## 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.
algebraic expression
Explanation:

Question 2.
The ? of a number uses exponents to write the repeated multiplication of the number called the base.
exponential form
Explanation:

Question 3.
Numbers that are easy to compute men-tally are called ? numbers.
compatible
Explanation:

Question 4.
A(n) ? is a symbol, such as n, that takes the place of a number or value.
variable
Explanation:

Variables

Evaluate each expression for x = 4 and x = 7.
Question 5.
3x + 8
20, 29
Explanation:

Question 6.
24 – 3x
12, 3
Explanation:

Question 7.
5 + 5 + x
14, 17
Explanation:

Question 8.
84 – x
21, 12
Explanation:

Question 9.
2x + 5 – x
9, 12
Explanation:

Question 10.
9x
36, 63
Explanation:

Question 11.
2x + 4
12, 18
Explanation:

Question 12.
28 – x
7, 4
Explanation:

Writing to Explain Write an answer for each question.
Question 13.
How are these terms alike: differences, sums, quotients, and products?
See margin.
Explanation:

Question 14.
What does it mean to evaluate an algebraic expression?
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
p + 22
Explanation:

Question 9.
15 divided by a number r
15 ÷ r
Explanation:

Question 10.
12 more points than a number p times 8
8p + 12
Explanation:

Question 11.
6 less than 7 times a number b
7b – 6
Explanation:

Question 12.
5 more than the product of x and 9
9x + 5
Explanation:

Question 13.
7 times the difference of yand 4
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.
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.
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.
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.
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.