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.
Envision Math Grade 6 Answers Topic 2.1 Using Variables to Write Expressions 1

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.
Envision Math Grade 6 Answers Topic 2.1 Using Variables to Write Expressions 2

Other Examples
The table shows algebraic expressions for given situations.
Envision Math Grade 6 Answers Topic 2.1 Using Variables to Write Expressions 3

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.
Envision Math Grade 6 Answers Topic 2.1 Using Variables to Write Expressions 4

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:

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