1. Translating Word Phrases to Expressions
1.6
Translating Word Phrases to Expressions
1. Translate word phrases to expressions.
2.5
Translating Word Sentences to Equations
1. Translate sentences to equations using key words, then solve.
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2. Translating Phrases Addition Subtraction Multiplication Division sum
plus
more than
added to
increased by
minus
subtracted from
difference of
less than
decreased by
less
product
twice
times
multiplied by of
divided by
quotient
ratio
divided into
Order is important!!
Order is important!!

3. Translating Phrases Operation Variable Expression Word Phrases
Addition
x + 3
Some number plus three
Three added to some number
The sum of some number and three
Three more than some number
Some number increased by three

4. Translating Phrases Operation Variable Expression Word Phrases
Subtraction
y – 6
Some number minus six
Six subtracted from some number
The difference of some number
and six
Six less than some number
Some number decreased by six
Some number less six

5. Translating Phrases Operation Variable Expression Word Phrases
Multiplication 2a
Twice some number
Two times some number
The product of two and some
number
Some number multiplied by two
Exponents c2
c squared
The square of c
c to the second power k3
k cubed
k to the third power
The cube of k
Roots
The square root of x

6. Translating Phrases Operation Variable Expression Word Phrases
Division
Some number divided by five
The quotient of some number and
five
The ratio of some number and five
Five divided into some number

7. Translating Phrases
The key words sum, difference, product, and quotient indicate the answer for their respective operations.
sum of x and 3
x + 3
difference of x and 3
x – 3
product of x and 3
quotient of x and 3
x  3 or 3x
x  3 or

8. Translating Phrases The product of a number and four
Use x for the variable if not specified.
The product of a number and four
The sum of b cubed and seven
Seven added to the quotient of x and y

9. Translating Phrases A number subtracted from 8
Use x for the variable if not specified.
A number subtracted from 8
Nine divided into a number
Five more than two times a number

10. Translating Phrases Seven times the sum of a and b
Use x for the variable if not specified.
Seven times the sum of a and b
The product of five and a number minus the sum of the number and two

11. Translating Phrases
Use x for the variable if not specified.
The sum of a and b divided by the difference of a and b

12. Translate the phrase to an algebraic expression
Translate the phrase to an algebraic expression. Twelve less than three times a number
a) 3n + 12
b) 12 – 3n
c) 3n – 12
d) 3n  12
Copyright © 2011 Pearson Education, Inc.
1.6

13. Translate the phrase to an algebraic expression.
Twelve less than three times a number
a) 3n + 12
b) 12 – 3n
c) 3n – 12
d) 3n  12
Copyright © 2011 Pearson Education, Inc.
1.6

14. a) (a – b) – (w + z) b) a – b – (w + z) c) ab – (w + z)
Translate the phrase to an algebraic expression.
The difference of a and b decreased by the sum of w and z
a) (a – b) – (w + z)
b) a – b – (w + z)
c) ab – (w + z)
d) (b – a) – (w + z)
Copyright © 2011 Pearson Education, Inc.
1.6

15. a) (a – b) – (w + z) b) a – b – (w + z) c) ab – (w + z)
Translate the phrase to an algebraic expression.
The difference of a and b decreased by the sum of w and z
a) (a – b) – (w + z)
b) a – b – (w + z)
c) ab – (w + z)
d) (b – a) – (w + z)
Copyright © 2011 Pearson Education, Inc.
1.6

16. Translating Word Sentences
Operation
Expression
Word Phrases
Equals = is
is equal to
is the same as
produces
yields
results in

17. Translate and Solve =
Fifteen more than a number is seventeen.

18. Translate and Solve
Thirteen more than the product of four and a number yields 25. =

19. Translate: Thirty-two less than three times a number is fifteen.
a) 32 – 3x = 15
b) 3x – 32 = 15
c) x = 15
d) 3x  32 = 15
2.5

20. Translate: Thirty-two less than three times a number is fifteen.
a) 32 – 3x = 15
b) 3x – 32 = 15
c) x = 15
d) 3x  32 = 15
2.5

21. Translate: The quotient of four less than a number and five is the same as the number divided by eight. a) b) c) d)
2.5

22. Translate: The quotient of four less than a number and five is the same as the number divided by eight. a) b) c) d)
2.5