What is a reciprocal? How can I find
the reciprocal of a number?
In this lesson you will learn
about reciprocals by thinking
about the inverse relationship
between multiplication and
division.
Let’sReview
Review
Let’s
2
2 = 4 = 1
x
24
6
3
8
3
_
4
11
44
11
88
1
4
11
88
2
8
1 whole
1
8
11
88
2
= 3
8
1
4
1
4
11
88
11
88
1 whole
2
2
8
8
1
1
8
8
Let’sReview
Review
Let’s
Multiplication and division are inverse
operations. You can use multiplication to
check your division. A set of related facts,
with inverse operations, is called a fact
family.
1
3
1
3
x
=2
2
3
4
1
1
3
2
_ 3
=
2
3
4
3
1
1
x 3
=2
2
3
4
1
3
1
2
_
= 3
2
3
4
A Common
Let’s
Review Mistake
Many people have an unclear understanding
of what a reciprocal truly is.
If I flip this
fraction over, I
will have a
reciprocal…
2
3
…but what
does that
mean?
3
2
Reciprocal
CoreReview
Lesson
Let’s
What is a reciprocal?
A reciprocal is one of a pair of numbers
whose product is 1.
y
1
1
y x
=
= 1, so
is the reciprocal of y.
y
y
y
a
b
ab
a
b
x
=
= 1, so
is the reciprocal of .
a
a
b
ab
b
CoreReview
Lesson
Let’s
How do I determine the reciprocal of a
whole number?
To find the reciprocal of a whole number,
divide “one” by the number.
1
1
1 _ y = , so
is the reciprocal of y.
y
y
CoreReview
Lesson
Let’s
1
1_3 =?
3
1
1
3
1
1
whole
3
3
1
1
1 _ 3 = , so
is the reciprocal of 3.
3
3
CoreReview
Lesson
Let’s
A reciprocal is one of a pair of numbers
whose product is 1.
1
3
result in a
product of 1 ?
Does 3 x
Let’s check…
1
1
1 whole
1
3
3
3
1
x 3=?
3
1
3 3
3
x
=
, and is equal to 1 whole.
1 3
3
3
Yes, they are reciprocals!
CoreReview
Lesson
Let’s
A reciprocal is one of a pair of numbers
whose product is 1.
1
1
Since
x 3 = 1, and 3 x
= 1,
3
3
I know that
1
3 and are a pair of reciprocals.
3
CoreReview
Lesson
Let’s
What is a reciprocal of a fraction?
A fraction reciprocal is one of a pair of
fractions whose product is 1.
When you invert a fraction (turn it
upside down), you have its reciprocal.
2
3
3
2
…but that still
doesn’t
explain how
it works!
CoreReview
Lesson
Let’s
To find the reciprocal of any number,
divide “one” by the number.
So I can find the
3
reciprocal of by
4
3
dividing 1 by
?
4
3
1_
=?
4
I have to ask myself,
3
“How many are there
4
in one whole?”
CoreReview
Lesson
Let’s
My answer
should be
more than 1.
1
3
1_
= ?1
3
4
1 whole
1
1
4
3
11 1 whole 1
3
2
34
3
One set of …
4
4
3
1
?
3
1
of
3
3
CoreReview
Lesson
Let’s
To find the reciprocal of any number,
divide “one” by the number.
So I can find the
3
reciprocal of by
4
3
dividing 1 by
?
4
3
1
4
1_
=1
=
3
4
3
3
4
1_
=
, and that’s how to
3
4
find the reciprocal of a fraction.
CoreReview
Lesson
Let’s
3
4
12
x
=
= 1
12
3
4
and
4
3
12
x
=
= 1
12
3
4
3
4
4
3
Since
x
= 1, and
x
= 1,
3
3
4
4
I know that
4
3
and are a pair of reciprocals.
3
4
In this lesson you have
learned about reciprocals by
thinking about the inverse
relationship between
multiplication and division.
Guided
Practice
Let’s
Review
First, determine the reciprocal of the
following numbers.
Then multiply to see if the product of
the number and its reciprocal is “one”.
4
5
8
Extension
Let’s
ReviewActivities
Use a deck of cards (1 – 10 only) to create
a fraction. Write the fraction on a
whiteboard or scrap paper. Then write its
reciprocal. Multiply to show that the
product is equal to one.
Place two
cards as
shown.
CARD
x
CARD
Write the
reciprocal
here.
Now SOLVE.
Check to be sure the product is “one”!
Extension
Let’s
ReviewActivities
Can a mixed number have a reciprocal?
Look at the mixed number. Write the number
that you think could be its reciprocal.
Multiply the number by the reciprocal. Does it
have a product of “one”?
3
2
5
Quick
Quiz
Let’s
Review
For each problem, first write the
reciprocal of the number. Then multiply
to show a product of “one”.
5
3
8