*Contributor: Briana Pincherri. Lesson ID: 11218*

Pancakes are flipped, lids are flipped, even houses are flipped! But numbers? That's what you have to do to find a number's (or fraction's) reciprocal! It's easy to do so practice online and flip out!

categories

subject

Math

learning style

Visual

personality style

Lion, Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Can you do a flip forward, backward, or even sideways? This lesson focuses on flipping, but not the tumbling, aerial type of flips you associate with gymnasts and high divers. This type of flipping involves numbers, and no trampolines or tumbling tracks are required. In fact, this flip is one of the easiest tricks you will ever learn (guaranteed to be easier than a backflip), and it's even quite useful!

"Reciprocal."

Say it out loud a few times (Ree-SIP-row-cal). It really is a fun word to say!

A "reciprocal" is simply what we take times a number to get "1," and it is VERY easy to find.

*Reciprocal* may sound fancy; however, all that it actually means is to turn a number upside down. Here are a few examples:

Do you notice anything from these examples?

Take a look at the examples that are *not* fractions, those that start with a whole number (4 and 22). What do you notice is similar about their reciprocals? What about the ones that start as fractions? Do you notice anything about their reciprocals?

Hopefully, you have noticed that to get a reciprocal, you do one of two things:

- For whole numbers (4 and 22), you simply put the number under 1.
- For fractions (½ and ¾), you simply "flip" the fraction so that what was the numerator (the top number) is now the denominator (bottom number).

There are no catches and no extra tricks — that is it!

You will use reciprocals in math when multiplying and dividing fractions, so it is a great (and easy) skill to learn now.

Before you get to practicing, let's take a quick look at one thing. What do you get when you multiply a number times its reciprocal?

As you can see, each number times its reciprocal is "1." This is because a reciprocal is a *multiplicative inverse* of a number. A multiplicative inverse is what we multiply a number by to get 1. See how the definition of reciprocal and multiplicative inverse are the same thing? That is because a reciprocal *is* a multiplicative inverse!

Now it is time for you to try your hand at flipping numbers to find the reciprocal!

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