Reciprocals: Flip Them! Educational Resources K12 Learning, Arithmetic, Fractions and Operations, Rules and Properties, Math Lesson Plans, Activities, Experiments, Homeschool Help

Lesson Plan - Get It!

Audio:

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:

Number			Reciprocal
^Number			^Reciprocal
	4	=		1
	4	=		4
^Number			^Reciprocal
	1	=		5
	5	=		1
^Number			^Reciprocal
	22	=		1
	22	=		22
^Number			^Reciprocal
	3	=		4
	4	=		3

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?

	4	x	1	=	1
			4
nnn
	1	x	5	=	1
	5		1
nnn
	22	x	1	=	1
			22
nnn
	3	x	4	=	1
	4		3

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.