# What is a reciprocal? How can I find 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. Lets Lets Review Review = = x _ 1 1 4 4

1 1 8 8 1 41 1 1 8 8 2 8 1 1 8 8

= 3 1 1 18whole 8 2 8 1 4 1 whole4 2 8

1 1 8 8 1 8 1 8 Lets Lets Review 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.

3 x =2 x 3 =2 2 _ 3 = 2 _ = 3 A Common Lets 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 2 3 3 2 2 3 2 3

but what does that mean? 3 3 2 2 Reciprocal CoreReview Lesson Lets What is a reciprocal? A reciprocal is one of a pair of numbers whose product is 1. y x x = = 1, so is the reciprocal of y.

= = 1, so is the reciprocal of . CoreReview Lesson Lets 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. CoreReview Lesson Lets 1 1 _3 = 3 ? 1 whole 1 _ 3 = , so is the reciprocal of 3.

CoreReview Lesson Lets A reciprocal is one of a pair of numbers whose product is 1. Does 3 x result in a product of 1? Lets check 1 whole x 3=? x = , and is equal to 1 whole. Yes, they are reciprocals! CoreReview

Lesson Lets A reciprocal is one of a pair of numbers whose product is 1. Since x 3 = 1, and 3 x = 1, I know that 3 and are a pair of reciprocals. CoreReview Lesson Lets 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 2 3 2 3 2 2 3 3 3 3 2 2 but that still doesnt explain how

it works! CoreReview Lesson Lets To find the reciprocal of any number, divide one by the number. 1_ =? So I can find the reciprocal of by dividing 1 by ? I have to ask myself, How many are there in one whole? CoreReview Lesson Lets My answer should be

more than 1. 1 _ = ?1 1 whole 1 1 1 3 4 1 1 1 1 1 whole 3 2 4

3 4 3 One set of 1 3? 1 3 of 3 4 CoreReview Lesson Lets To find the reciprocal of any number, divide one by the number.

So I can find the reciprocal of by dividing 1 by ? 1_ =1 = 1 _ = , and thats how to find the reciprocal of a fraction. CoreReview Lesson Lets x = = 1

Since and x x = = 1 = 1, and x = 1, I know that and are a pair of reciprocals. In this lesson you have learned about reciprocals by thinking about the inverse relationship between multiplication and

division. Guided Practice Lets 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 Extension Lets Review 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. Place two cards as shown. CARD x CARD Write the reciprocal here. Now SOLVE. Check to be sure the product is one!

Extension Lets Review 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? 2 3 5 Quick Quiz Lets Review For each problem, first write the reciprocal of the number. Then multiply to show a product of one.

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