A reciprocal in math is a number that is multiplied by another number to get the product of 1. Two numbers whose product is 1 are called reciprocal pairs. To find the reciprocal of a number, write the number as a fraction and flip the numerator and denominator. For whole numbers, write the number as a fraction first before flipping. To find the reciprocal of a mixed number, first write it as an improper fraction and then flip the numerator and denominator.

1. Reciprocals

2. 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 each
other.

3. 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.

4. 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

5. 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

6. 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

7. 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!!!

8. You think
because you simply
the fraction to get the
reciprocal!

9. Let’s practice finding reciprocal – of some
numbers.
4
15
1
6

10. Some more –
26
9
4
31

11. What if it’s a whole number?
Write the whole number as a fraction,
then FLIP it!
7
33
whole number
written as a fraction reciprocal

12. If it’s a whole number, write the whole
number as a fraction, then FLIP it!
16
57
whole number
written as a fraction reciprocal

13. 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

14. Let’s review what we’ve learned so far.
Find the missing fraction for each
number sentence.
4
9
x = 1
?
13 1
x?=

15. Let’s review what we’ve learned so far.
Find the missing fraction for each
number sentence.
1
5
x = 1
?
70 1
x?=

16. 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:
3
16

17. Let’s practice finding the refliprocal of some
mixed numbers.
10
6
1
8
2
7
3
5
4
Improper
Fraction: Reciprocal

18. Let’s practice finding the refliprocal of some
mixed numbers.
30
4
1
3
2
20
7
2
1
Improper
Fraction: Reciprocal

19. Let’s review what we’ve learned so far.
Find the missing fraction for each
number sentence.
1
5
x = 1
?
7 1
x ? =
4
3
10