 × w + 3.5 × 7
3.5w + 24.5
Thus 3.5(w + 7) = 3.5w + 24.5

Question 8.
$$\frac{1}{2}$$(f + 10)
Type below:
_____________

Answer: $$\frac{1}{2}$$f + 5

Explanation:
$$\frac{1}{2}$$(f + 10)
Use the distributive property.
Multiply within the parentheses.
$$\frac{1}{2}$$ × f + $$\frac{1}{2}$$ × 10
= $$\frac{1}{2}$$f + 5
Thus $$\frac{1}{2}$$(f + 10) = $$\frac{1}{2}$$f + 5

Question 9.
4(3z + 2)
Type below:
_____________

Explanation:
Use the distributive property.
Multiply within the parentheses.
4(3z + 2) = 4 × 3z + 4 × 2
= 12z + 8
So, 4(3z + 2) = 12z + 8

Question 10.
20b + 16c
Type below:
_____________

Explanation:
20b + 16c
Use the distributive property.
Multiply within the parentheses.
Take 4 as a common factor.
20b + 16c = 4 × 5b + 4 × 4c = 4 (5b + 4c)
Thus the expression 20b + 16c = 4 (5b + 4c)

Question 11.
30d + 18
Type below:
_____________

Explanation:
30 and 18 are the factors of 6.
So, take 6 as a common factor.
30d + 18 = 6 × 5d + 6 × 3
6 (5d + 3)
30d + 18 = 6 (5d + 3)

Question 12.
24g − 8h
Type below:
_____________

Explanation:
Given the expression 24g − 8h
24 and 8 are the factors of 8.
So, let us take 8 as a common factor.
24g − 8h = 8 × 3g – 8 × 1h
= 8(3g – h)

Question 13.
Write an Expression The lengths of the sides of a triangle are 3t, 2t + 1, and t + 4. Write an expression for the perimeter (sum of the lengths). Then, write an equivalent expression with 2 terms.
Type below:
_____________

Explanation:
Given that, The lengths of the sides of a triangle are 3t, 2t + 1, and t + 4.
We know that the perimeter of the triangle is P = a + b + c
P = 3t + 2t + 1 + t + 4
Combine the like terms.
P = 6t + 5

Question 14.
Use properties of operations to write an expression equivalent to the sum of the expressions 3(g + 5) and 2(3g − 6).
Type below:
_____________

Explanation:
Given two expressions 3(g + 5) and 2(3g − 6).
Use the distributive property to simplify the expressions.
3(g + 5) = 3 × g + 3 × 5 = 3g + 15
2(3g − 6) = 2 × 3g – 2 × 6 = 6g – 12
Add both expressions and combine the like terms
3g + 15 + 6g – 12 = 9g + 3 = 3(3g + 1)

### Problem Solving + Applications – Page No. 404

Question 15.
Sense or Nonsense Peter and Jade are using what they know about properties to write an expression equivalent to 2 × (n + 6) + 3. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Peter’s Work:
Expression: 2 × (n + 6) + 3
Associative Property of Addition: 2 × n + (6 + 3)
Add within parentheses: 2 × n + 9
Multiply: 2n + 9

Expression: 2 × (n + 6) + 3
Distributive Property: (2 × n) + (2 × 6) + 3
Multiply within parentheses: 2n + 12 + 3
Associative Property of Addition: 2n + (12 + 3)
Add within parentheses: 2n + 15
For the answer that is nonsense, correct the statement.
Type below:
_____________

He must have multiplied n + 6 with 2 but he added 6 with 3.
2 × (n + 6) + 3
2 × n + 2 × 6 + 3 = 2n + 12 + 3
= 2n + 15

Question 16.
Write the algebraic expression in the box that shows an equivalent expression.

Type below:
_____________

6(z + 5) = 6 × z + 6 × 5 = 6z + 30
6z + 5z = z(6 + 5) = 11z
2 + 6z + 3 = 6z + 5

### Generate Equivalent Expressions – Page No. 405

Use properties of operations to write an equivalent expression by combining like terms.

Question 1.
7h − 3h
Type below:
_____________

Explanation:
Combine the like terms
7h and 3h are the common terms
Now subtract 3h from 7h
7h – 3h = 4h

Question 3.
16 + 13p − 9p
Type below:
_____________

Explanation:

Combine the like terms for the above expressions.
The like terms are 13p and 9p
16 + 13p − 9p = 16 + 4p

Question 4.
y2 + 13y − 8y
Type below:
_____________

Explanation:
The given expression is y2 + 13y − 8y
The like terms are 13y and 8y
y2 + 13y − 8y = y2 + 5y

Question 6.
12 + 18n + 7 − 14n
Type below:
_____________

Explanation:
The expression is 12 + 18n + 7 − 14n
The like terms are 18n and 14n
12 + 18n + 7 − 14n = 19 + 4n

Use the Distributive Property to write an equivalent expression.

Question 8.
4d + 8
Type below:
_____________

Explanation:
Use the Distributive property
Multiply within the parentheses.
4d + 8 = 4 × d + 4 × 2
The common term is 4.
Take 4 as a common factor.
4d + 8 = 4 (d + 2)

Question 9.
21p + 35q
Type below:
_____________

Explanation:
Use the Distributive property
Multiply within the parentheses.
7 × 3p + 7 × 5q
The common term is 7.
7(3p + 5q)
21p + 35q = 7(3p + 5q)

Problem Solving

Question 10.
The expression 15n + 12n + 100 represents the total cost in dollars for skis, boots, and a lesson for n skiers. Simplify the expression 15n + 12n + 100. Then find the total cost for 8 skiers.
Type below:
_____________

Answer: 27n + 100, $316 Explanation: The terms that have n can be operated: 15n +12n + 100 = 27n +100. Then, we have that total cost = 27n +100 for n skiers. So, for 8 skiers we have total cost = 27(8) +100 = 216 + 100 = 316. Then, the total cost of 8 skiers is$316.

Question 11.
Casey has n nickels. Megan has 4 times as many nickels as Casey has. Write an expression for the total number of nickels Casey and Megan have. Then simplify the expression.
Type below:
_____________

Explanation:
Casey has n nickels. Megan has 4 times as many nickels as Casey has.
The sum of n and 4n
Add the common terms n and 4n.
n + 4n = 5n

Question 12.
Explain how you would use properties to write an expression equivalent to 7y + 4b – 3y.
Type below:
_____________

1st you combine like terms so subtract 7y and 3y and you get 4y.
So this is the final answer: 4y+4b.

### Lesson Check – Page No. 406

Question 1.
A ticket to a museum costs $8. A ticket to the dinosaur exhibit costs$5. The expression 8n + 5n represents the cost in dollars for n people to visit the museum and the exhibit. What is a simpler form of the expression 8n + 5n?
Type below:
_____________

Explanation:
A ticket to a museum costs $8. A ticket to the dinosaur exhibit costs$5.
The expression is the sum of 8n and 5n.
Thus the simpler form of the expression is 8n + 5n = 13n

Question 3.
A Mexican restaurant received 60 take-out orders. The manager found that 60% of the orders were for tacos and 25% of the orders were for burritos. How many orders were for other items?
______ orders

Explanation:
Given,
A Mexican restaurant received 60 take-out orders.
The manager found that 60% of the orders were for tacos and 25% of the orders were for burritos.
The answer is 9 because 25% of 60 is 15 plus 60% of 60 is 36 so 36+15=51 and 60-51=9
Thus 9 orders were for other items.

Question 4.
The area of a rectangular field is 1,710 square feet. The length of the field is 45 feet. What is the width of the field?
______ feet

Explanation:
The area of a rectangular field is 1,710 square feet.
The length of the field is 45 feet.
The width of the field is x feet
A = l × w
1710 square feet = 45 feet × x
x = 1710/45 = 38 feet
Thus the width of the rectangular field is 38 feet.

Question 6.
Boxes of cereal usually cost $4, but they are on sale for$1 off. A gallon of milk costs $3. The expression 4b – 1b + 3 can be used to find the cost in dollars of buying b boxes of cereal and a gallon of milk. Write the expression in a simpler form. Type below: _____________ Answer: 3b + 3 Explanation: Boxes of cereal usually cost$4, but they are on sale for $1 off. A gallon of milk costs$3.
The expression is 4b – 1b + 3
Combine the like terms for the above expression.
4b – 1b + 3 = 3b + 3 = 3(b + 1)

### Share and Show – Page No. 409

Use properties of operations to determine whether the expressions are equivalent.

Question 2.
9a × 3 and 12a
The expressions are _____________

Explanation:
Multiply 9a by 3.
9a × 3 = 27a
27a and 12a are not equivalent.
Thus the expressions are not equivalent.

Question 3.
8p + 0 and 8p × 0
The expressions are ______

Explanation:
8p + 0 = 8p
8p × 0 = 0
8p and 0 are not equivalent.
The expressions 8p + 0 and 8p × 0 are not equivalent.

Question 4.
5(a + b) and (5a + 2b) + 3b
The expressions are _____________

Explanation:
5(a + b) = 5a + 5b
(5a + 2b) + 3b
The like terms are 5a and 2b, 3b
Add the combine terms 5a + 2b + 3b = 5a + 5b
Thus the expressions 5(a + b) and (5a + 2b) + 3b are equivalent.

Use properties of operations to determine whether the expressions are equivalent.

Question 5.
3(v + 2) + 7v and 16v
The expressions are _____________

Explanation:
3(v + 2) + 7v
Combine the like terms 3v and 7v
3(v + 2) + 7v = 3v + 6 + 7v = 10v + 6
The expressions 10v + 6 and 16v are not equivalent.

Question 6.
14h + (17 + 11h) and 25h + 17
The expressions are _____________

Explanation:
14h + (17 + 11h)
Combine the like terms 14h and 11h.
14h + 17 + 11h = 25h + 17
The expressions 14h + (17 + 11h) and 25h + 17 are equivalent.

Question 7.
4b × 7 and 28b
The expressions are _____________

Explanation:
Multiply 4b with 7.
4b × 7 = 28b
The expressions 4b × 7 and 28b are equivalent.

Question 8.
Each case of dog food contains c cans. Each case of cat food contains 12 cans. Four students wrote the expressions below for the number of cans in 6 cases of dog food and 1 case of cat food. Which of the expressions are correct?
6c + 12     6c × 12      6(c + 2)      (2c + 4) × 3
Type below:
_____________

Answer: The correct expressions are 6c + 12, 6(c + 2), (2c + 4) × 3
6(c + 2) is the distributive form of the expression.

### Problem Solving + Applications – Page No. 410

Use the table for 9–11.

Question 9.
Marcus bought 4 packets of baseball cards and 4 packets of animal cards. Write an algebraic expression for the total number of cards Marcus bought.
Type below:
_____________

Explanation:
Marcus bought 4 packets of baseball cards and 4 packets of animal cards.
b represents the number per packet
Multiply 4 with b
4 × b = 4b
a represents the number per packet of animal cards.
Multiply 4 with a.
4 × a = 4a
Therefore the algebraic expression for the total number of cards Marcus bought is the sum of 4a and 4b.
The expression is 4a + 4b

Question 10.
Make Arguments Is the expression for the number of cards Marcus bought equivalent to 4(a + b)? Justify your answer.
Type below:
_____________

Use the distributive property to simplify the expression 4a + 4b.
Take 4 as the common factor for the expression 4a + 4b.
4a + 4b = 4(a + b)

Question 11.
Angelica buys 3 packets of movie cards and 6 packets of cartoon cards and adds these to the 3 packets of movie cards she already has. Write three equivalent algebraic expressions for the number of cards Angelica has now
Type below:
_____________

Answer: 3m + 6c + 3m

Explanation:
Angelica buys 3 packets of movie cards and 6 packets of cartoon cards and adds these to the 3 packets of movie cards she already has.
The expression for 3 packets of movie cards is 3m
The expression for 6 packets of cartoon cards is 6c.
Now we have to add 3m to the expression.
3m + 6c + 3m
Thus the three equivalent algebraic expressions for the number of cards Angelica has now is 3m + 6c + 3m

Question 12.
Select the expressions that are equivalent to 3(x + 2). Mark all that apply.
Options:
a. 3x + 6
b. 3x + 2
c. 5x
d. x + 5

Explanation:
Use the distributive property to solve the expression 3(x + 2).
3(x + 2) = 3 × x + 3 × 2 = 3x + 6
Thus the correct answer is option A.

### Identify Equivalent Expressions – Page No. 411

Use properties of operations to determine whether the expressions are equivalent.

Question 1.
2s + 13 + 15s and 17s + 13
The expressions are _____________

Explanation:
2s + 13 + 15s
Combine the like terms
2s + 13 + 15s = 17s + 13
17s + 13 = 17s + 13
Thus the expressions 2s + 13 + 15s and 17s + 13 are equivalent.

Question 2.
5 × 7h and 35h
The expressions are _____________

Explanation:
5 × 7h = 35h
35h = 35h
The expressions 5 × 7h and 35h are equivalent.

Question 4.
(9w × 0)−12 and 9w – 12
The expressions are _____________

Explanation:
(9w × 0)−12 = 0 – 12 = – 12
– 12 ≠ 9w – 12
So, the expressions (9w × 0)−12 and 9w – 12 are not equivalent.

Question 5.
11(p + q) and 11p + (7q + 4q)
The expressions are _____________

Explanation:
11(p + q) = 11p + 11q
Combine the terms 7q and 4q
11p + (7q + 4q) = 11p + 11q = 11(p + q)
So, the expressions 11(p + q) and 11p + (7q + 4q) are equivalent.

Question 6.
6(4b + 3d) and 24b + 3d
The expressions are _____________

Explanation:
6(4b + 3d) = 24b + 18d
24b + 18d ≠ 24b + 3d
So, the expressions 6(4b + 3d) and 24b + 3d are not equivalent.

Question 8.
(y × 1) + 2 and y + 2
The expressions are _____________

Explanation:
(y × 1) + 2 = y + 2
y + 2 = y + 2
Thus the expressions (y × 1) + 2 and y + 2 are equivalent.

Question 9.
4 + 5(6t + 1) and 9 + 30t
The expressions are _____________

Explanation:
4 + 5(6t + 1) = 4 + 30t + 5 = 9 + 30t
9 + 30t = 9 + 30t
Thus the expressions 4 + 5(6t + 1) and 9 + 30t are equivalent.

Question 10.
9x + 0 + 10x and 19x + 1
The expressions are _____________

Explanation:
9x + 0 + 10x
Combine the like terms 9x and 10x.
9x + 10x = 19x
19x ≠ 19x + 1
Thus the expressions 9x + 0 + 10x and 19x + 1 are not equivalent.

Question 11.
12c − 3c and 3(4c − 1)
The expressions are _____________

Explanation:
12c − 3c
Take 3 as a common factor.
3c(4 – 1) or 3 (4c – 1c)
3 (4c – 1c) ≠ 3(4c − 1)
Thus the expressions 12c − 3c and 3(4c − 1) are not equivalent.

Question 12.
6a × 4 and 24a
The expressions are _____________

Explanation:
6a × 4 = 24a
24a = 24a
The expressions 6a × 4 and 24a are equivalent.

Problem Solving

Question 13.
Rachel needs to write 3 book reports with b pages and 3 science reports with s pages during the school year. Write an algebraic expression for the total number of pages Rachel will need to write.
Type below:
_____________

Explanation:
Rachel needs to write 3 book reports with b pages and 3 science reports with s pages during the school year.
Multiply 3 book reports with b pages = 3b.
Multiply 3 science books with s pages = 3s.
The algebraic expression for the total number of pages Rachel will need to write is 3b + 3s.

Question 14.
Rachel’s friend Yassi has to write 3(b + s) pages for reports. Use properties of operations to determine whether this expression is equivalent to the expression for the number of pages Rachel has to write.
This expression is _____________

Explanation:
Rachel’s friend Yassi has to write 3(b + s) pages for reports.
The equivalent expression of 3(b + s) = 3b + 3s

Question 15.
Use properties of operations to show whether 7y + 7b + 3y and 7(y + b) + 3b are equivalent expressions. Explain your reasoning.
Type below:
_____________

Use Distributive property to simplify the expressions.
The equivalent expression of 7y + 7b + 3y = 7(y + b) + 3y
Thus 7y + 7b + 3y and 7(y + b) + 3b are equivalent.

### Lesson Check – Page No. 412

Question 1.
Ian had 4 cases of comic books and 6 adventure books. Each case holds c comic books. He gave 1 case of comic books to his friend. Write an expression that gives the total number of books Ian has left.
Type below:
_____________

Explanation:
Ian had 4 cases of comic books and 6 adventure books. Each case holds c comic books. He gave 1 case of comic books to his friend.
4c + 6 – 1c
Combine the like terms
3c + 6

Question 2.
In May, Xia made 5 flower planters with f flowers in each planter. In June, she made 8 flower planters with f flowers in each planter. Write an expression in the simplest form that gives the number of flowers Xia has in the planters.
Type below:
_____________

Explanation:
In May, Xia made 5 flower planters with f flowers in each planter.
The expression is 5f
In June, she made 8 flower planters with f flowers in each planter.
The expression is 8f.
Sum of 5f and 8f is 8f + 5f = 13f

Spiral Review

Question 3.
Keisha wants to read for 90 minutes. So far, she has read 30% of her goal. How much longer does she need to read to reach her goal?
________ minutes

Explanation:
Keisha wants to read for 90 minutes.
So far, she has read 30% of her goal.
30% = 30/100 = 0.3
Multiply 90 with 0.3
90 × 0.3 = 27
Subtract 27 from 90
90 – 27 = 63
She needs to read 63 minutes to reach her goal.

Question 4.
Marvyn travels 105 miles on his scooter. He travels for 3 hours. What is his average speed?
________ miles per hour

Explanation:
Divide the number of miles by hours traveled.
Average speed = 105 miles/3 hours = 35 miles per hour
Thus the average speed is 35 miles per hour.

Question 6.
At the library book sale, hardcover books sell for $4 and paperbacks sell for$2. The expression 4b + 2b represents the total cost for b hardcover books and b paperbacks. Write a simpler expression that is equivalent to 4b + 2b.
Type below:
_____________

Explanation:
Given expression is 4b + 2b
The terms are 4b and 2b
Now combine the like terms
That means 4b + 2b = 6b

### Chapter 7 Review/Test – Page No. 413

Question 1.
Use exponents to rewrite the expression.
3 × 3 × 3 × 3 × 5 × 5
Type below:
_____________

Explanation:
3 is a repeated factor.
The number 3 is repeated four times.
5 is a repeated factor.
The number 5 is repeated two times.
The exponential form of 3 × 3 × 3 × 3 × 5 × 5 is 34 × 52

Question 2.
A plumber charges $10 for transportation and$55 per hour for repairs. Write an expression that can be used to find the cost in dollars for a repair that takes h hours.
Type below:
_____________

Explanation:
A plumber charges $10 for transportation and$55 per hour for repairs.
Multiply 55 with an hour
Sum of 10 and product of 55 and h.
The expression is 10 + 55h.

Question 3.
Ellen is 2 years older than her brother Luke. Let k represent Luke’s age. Identify the expression that can be used to find Ellen’s age.
Options:
a. k−2
b. k+2
c. 2k
d. $$\frac{k}{2}$$

Explanation:
Given, Ellen is 2 years older than her brother Luke. Let k represent Luke’s age.
Older is nothing but more so we have to add 2 years to k.
That means k + 2.
Thus the correct answer is option B.

Question 5.
Jasmine is buying beans. She bought r pounds of red beans that cost $3 per pound and b pounds of black beans that cost$2 per pound. The total amount of her purchase is given by the expression 3r + 2b. Select the terms of the expression. Mark all that apply
Options:
a. 2
b. 2b
c. 3
d. 3r

Explanation:
The expression is 3r + 2b
The terms of the expressions are 3r and 2b.
Thus the correct answers are B and D.

### Chapter 7 Review/Test – Page No. 414

Question 6.
Choose the number that makes the sentence true. The formula V= s3 gives the volume V of a cube with side length s.
The volume of a cube that has a side length of 8 inches
inches is _____________ cubed

Explanation:
Use the formula V= s3
s = 8
V = 83 = 8 × 8 × 8 = 512

Question 7.
Liang is ordering new chairs and cushions for his dining room table. A new chair costs $88 and a new cushion costs$12. Shipping costs $34. The expression 88c + 12c + 34 gives the total cost for buying c sets of chairs and cushions. Simplify the expression by combining like terms. Type below: _____________ Answer: 100c + 34 Explanation: Liang is ordering new chairs and cushions for his dining room table. A new chair costs$88 and a new cushion costs $12. Shipping costs$34.
The expression is 88c + 12c + 34.
Combine the like terms
88c + 12c + 34 = 100c + 34

Question 8.
Mr. Ruiz writes the expression 5 × (2 + 1)2 ÷ 3 on the board. Chelsea says the first step is to evaluate 12. Explain Chelsea’s mistake. Then, evaluate the expression
_____________

She should have done what was in the parentheses (2 + 1) and then the exponent 32= 9
5 × (2 + 1)2 ÷ 3 = 5 × 9 ÷ 3
5 × 3 = 15

Question 9.
Jake writes this word expression.

Write an algebraic expression for the word expression. Then, evaluate the expression for m = 4. Show your work.
________

The expression is 7m
Replace m = 4 with m
7m = 7 × 4 = 28

### Chapter 7 Review/Test – Page No. 415

Question 10.
Sora has some bags that each contain 12 potatoes. She takes 3 potatoes from each bag. The expression 12p – 3p represents the number of potatoes p left in the bags. Simplify the expression by combining like terms. Draw a line to match the expression with the simplified expression.

Type below:
_____________

Question 11.
Logan works at a florist. He earns $600 per week plus$5 for each floral arrangement he delivers. Write an expression that gives the amount in dollars that Logan earns for delivering f floral arrangements. Use the expression to find the amount Logan will earn if he delivers 45 floral arrangements in one week. Show your work.
$________ Answer:$825

Explanation:
Logan works at a florist. He earns $600 per week plus$5 for each floral arrangement he delivers. Write an expression that gives the amount in dollars that Logan earns for delivering f floral arrangements.
The expression is 600 + 5f
f = 45
600 + 5f = 600 + 5(45)
600 + 225 = 825
Thus Logan earned $825 for delivering f floral arrangements. Question 12. Choose the word that makes the sentence true. Dara wrote the expression 7 × (d + 4) in her notebook. She used the _____ Property to write the equivalent expression 7d + 28. Answer: Dara wrote the expression 7 × (d + 4) in her notebook. She used the Distributive Property to write the equivalent expression 7d + 28. Use the distributive property to simplify the expression. 7 × (d + 4) = 7d + 28 ### Chapter 7 Review/Test – Page No. 416 Question 14. Alisha buys 5 boxes of peanut butter granola bars and 5 boxes of cinnamon granola bars. Let p represent the number of bars in a box of peanut butter granola bars and c represents the number of bars in a box of cinnamon granola bars. Jaira and Emma each write an expression that represents the total number of granola bars Alisha bought. Are the equivalent of the expression? Justify your answer Jaira 5p + 5c Emma 5(p + c) Type below: _____________ Answer: They are equivalent statements. 5p + 5c = 5(p + c) by the distributive property. Question 15. Abe is 3 inches taller than Chen. Select the expressions that represent Abe’s height if Chen’s height is h inches. Mark all that apply Options: a. h−3 b. h+3 c. the sum of h and 3 d. the difference between h and 3 Answer: Abe is 3 inches taller than Chen. Let Chen’s height is h. The expression is the sum of Chen’s height and 3. So, the suitable answers are h + 3 and the sum of h and 3. Thus the correct answers are option B and C. Question 16. Write the algebraic expression in the box that shows an equivalent expression. Type below: _____________ Answer: 3(k + 2) = 3k + 6 3k + 2k = 5k 2 + 6k + 3 = 6k + 5 ### Chapter 7 Review/Test – Page No. 417 Question 17. Draw a line to match the property with the expression that shows the property. Type below: _____________ Answer: Question 18. A bike rental company charges$10 to rent a bike plus $2 for each hour the bike is rented. An expression for the total cost of renting a bike for h hours is 10 + 2h. Complete the table to find the total cost of renting a bike for h hours. Type below: _____________ Answer: Question 19. An online sporting goods store charges$12 for a pair of athletic socks. Shipping is $2 per order Part A Write an expression that Hana can use to find the total cost in dollars for ordering n pairs of socks. Type below: _____________ Answer: 12n + 2 Explanation: Let n represents a pair of socks. Multiply the price of pair of athletic socks with pair of socks = 12 × n Shipping is$2 per order
The expression for the total cost in dollars for ordering n pairs of socks is 12n + 2

Question 19.
Part B
Hana orders 3 pairs of athletic socks and her friend, Charlie, order 2 pairs of athletic socks. What is the total cost, including shipping, for both orders? Show your work.
\$ ________

The cost of Hannah’s order is 12 × 3 + 2 = 36 + 2 = 38
The cost of Charlie’s order is 12 × 2 + 2 = 24 + 2 = 26
The total cost for both is 38 + 26 = 64

### Chapter 7 Review/Test – Page No. 418

Question 20.
Fernando simplifies the expression (6 + 2)2 – 4 × 3.
Part A
Fernando shows his work on the board. Use numbers and words to explain his mistake.
(6 + 2)2 – 4 × 3
(6 + 4) – 4 × 3
10 − 4 × 3
6 × 3
18
Type below:
_____________

Answer: Fernando did not use the correct order of operations. He should have added 6 and 2, then evaluate the exponent. He also subtracted before multiplying. He should have multiplied first.

Question 20.
Part B
Simplify the expression (6 + 2)2 − 4 × 3 using the order of operations.
_______