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Reciprocals
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.
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!!!
You think
because you simply
the fraction to get the
reciprocal!
Let’s practice finding reciprocal – of some
numbers.
4
15
1
6
Some more –
26
9
4
31
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
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
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.
4
9
x = 1
?
13 1
x?=
Let’s review what we’ve learned so far.
Find the missing fraction for each
number sentence.
1
5
x = 1
?
70 1
x?=
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
Let’s practice finding the refliprocal of some
mixed numbers.
10
6
1
8
2
7
3
5
4
Improper
Fraction: Reciprocal
Let’s practice finding the refliprocal of some
mixed numbers.
30
4
1
3
2
20
7
2
1
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 1
x ? =
4
3
10

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Reciprocals ppt lesson 1

  • 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
  • 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