<< Chapter < Page Chapter >> Page >

Translate an english phrase to an algebraic expression

In the last section, we listed many operation symbols that are used in algebra, then we translated expressions and equations into English phrases and sentences. Now we’ll reverse the process. We’ll translate English phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that. [link] summarizes them.

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
a decreased by b
b less than a
b subtracted from a
a b
Multiplication a times b
the product of a and b
twice a
a · b , a b , a ( b ) , ( a ) ( b )

2 a
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:

Four phrases are shown. The first reads “the sum of a and b”, where the words “of” and “and” are written in red. The second reads “the difference of a and b”, where the words “of” and “and” are written in red. The third reads “the product of a and b”, where the words “of” and “and” are written in red. The fourth reads “the quotient of a and b”, where the words “of” and “and” are written in red.

Each phrase tells us to operate on two numbers. Look for the words of and and to find the numbers.

Translate each English phrase into an algebraic expression: the difference of 17 x and 5 the quotient of 10 x 2 and 7 .

Solution

  1. The key word is difference , which tells us the operation is subtraction. Look for the words of and and t o find the numbers to subtract.
    The phrase “the difference of 17x and 5”, where the words “of” and “and” are written in red, is written above the phrase “17 x minus 5”. a final phrase written below reads “17 x, minus sign, 5”.

  2. The key word is “quotient,” which tells us the operation is division.
The phrase “the quotient of 10x squared and 7”, where the words “of” and “and” are written in red, is written above the expression “divide 10x squared by 7”. The expression written below reads “10x squared, division sign,v7”.

This can also be written 10 x 2 / 7 or 10 x 2 7 .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: the difference of 14 x 2 and 13 the quotient of 12 x and 2.

14 x 2 13 12 x ÷ 2

Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: the sum of 17 y 2 and 19 the product of 7 and y .

17 y 2 + 19 7 y

Got questions? Get instant answers now!

How old will you be in eight years? What age is eight more years than your age now? Did you add 8 to your present age? Eight “more than” means 8 added to your present age. How old were you seven years ago? This is 7 years less than your age now. You subtract 7 from your present age. Seven “less than” means 7 subtracted from your present age.

Translate the English phrase into an algebraic expression: Seventeen more than y Nine less than 9 x 2 .

Solution

  1. The key words are more than. They tell us the operation is addition. More than means “added to.”
    Seventeen more than y Seventeen added to y y + 17
  2. The key words are less than . They tell us to subtract. Less than means “subtracted from.”
    Nine less than 9 x 2 Nine subtracted from 9 x 2 9 x 2 9
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: Eleven more than x Fourteen less than 11 a .

x + 11 11 a 14

Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: 13 more than z 18 less than 8 x .

z + 13 8 x 18

Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: five times the sum of m and n the sum of five times m and n .

Solution

There are two operation words— times tells us to multiply and sum tells us to add.

  1. Because we are multiplying 5 times the sum we need parentheses around the sum of m and n , ( m + n ) . This forces us to determine the sum first. (Remember the order of operations.)
    five times the sum of m and n 5 ( m + n )
  2. To take a sum, we look for the words “of” and “and” to see what is being added. Here we are taking the sum of five times m and n .
    the sum of five times m and n 5 m + n
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Translate the English phrase into an algebraic expression: four times the sum of p and q the sum of four times p and q .

4 ( p + q ) 4 p + q

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask