Reciprocals
I can…
find reciprocals of fractions, whole
numbers, and mixed numbers.
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 the refliprocal – uh, I
mean 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!
whole number
written as a fraction
7
33
reciprocal
If it’s a whole number, write the whole
number as a fraction, then FLIP it!
whole number
written as a fraction
16
57
reciprocal
Let’s review what we’ve learned so far.
Write the reciprocal for each fraction or
whole number.
2/5
5/2
4
1/4
1/2
2/1 or 2
12
1/12
6/10 10/6
55 1/55
1/3
47
3/1 or 3
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
5⅓
16
=3
Now
FLIP the
improper
fraction:
3
16
Let’s practice finding the refliprocal of some
mixed numbers.
Improper
10
6
1
2
8
3
7
4
5
Fraction:
Reciprocal
Let’s practice finding the refliprocal of some
mixed numbers.
Improper
30
4
1
2
3
7
20
1
2
Fraction:
Reciprocal
Let’s review what we’ve learned so far.
Find the missing fraction for each
number sentence.
1
5
4 x?= 1
3
x
710
? =1