Phrases to Algebraic Expressions Sample Problems

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Here are some tips for Phrases to Algebraic Expressions, which aligns with Arizona 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)