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Writing Expressions



In this lesson, we will learn how to write algebraic expressions for word problems. We will start with some common phrases found in word problems.

Related Topics:
More Algebra Word Problems

More Algebra Topics

Phrase to Algebraic Expression

To write an expression, we often have to interpret a written phrase.

For example, the phrase “ 6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.

Some examples of common phrases and corresponding expressions that involve addition are:

Phrase

Expression

4 more than some number

x + 4

a number increased by 10

y + 10

8 plus some number

t + 8

the sum of a number and 12

w + 12


Some examples of common phrases and corresponding expressions that involve subtraction are:

Phrase

Expression

4 less than some number

x – 4

a number decreased by 10

y – 10

8 minus some number

8 – t

the difference between a number and 12

w – 12


Some examples of common phrases and corresponding expressions that involve multiplication are:

Phrase

Expression

4 times some number

4x

twice a number

2y

one-third of some number

the product of a number and 12

12w


Some examples of common phrases and corresponding expressions that involve division are:

Phrase

Expression

the quotient of 4 and some number

a number divided by 2

the ratio of 8 and some number

the quotient of a number and 12


Some examples of common phrases and corresponding expressions that involve two operations are:

Phrase

Expression

6 more than 5 times a number

5x + 6

4 times the sum of a number and 7

4(y + 7)

5 less than the product of 3 and a number

3w – 5

twice the difference between a number and 9

2(z – 9)


Some examples of common phrases and corresponding expressions that involve division are:

Phrase

Expression

the quotient of 4 and some number

a number divided by 2

the ratio of 8 and some number

the quotient of a number and 12


Some examples of common phrases and corresponding expressions that involve two operations are:

Phrase

Expression

6 more than 5 times a number

5x + 6

4 times the sum of a number and 7

4(y + 7)

5 less than the product of 3 and a number

3w – 5

twice the difference between a number and 9

2(z – 9)



 



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