Phrases to Algebraic Expressions Sample Problems

Math Practice Online > free > lessons > Texas > 8th grade > Phrases to Algebraic Expressions

If your child needs math practice, click here.

For sample problems, click here.
Here are some tips for Phrases to Algebraic Expressions, which aligns with Texas state standards:

Phrases to Algebraic Expressions

Note: When writing the algebraic expressions, follow the phrases exactly. So pay close attention to what the problem says.

For example, '5 subtracted from x' has only one translation: 'x - 5'
The phrase '5 added to x' only translates to 'x + 5' for this topic.
The phrase '5 added to x' does not translates to '5 + x' even though that is an equivalent expression.

This table shows you basic phrases translated to algebraic expressions.

	Phrases	Expressions
Addition:	30 added to k	k + 30
	30 increased by k	30 + k
	30 plus k	30 + k
Subtraction:	h subtracted by m	h - m
	h subtracted from m	m - h
	the difference of h and m	h - m
	h minus m	h - m
Multiplication:	the product of -31 and negative seven	-31*-7
	the product of -31 and negative seven and x	-31*-7x
	31 times negative seven	31*-7
	31 times x	31x
Inequalities:	b is greater than 12	b > 12
	b is greater than or equal to 12	b >= 12
	b is less than or equal to 12	b <= 12
	b is equal to 12	b = 12

Example 1:

Convert to an algebraic expression. Use * for multiplication and / for division.
the product of -39 and (f added to c) is equal to b increased by 14 minus g

The statement can be broken into 3 parts and translated:

the product of -39 and (f added to c) is equal to b increased by 14 minus g

the product of -39 and (c + f) = b + 14 minus g

the product of -39 and (c + f) = b + 14 minus g

-39*(c + f) = b + 14 - g

The statement becomes

Example 2:

Convert to an algebraic expression. Use * for multiplication and / for division.
the product of -6, eleven, and c is greater than or equal to -13 times (one added to negative thirty-two)

The statement can be broken into 3 parts and translated:

the product of -6, eleven, and c is greater than or equal to -13 times (one added to negative thirty-two)

the product of -6, 11, and c >= -13 times (-32 + 1)

the product of -6, 11, and c >= -13 times (-32 + 1)

the -6*11*c >= -13*(-32 + 1)

The statement becomes

the product of -39 and (f added to c)	is equal to	b increased by 14 minus g
the product of -39 and (c + f)	=	b + 14 minus g
the product of -39 and (c + f)	=	b + 14 minus g
-39*(c + f)	=	b + 14 - g

the product of -6, eleven, and c	is greater than or equal to	-13 times (one added to negative thirty-two)
the product of -6, 11, and c	>=	-13 times (-32 + 1)
the product of -6, 11, and c	>=	-13 times (-32 + 1)
the -611c	>=	-13*(-32 + 1)