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’s ReviewLet’s Review

x

_ = 3

1 whole

1 whole

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14

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14

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18

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= =

Let’s ReviewLet’s Review

2 _ = 3

2 _ 3 =

3 x = 2

x 3 = 2

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.

Let’s ReviewA Common Mistake

Many people have an unclear understanding of what a reciprocal truly is.

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If I flip this fraction over, I

will have a reciprocal…

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…but what does that

mean?

Reciprocal

Let’s ReviewCore Lesson

What is a reciprocal?

A reciprocal is one of a pair of numbers whose product is 1.

y x = = 1, so is the reciprocal of y.

x = = 1, so is the reciprocal of .

Let’s ReviewCore Lesson

How do I determine the reciprocal of a whole number?To find the reciprocal of a whole number, divide “one” by the number.

1 _ y = , so is the reciprocal of y.

Let’s ReviewCore Lesson

1 _ = ?

3

1 whole

1 _ 3 = , so is the reciprocal of 3.

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Let’s ReviewCore Lesson

1 whole x 3 = ?

Let’s check…

x = , and is equal to 1 whole.

Yes, they are reciprocals!

Does 3 x result in a product of

1 ?

A reciprocal is one of a pair of numbers whose product is 1.

Let’s ReviewCore Lesson

A reciprocal is one of a pair of numbers whose product is 1.

Since x 3 = 1, and 3 x = 1,

3 and are a pair of reciprocals.

I know that

Let’s ReviewCore Lesson

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.

…but that still doesn’t explain how

it works!

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Let’s ReviewCore Lesson

To find the reciprocal of any number, divide “one” by the number.

So I can find the reciprocal of by dividing 1 by ?

1 _ = ?

I have to ask myself, “How many are there

in one whole?”

Let’s ReviewCore Lesson

1 _ = ?

My answer should be

more than 1.

1 whole

1 whole

One set of …

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141 2 31

313

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13  of  

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1

Let’s ReviewCore Lesson

1 _ = 1

=

To find the reciprocal of any number, divide “one” by the number.

So I can find the reciprocal of by dividing 1 by ?

1 _ = , and that’s how to find the reciprocal of a fraction.

Let’s ReviewCore Lesson

x = = 1 x = = 1and

Since x = 1, and x = 1,

and are a pair of reciprocals. I know that

In this lesson you have learned about reciprocals by thinking about the inverse relationship

between multiplication and division.

Let’s ReviewGuided Practice

First, determine the reciprocal of the following numbers.

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Then multiply to see if the product of the number and its reciprocal is “one”.

Let’s ReviewExtension Activities

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.

Now SOLVE.

Place two cards as shown.

xCARD

CARD

Check to be sure the product is “one”!

Write the reciprocal here.

Let’s ReviewExtension Activities

Can a mixed number have a reciprocal?

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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”?

Let’s ReviewQuick Quiz

For each problem, first write the reciprocal of the number. Then multiply to show a product of “one”.

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