Section 2.5 (1.6)

```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.
Translating Phrases
sum
plus
more than
increased by
Subtraction Multiplication
minus
subtracted from
difference of
less than
decreased by
less
Order is
important!!
product
twice
times
multiplied by
of
Division
divided by
quotient
ratio
divided into
Order is
important!!
Translating Phrases
Operation
Variable Expression Word Phrases
x+3
Some number plus three
The sum of some number and three
Three more than some number
Some number increased by three
Translating Phrases
Operation
Subtraction
Variable Expression Word Phrases
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
Translating Phrases
Operation
Multiplication
Exponents
Roots
Variable Expression Word Phrases
2a
Twice some number
Two times some number
The product of two and some
number
Some number multiplied by two
c2
c squared
The square of c
c to the second power
k3
k cubed
k to the third power
The cube of k
x
The square root of x
Translating Phrases
Operation
Division
Variable Expression
x
5
Word Phrases
Some number divided by five
The quotient of some number and
five
The ratio of some number and five
Five divided into some number
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
x  3 or
3
Translating Phrases
Use x for the variable if not specified.
The product of a number and four
4x
The sum of b cubed and seven
b3  7
Seven added to the quotient of x and y
x
7
y
x
y
Translating Phrases
Use x for the variable if not specified.
A number subtracted from 8
8x
Nine divided into a number
x
9
Five more than two times a number
2x
5  2x or 2x  5
Translating Phrases
Use x for the variable if not specified.
ab
Seven times the sum of a and b
7a  b 
5x
The product of five and a number
minus the sum of the number and two
x 2
5x  x  2
5x   x  2
Translating Phrases
Use x for the variable if not specified.
ab
The sum of a and b divided by the
difference of a and b
ab
ab
ab
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
Slide 1- 12
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
Slide 1- 13
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
Slide 1- 14
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
Slide 1- 15
Translating Word Sentences
Operation
Equals
Expression
=
Word Phrases
is
is equal to
is the same as
produces
yields
results in
Translate and Solve
=
Fifteen more than a number is negative seven.
15  x
15  x  7
 15
 15
x  22
7
Translate and Solve
13  4 x
4x
Thirteen more than the product of four and a number
yields 9.
=
13  4 x  9
 13
 13
4 x  4
4
4
x  1
Translate and Solve
3 x  5
x5
Three times the difference of a number and five
is equal to seven times the number, minus twelve.
7x
=
7x  12
3 x  5  7 x  12
3x  15  7x  12
 7x
 7x
 4 x  15  12
 15  15
 4x  3
4 4
3
x
4
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
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
Translate: The quotient of four less than a
number and five is the same as the number
divided by eight.
a) 4  n  8n
5
b) 5(n  4)  8n
5
8
c)

n4 n
d) n  4  n
5
2.5
8
Translate: The quotient of four less than a
number and five is the same as the number
divided by eight.
a) 4  n  8n
5
b) 5(n  4)  8n
5
8
c)

n4 n
d) n  4  n
5
2.5
8
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