Reciprocals

I can…find reciprocals of fractions, whole numbers, and mixed numbers.

76 6

7

15

2 9

4 38 9 5

What is a reciprocal?Webster’s dictionary defines the word as “done, given, or felt equally on both sides”.

Examples: The two countries made a reciprocal trade agreement.

The two business partners had a reciprocal friendship based on respect for eachother.

But what does the word reciprocal mean in math?

A reciprocal in math is a number you

multiply by so that the result is 1.

Two numbers whose product is 1 are called reciprocal pairs.

Let’s look at some reciprocal pairs. Notice how when we multiply them, the

product is 1.

5 and 1/5

26 and 1/26

1/9 and 9

Here’s more examples of reciprocal pairs. Again, notice how when we multiply

them, the product is 1.

2/3 and 3/2

4/15 and 15/4

8/3 and 3/8

One last look at reciprocal pairs.

You’re catching on!!! The product is 1!

2 ½ and 2/5

6 ⅗ and 5/33

7 ⅔ and 3/23

So, now that you know what reciprocals are –

how do you find the reciprocal of a number?

It’s so easy!!! When you hear reciprocal –

think RE-FLIP-RO-CAL!!!

RE – FLIP – RO - CAL

RE – FLIP – RO - CAL

RE – FLIP – RO - CAL

RE – FLIP – RO - CAL

You think

because you simply the fraction to get the

reciprocal!

RE – FLIP – RO - CAL

FLIP

Let’s practice finding the refliprocal – uh, I mean reciprocal – of some numbers.

415

16

Some more –

26 9

431

What if it’s a whole number?

Write the whole number as a fraction, then FLIP it!

7 33

whole numberwritten as a fraction reciprocal

If it’s a whole number, write the whole number as a fraction, then FLIP it!

16 57

whole numberwritten as a fraction reciprocal

Let’s review what we’ve learned so far.Write the reciprocal for each fraction or whole number.

2/5 5/2 4

1/2 2/1 or 2

6/10

1/3

10/6

3/1 or 3

1/4

12

55

47

1/12

1/55

1/47

Let’s review what we’ve learned so far.Find the missing fraction for each number sentence.

49

x = 1?

13 1x? =

Let’s review what we’ve learned so far.Find the missing fraction for each number sentence.

15

x = 1?

70 1x? =

There’s one more part to today’s lesson—

What to do when finding the reciprocal of a mixed number?

• Write the mixed number as an improper fraction• Flip the improper fraction

5 ⅓ =16 3

Now FLIP the improper fraction:

316

reciprocal

Let’s practice finding the refliprocal of some mixed numbers.

10

6 1

82

73

54

Improper Fraction: Reciprocal

Let’s practice finding the refliprocal of some mixed numbers.

30

4 1

32

207

21

Improper Fraction: Reciprocal

Let’s review what we’ve learned so far.Find the missing fraction for each number sentence.

1 5

x = 1?

7 1x ? =

4

310