Inversion

Lyrics

Chorus
Inversion, you’ve got two types
One kind you add, one kind you multiply
(×4)

Verse I
The additive inverse of a number is its opposite
So when you add them together, you get zero out of it
It might sound a little complicated, but
I’m here to give you examples so you don’t have to fake it
(−7) + 7 is ZERO
3.2 + (−3.2), ZERO
1∕5 + (−1∕5), ZERO
Now watch your mathematical fear turn to ZERO

Chorus

Verse II
The multiplicative inverse is a number’s reciprocal
So when you multiply them, you know the typical answer is 1
And that’s why I’ve come
So let me tell everybody how it’s done
First off, you gotta have a fraction to start with
If you have an integer, put a 1 below
To find the multiplicative inverse, you know
Bring the bottom number up and put the top one below
7 × 1∕7 is ONE
8∕3 × 3∕8 is ONE
0.25 × 4 is ONE
Without a doubt, if you can’t do decimals, you better find out!

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Description

This song teaches the additive inverse, the number's opposite, explaining that the sum of the two will be zero. This song also explains the multiplicative inverse found by switching the numerator and denominator so that the product of the two numbers equals one. The teaching materials at the bottom of the page including worksheets, and lesson plans are resources for teachers and homeschool parents to generate teaching ideas for the song topic. Students will understand inversions and how to find them.

This math song is suitable to help teach inversions to elementary school students (4th grade, 5th grade and 6th grade), middle school, high school, home school, and college classes.

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Related Reading and Activities

Reading

Math is Fun
Inverse Relationships
This site provides clear simple explanations on inverse relationships in addition and multiplication.
Grades 5-8

Reciprocal
Using examples, this website explains how to form reciprocals for use in algebra. Simple and clear explanation.
Grades 5-8

Lesson Plans & Activities

Illinois Institute of Technology
Adding Integers
This activity teaches students about the additive inverse. A little tricky but useful.
Grades 6-8

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State Standards

State standards listed here are representative of school standards across the United States.

Illinois

7th & 8th Grades
8.C.3 - Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences.
8.A.3a - Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems.

Massachusetts

5th & 6th Grades
6.N.12 - Demonstrate understanding of inverse relationship of addition and subtraction. Use that understanding to simplify computation and solve problems.

7th & 8th Grades
8.N.9 - Use inverse relationships of addition and subtraction multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2.

New York

6th Grade
6.N.4 - Define and identify identity and inverse properties of addition and multiplication.
5.N.19 - Identify multiplicative inverse (reciprocal) of a number

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