## Envision Math 6th Grade Textbook Answer Key Topic 2.1 Using Variables to Write Expressions

**Review What You Know**

**Vocabulary**

Choose the best term from the box.

Question 1.

A(n) ? is a mathematical phrase that includes at least one variable and one operation.

Answer:

algebraic expression

Explanation:

Question 2.

The ? of a number uses exponents to write the repeated multiplication of the number called the base.

Answer:

exponential form

Explanation:

Question 3.

Numbers that are easy to compute men-tally are called ? numbers.

Answer:

compatible

Explanation:

Question 4.

A(n) ? is a symbol, such as n, that takes the place of a number or value.

Answer:

variable

Explanation:

**Variables**

Evaluate each expression for x = 4 and x = 7.

Question 5.

3x + 8

Answer:

20, 29

Explanation:

Question 6.

24 – 3x

Answer:

12, 3

Explanation:

Question 7.

5 + 5 + x

Answer:

14, 17

Explanation:

Question 8.

84 – x

Answer:

21, 12

Explanation:

Question 9.

2x + 5 – x

Answer:

9, 12

Explanation:

Question 10.

9x

Answer:

36, 63

Explanation:

Question 11.

2x + 4

Answer:

12, 18

Explanation:

Question 12.

28 – x

Answer:

7, 4

Explanation:

**Answer Terms**

Writing to Explain Write an answer for each question.

Question 13.

How are these terms alike: differences, sums, quotients, and products?

Answer:

See margin.

Explanation:

Question 14.

What does it mean to evaluate an algebraic expression?

Answer:

See margin.

Explanation:

**Using Variables to Write Expressions**

How can you write an algebraic expression?

Donnie bought CDs for $10 each. How can you represent the total cost of the CDs?

Answer:

A variable is a quantity that can change or vary and is often represented with a letter. Variables help you translate word phrases into algebraic expressions.

**Other Examples**

The table shows algebraic expressions for given situations.

**Guided Practice**

**Do you know HOW?**

Write an algebraic expression for each situation.

Question 1.

the difference of a number tand 22

Answer:

t – 22

Explanation:

Question 2.

m bicycles added to 18 bicycles

Answer:

18 + m

Explanation:

Question 3.

11 times a number z

Answer:

11z

Explanation:

Question 4.

4 less than 5 times a number g

Answer:

5g – 4

Explanation:

**Do you UNDERSTAND?**

Question 5.

In the problem at the top of the page, what does the variable n represent?

Answer:

The number of CDs Donnie bought

Explanation:

Question 6.

Identify the variable and the operation in the algebraic expression 8y.

Answer:

See margin.

Explanation:

Question 7.

Write an algebraic expression for this situation: n more students than the 8 students sitting in each of the 3 rows.

Answer:

n + 3(8)

Explanation:

CDs cost $10 each. The operation is multiplication.

Use the variable n to represent the number of CDs and write an algebraic expression.

$10 × n

An algebraic expression is a mathematical phrase that has at least one variable and one operation.

The total cost of the CDs is represented by

10 × n or 10n.

The operation is multiplication. The variable is n.

**Independent Practice**

For 8 through 13, write algebraic expressions.

Question 8.

A number p increased by 22

Answer:

p + 22

Explanation:

Question 9.

15 divided by a number r

Answer:

15 ÷ r

Explanation:

Question 10.

12 more points than a number p times 8

Answer:

8p + 12

Explanation:

Question 11.

6 less than 7 times a number b

Answer:

7b – 6

Explanation:

Question 12.

5 more than the product of x and 9

Answer:

9x + 5

Explanation:

Question 13.

7 times the difference of yand 4

Answer:

7 (y – 4)

Explanation:

**Problem Solving**

Question 14.

The distance around a closed shape can be expressed as 3 times side s, or 3s. Draw an example of this geometric shape.

Answer:

Students should draw an equilateral triangle.

Explanation:

Question 15.

Manuel sold 5 cartons of apple juice and 8 cartons of orange juice. Write an algebraic expression to represent how many cartons of each kind were sold.

Answer:

Sample answer: 5a + 8r

Explanation:

Question 16.

One float for the Tournament of Roses parade uses as many flowers as a florist usually uses in 5 years. If x is the number of flowers a florist uses in 1 year, write an algebraic expression for the number of flowers used to make a float.

Answer:

5x

Explanation:

Question 17.

Writing to Explain Devin’s DVD case has 3 rows of slots, but 5 slots are broken. If x equals the number of slots in a row, explain how the expression 3x – 5 relates to Devin’s DVD case.

Answer:

See margin.

Explanation:

Question 18.

A hen laid the same number of eggs each day for a week. Kelly collected the eggs for six days. Write an expression to show the number of eggs Kelly did not collect.

Answer:

7x – 6x

Explanation:

Question 19.

Think About the Process Which expression shows a quantity of rolls added to 8 bagels?

A. 8 – r

B. 8r

C. 8 + r

D. r ÷ 8

Answer:

C. 8 + r

Explanation: