Answer:
Translating Algebraic Expressions From Words
LEARNING OUTCOMES
Translate word phrases into algebraic expressions
Write an algebraic expression that represents the relationship between two measurements such as length and width or the amount of different types of coins
Translate Words to Algebraic Expressions
In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we’ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that. They are summarized below.
Operation Phrase Expression
Addition
a
plus
b
the sum of
a
and
b
a
increased by
b
b
more than
a
the total of
a
and
b
b
added to
a
a
+
b
Subtraction
a
minus
b
the difference of
a
and
b
b
subtracted from
a
a
decreased by
b
b
less than
a
a
−
b
Multiplication
a
times
b
the product of
a
and
b
a
⋅
b
,
a
b
,
a
(
b
)
,
(
a
)
(
b
)
Division
a
divided by
b
the quotient of
a
and
b
the ratio of
a
and
b
b
divided into
a
a
÷
b
,
a
/
b
,
a
b
,
b
¯¯¯¯¯
)
a
Look closely at these phrases using the four operations:
the sum of
a
and
b
the difference of
a
and
b
the product of
a
and
b
the quotient of
a
and
b
Each phrase tells you to operate on two numbers. Look for the words of and and to find the numbers.
EXAMPLE
Translate each word phrase into an algebraic expression:
1. The difference of
20
and
4
2. The quotient of
10
x
and
3
Solution
1. The key word is difference, which tells us the operation is subtraction. Look for the words of and and to find the numbers to subtract.
the difference of
20
and
4
20
minus
4
20
−
4
2. The key word is quotient, which tells us the operation is division.
the quotient of
10
x
and
3
divide
10
x
by
3
10
x
÷
3
This can also be written as
10
x
/
3
or
10
x
3
Step-by-step explanation:
