The document provides examples for translating word phrases and sentences into mathematical expressions and equations. It includes tables listing common words associated with addition, subtraction, multiplication, division and their corresponding operations. There are also examples of translating phrases and solving equations derived from word sentences. Students are asked to translate phrases and sentences into algebraic expressions and equations.

1. Slide 1- 1
Copyright © 2011 Pearson Education, Inc.
Translating
English to
Mathematical
Expressions
LEE MARIE M.
MARFIEL

2. Slide 1- 2
Translating Word Phrases to
Expressions
1.6
1. Translate word phrases to expressions.
Translating Word Sentences to Equations
2.5
1. Translate sentences to equations using key words, then
solve.

3. 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!!

4. 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

5. 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

6. 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
x

7. 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
5
x

8. 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
product of x and 3 quotient of x and 3
x – 3
x  3 or 3x
x  3 or
Translating Phrases
3
x

9. Translating Phrases
The product of a number and four
Use x for the variable if not specified.
x
4
The sum of b cubed and seven
7
3

b
Seven added to the quotient of x and y
y
x
y
x

7

10. Translating Phrases
A number subtracted from 8
Use x for the variable if not specified.
x

8
Nine divided into a number
9
x
Five more than two times a number
x
2
x
2
5  5
2
or 
x

11. Translating Phrases
The product of five and a number
minus the sum of the number and two
Use x for the variable if not specified.
 
2
5 
 x
x
x
5
2

x
Seven times the sum of a and b
b
a 
 
b
a 
7
2
5 
 x
x

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

13. Slide 1- 13
Copyright © 2011 Pearson Education, Inc.
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
1.6

14. Slide 1- 14
Copyright © 2011 Pearson Education, Inc.
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
1.6

15. Slide 1- 15
Copyright © 2011 Pearson Education, Inc.
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)
1.6

16. Slide 1- 16
Copyright © 2011 Pearson Education, Inc.
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)
1.6

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

18. Translate and Solve
Fifteen more than a number is negative seven.
7
15 

 x
x

15 7

=
15
15 

22


x

19. Translate and Solve
Thirteen more than the product of four and a number
yields 9.
9
4
13 
 x
x
4
13  x
4
=
13
13 

4
4 

x
4
4
1


x

20. Translate and Solve
Three times the difference of a number and five
is equal to seven times the number, minus twelve.
  12
7
5
3 

 x
x
 
5
3 
x 5

x
=
15
15 

3
4 
 x
4
4 

4
3


x
x
7 12
7 
x
12
7
15
3 

 x
x
x
x 7
7 

12
15
4 


 x

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

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

23. Translate: The quotient of four less than a
number and five is the same as the number
divided by eight.
a)
b)
c)
d) 4
5 8
n n


4
8
5
n
n


5( 4) 8
n n
 
5 8
4
n n


2.5

24. Translate: The quotient of four less than a
number and five is the same as the number
divided by eight.
a)
b)
c)
d) 4
5 8
n n


4
8
5
n
n


5( 4) 8
n n
 
5 8
4
n n


2.5