Integer Equivalence Sample Problems

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Here are some tips for Integer Equivalence, which aligns with New York state standards:

Integer Equivalence

This topic will be easier if you know how to add and subtract integers.
To review the topic Integer Addition,see here.
To review the topic Integer Subtraction,see here.

An equivalent expression is created by 1) exchanging the position of the two integers and then, 2) simplifying the expression.

Expression Simplified expression Equivalent expression

a + b none b + a

a + ^- b a - b ^- b + a

a - b none ^- b + a

a - ^- b a + b b + a

Expression	Simplified expression	Equivalent expression
a + b	none	b + a
a + ^- b	a - b	^- b + a
a - b	none	^- b + a
a - ^- b	a + b	b + a

Example 1: Addition

Create an equivalent expression by reversing the two integers. Answer in simplest terms. Example: -4 + 3 = 3 - 4.

a. 10 + 7 =

b. 10 + ^- 7 =

c. ^- 10 + 7 = 7 + ^- 10 =

d. ^- 10 + ^- 7 = ^- 7 + ^- 10 =

Example 2: Subtraction

Create an equivalent expression by reversing the two integers. Answer in simplest terms. Example: -4 + 3 = 3 - 4.
For subtraction, it will be easier to first convert it into an addition problem and then reverse the integers.

a. 6 - 3 = 6 + ^- 3 =

b. 6 - ^- 3 = 6 + 3 =

c. ^- 6 - 3 = ^- 6 + ^- 3 = ^- 3 + ^- 6 =

d. ^- 6 - ^- 3 = ^- 6 + 3 = 3 + ^- 6 =