Transcript 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.
Copyright © 2011 Pearson Education, Inc.
Translating Phrases
Addition
sum plus more than added to increased by
Subtraction Multiplication
minus subtracted from difference of less than decreased by less product twice times multiplied by of
Division
divided by quotient ratio divided into
Order is important!!
Order is important!!
Translating Phrases
Operation
Addition
Variable Expression
x + 3
Word Phrases
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
Translating Phrases
Operation
Subtraction
Variable Expression
y – 6
Word Phrases
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
2a c k 2 3
x
Word Phrases Twice
some number Two
times
some number The
product
of two and some number Some number
multiplied
by two c squared The square of c c to the second power k cubed k to the third power The cube of k 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
x
3 or 3
x
quotient of
x
and 3
x
3 or
x
3
Translating Phrases Use x for the variable if not specified.
The product of a number and four 4
x
The sum of b cubed and seven
b
3 7 Seven added to the quotient of x and y 7
x 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 2
x
5 2
x
or 2
x
5
Translating Phrases Use x for the variable if not specified.
a
b
Seven times the sum of
a
and
b
7
a
b
5
x
The product of five and a number minus the sum of the number and two
x
2 5
x
x
2 5
x
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 a
b b
1.6
Translate the phrase to an algebraic expression.
Twelve less than three times a number
a) 3
n
+ 12 b) 12 – 3
n
c) 3
n
– 12 d) 3
n
12 Copyright © 2011 Pearson Education, Inc.
Slide 1- 12
1.6
Translate the phrase to an algebraic expression.
Twelve less than three times a number
a) 3
n
+ 12 b) 12 – 3
n
c) 3
n
– 12 d) 3
n
12 Copyright © 2011 Pearson Education, Inc.
Slide 1- 13
1.6
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
)
Slide 1- 14
Copyright © 2011 Pearson Education, Inc.
1.6
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
)
Slide 1- 15
Copyright © 2011 Pearson Education, Inc.
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
7 15 15
x
7 15
x
22
Translate and Solve 13 4
x
4
x
Thirteen more than the product of four and a number yields 9.
= 13 13 4
x
9 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.
= 7
x
7
x
12 3
x
5 7
x
12 3 7 4
x x x
4
x
4 15 15 15 3 4 7 7
x x
12 15 12
x
3 4
2.5
Translate: Thirty-two less than three times a number is fifteen.
a) 32 – 3
x
= 15 b) 3
x
– 32 = 15 c) 32 + 3
x
= 15 d) 3
x
32 = 15
2.5
Translate: Thirty-two less than three times a number is fifteen.
a) 32 – 3
x
= 15 b) 3
x
– 32 = 15 c) 32 + 3
x
= 15 d) 3
x
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
5 8
n
b) 5(
n
4) 8
n
c) 5
n
4 8
n
d)
n
4 5
n
8
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
5 8
n
b) 5(
n
4) 8
n
c) 5
n
4 8
n
d)
n
4 5
n
8