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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