# What is a reciprocal? How can I find the reciprocal of a number?

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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 Review 1 whole

Let’s Review 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.

A Common Mistake Many people have an unclear understanding of what a reciprocal truly is. If I flip this fraction over, I will have a reciprocal… …but what does that mean? Reciprocal

Let’s Review Core Lesson What is a reciprocal? A reciprocal is one of a pair of numbers whose product is 1.

Let’s Review Core Lesson How do I determine the reciprocal of a whole number? To find the reciprocal of a whole number, divide “one” by the number.

Let’s Review Core Lesson 1 _ = ? 3 1 whole

Let’s Review Core Lesson 1 whole Let’s check… Yes, they are reciprocals! A reciprocal is one of a pair of numbers whose product is 1.

Let’s Review Core Lesson A reciprocal is one of a pair of numbers whose product is 1. I know that

Let’s Review Core 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!

Let’s Review Core Lesson To find the reciprocal of any number, divide “one” by the number.

Let’s Review Core Lesson My answer should be more than 1. 1 whole ? 12 3

Let’s Review Core Lesson To find the reciprocal of any number, divide “one” by the number.

Let’s Review Core Lesson and I know that

In this lesson you have learned about reciprocals by thinking about the inverse relationship between multiplication and division.

Let’s Review Guided Practice First, determine the reciprocal of the following numbers. 4 Then multiply to see if the product of the number and its reciprocal is “one”.

Let’s Review Extension 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. x CARD Check to be sure the product is “one”! Write the reciprocal here.

Let’s Review Extension Activities 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”?

Let’s Review Quick Quiz For each problem, first write the reciprocal of the number. Then multiply to show a product of “one”. 5

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