Writing an algebraic expression

Writing an algebraic expression when a phrase is given is what this lesson will show you. With each example, we show you the key word that is important to identify and understand in order to write the expression correctly.

Example #1

6 more than n

Key word : more than

More than indicates addition. Add the first number 6 to the second number n

The algebraic expression is  n + 6

Notice that we added 6 to n and not n to 6.  Technically, 6 + n is n more than 6 although n + 6 will yield the same answer as 6 + n. 

Example #2

The difference of x and 9.

Key word : difference

Difference indicates subtraction. Start with the first number x. Then, subtract the second number 9.

The algebraic expression is x - 9

Notice that we wrote x first. The number after ' of ' is written down first.

Example #3

The difference of 9 and x.

The expression is 9 - x



Example #4

two less than m.

Key word : less than

Less than indicates subtraction. Subtract the first number 2 from the second number m

The algebraic expression is  m - 2

Notice that the phrase " two subtracted from m " is the same as the phrase " two less than m " 

Be careful! 

Two less than m is not the same as m less than two.

Let m = 5 for instance. two less than m is m - 2 = 5 - 2 = 3

However, m less than 2 is 2 - m = 2 - 5 = -3

Example #5

The product of x and 10

Key word : product

Product indicates multiplication. Multiply the first number x by the second number 10. We get x10, but we prefer to write 10x

The algebraic expression is  10x

Example #6

The quotient of n and 5

Key word : quotient

Quotient indicates division. Divide the first number n by the second number 5. 

The algebraic expression is  n / 5

Example #7

Six less than the product of 12 and y

Key word : six less and product

Product of 12 and y is 12y

Six less than the product of 12 and y is 12y - 6

Example #8

15 more than twice a number

Key word : more than and twice

Twice = two times

Let n be the number. 

The algebraic expression is 2n + 15





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