Name Class Date 2-2
Translating Between Words and Math
Going Deeper
Essential question: How do you write algebraic expressions?
CC.6.EE.2a
1
EXPLORE
Writing Expressions from Models
video tutor
Write a description in words for each situation. Then write an
algebraic expression from the description. Use x as the variable.
A
Andrew has a bag containing an unknown number of counters. He
reaches in and removes 5 counters.
Description in Words
B
Algebraic Expression
Mercedes folds a piece of paper in half.
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Description in Words
Algebraic Expression
REFLECT
1a. What are some words that can describe addition and subtraction?
1b. What are some words that can describe multiplication and division?
1c.
Write three algebraic expressions that represent the phrase “5 times y.”
TRY THIS!
Write each phrase as an algebraic expression.
1d. 8 fewer than m
Chapter 2
1e. the product of 10 and c
51
Lesson 2
Expressions can be written with constants and variables, or they may be
described in words. When given an expression in words, it is important to
be able to translate the words into algebra.
There are several different ways to describe expressions with words.
Operation
Words
Addition
• added to
• plus
• sum
• more than
Subtraction
Multiplication
Division
• subtracted from
• minus
• difference
• less than
• take away
• taken from
• times
• multiplied by
• product
• groups of
• divided by
• divided into
• quotient
CC.6.EE.2a
2
EXAMPLE
Writing Algebraic Expressions
Write each phrase as an algebraic expression.
A
5 subtracted from y
The operation is
The algebraic expression is y
B
.
5.
The product of 9 and p
The operation is
.
The algebraic expression is
.
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TRY THIS!
Write each phrase as an algebraic expression.
2a. n times 7
2b. 4 minus y
2c. 13 added to x
2d. x divided by 9
2e. 9 divided by x
2f. c plus 3
REFLECT
2g. Error Analysis Erica wrote “5 added to y” as 5 + y and “5 subtracted from y”
as 5 – y. Why is the first expression correct but the second incorrect? When is
order important in writing an expression?
Chapter 2
52
Lesson 2
When solving real-world problems, you may need to identify the action taking
place to know which operation to use.
Action
Operation
Put parts together
Addition
Put equal parts together
Multiplication
Find how much more or less
Subtraction
Separate into equal parts
Division
CC.6.EE.2
3
EXAMPLE
Translating Words into Algebraic Expressions
Center City is 10 miles farther from Sam’s house than Westonville is.
Write an algebraic expression to represent the distance from Sam’s
house to Center City.
Let w represent the distance from Sam’s house to Westonville.
The distance from Sam’s house to Center City is 10 miles more / less than w.
So, to find the distance from Sam’s house to Center City, put together
and
.
Which operation represents this action?
The distance from Sam’s house to Center City can be represented by the
expression
.
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TRY THIS!
3a. Sonia worked 25 hours last week. She was paid the same amount of money
per hour that she worked. Let h represent Sonia’s hourly pay. Write an algebraic
­expression that ­represents Sonia’s total pay last week.
3b. Noah is saving to buy a new laptop computer. He has saved $119 so far.
Let c represent the cost of the laptop. Write an algebraic expression that
represents the amount of money Noah still needs to save.
REFLECT
3c. What If…? Suppose Center City was 10 miles closer to Sam’s house than
Westerville. How would the expression you wrote in 3 change?
3d. Are the expressions w – 10 and 10 – w equivalent expressions? Explain.
Chapter 2
53
Lesson 2
pra c t i c e
Write each phrase as an algebraic expression.
1. n divided by 8
2. p multiplied by 4
3. 3 groups of w
4. the sum of 1 and q
5. the quotient of 13 and z
6. c added to 45
7. h less than 30
8. 47 subtracted from m
Write a phrase in words for each algebraic expression.
9. m + 8
10. 42s
v   ​ 
11.​ ___
12
12. t – 29
13. 32 – r
14. 9b
20 ​ 
15.​ ___
d
16. k + 32
17. Kai’s score on a test was 12 points greater than Julia’s
score. Let k represent Kai’s score. Write an algebraic
expression to represent Julia’s score.
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18. The town of Rayburn received 6 more inches of snow than
the town of Greenville. Let g represent the amount of snow
in Greenville. Write an algebraic expression to represent
the amount of snow in Rayburn.
19. Abby baked 48 cookies and divided them evenly into bags.
Let b represent the number of bags. Write an algebraic
expression to represent the number of cookies in each bag.
20. Eli is driving at a speed of 55 miles per hour. Let h represent
the number of hours that Eli drives at this speed. Write an
algebraic expression to represent the number of miles that
Eli travels during this time.
21. Explain the difference between “b divided by 10” and “b divided into 10.”
Chapter 2
54
Lesson 2
Name Class 2-2
Date Name ________________________________________ Date __________________ Class__________________
Introduction
to Algebra
Additional
Practice
X
2
Practice B: Translating Between Words and Math
LESSON
1. Terry’s essay has 9 more pages than Stacey’s essay. If s
represents the number of pages in Stacey’s essay, write an
expression for the number of pages in Terry’s essay.
_________________________________________________________________________________________
2. Let z represent the number of students in a class. Write an
expression for the number of students in 3 equal groups.
_________________________________________________________________________________________
Write each phrase as a numerical or algebraic expression.
3. 24 multiplied by 3
________________________
4. n multiplied by 14
5. w added to 64
_______________________
________________________
6. the difference of 58 and 6 7. m subtracted from 100
8. the sum of 180 and 25
________________________
9. the product of 35 and x
________________________
_______________________
10. the quotient of 63 and 9
_______________________
________________________
11. 28 divided by p
________________________
Write two phrases for each expression.
13. 35  r ______________________________________________________________
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12. n  91______________________________________________________________
14. 20  s______________________________________________________________
15. Charles is 3 years older than Paul.
If y represents Paul’s age, what
expression represents Charles’s age?
16. Maya bought some pizzas for $12
each. If p represents the number of
pizzas she bought, what expression
shows the total amount she spent?
________________________________________
Chapter 2
________________________________________
55
Practice and Problem Solving
7
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
Introduction
to Algebra
Problem
Solving
LESSON
2
Problem Solving: Translating Between Words and Math
Write the correct answer.
1. Holly bought 10 comic books. She
gave a few of them to Kyle. Let c
represent the number of comic
books she gave to Kyle. Write an
expression for the number of comic
books Holly has left.
2. Last week, Peter worked 40 hours
for $15 an hour. Write a numerical
expression for the total amount Peter
earned last week. Write an algebraic
expression to show how much Peter
earns in h hours at that rate.
________________________________________
3. The temperature dropped 5°F, and
then it went up 3°F. Let t represent
the beginning temperature. Write an
expression to show the ending
temperature.
________________________________________
4. Teri baked 48 cookies and divided
them evenly into bags. Let n
represent the number of cookies Teri
put in each bag. Write an expression
for the number of bags she filled.
________________________________________
________________________________________
5. Marisa purchased canned soft drinks
for a family reunion. She purchased
1 case of 24 cans and several
packages containing 6 cans each. If
p represents the number of 6-can
packages she purchased, which of the
following expressions represents the
total number of cans Marisa
purchased for the reunion?
6. Becky has the addresses of many
people listed in her e-mail address
book. She forwarded a copy of an
article to all but 5 of those people.
If a represents the number of
addresses, which of the following
expressions represents how many
people she sent the article to?
F a+5
A 24 + 6p
G 5a
B 24 − 6p
H a−5
C 6 + 24p
J a÷5
D 6 − 24p
7. Mei bought several CDs for $12 each.
Which of the following expressions
could you use to find the total amount
she spent on the CDs?
A 12 + x
F 2 + 50 + 30
B 12 − x
G (2 • 50) + 30
C 12x
H (2 • 30) + 50
D 12 ÷ x
Chapter 2
8. Tony bought 2 packs of 50 plates and
1 pack of 30 plates. Which of the
following expressions could you use
to find the total number of plates Tony
bought?
J 2(30 + 50)
567
Practice
Problem
Solving
Holtand
McDougal
Mathematics
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© Houghton Mifflin Harcourt Publishing Company
Circle the letter of the correct answer.