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Understanding Reciprocals of Fractions, Whole Numbers, and Mixed Numbers

Discover the concept of reciprocals, integral in mathematics! A reciprocal is a number you multiply by to achieve a product of 1. We'll explore how to find reciprocals of fractions, whole numbers, and mixed numbers through simple methods. Whether it's flipping fractions or converting whole numbers into fractions, this guide will help you master the art of finding reciprocals. Learn through engaging examples, practice problems, and memorable tips to reinforce your understanding of this essential concept.

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Understanding Reciprocals of Fractions, Whole Numbers, and Mixed Numbers

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Presentation Transcript

  1. 7 6 1 5 4 2 9 38 9 6 7 5 Reciprocals I can… find reciprocals of fractions, whole numbers, and mixed numbers.

  2. 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.

  3. 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.

  4. 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

  5. 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

  6. 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

  7. So, now that you know what reciprocals are – how do you find the reciprocal of anumber? It’s so easy!!! When you hear reciprocal – think RE-FLIP-RO-CAL!!!

  8. RE – FLIP – RO - CAL

  9. RE – FLIP – RO - CAL

  10. RE – FLIP – RO - CAL

  11. RE – FLIP – RO - CAL

  12. RE – FLIP – RO - CAL FLIP You think because you simply the fraction to get the reciprocal!

  13. Let’s practice finding the refliprocal – uh, I mean reciprocal – of some numbers. 4 15 1 6

  14. Some more – 26 9 4 31

  15. whole number written as a fraction reciprocal What if it’s a whole number? Write the whole number as a fraction, then FLIP it! 7 33

  16. whole number written as a fraction reciprocal If it’s a whole number, write the whole number as a fraction, then FLIP it! 16 57

  17. 2/5 5/2 4 1/4 Let’s review what we’ve learned so far. Write the reciprocal for each fraction or whole number. 1/2 2/1 or 2 12 1/12 6/10 10/6 55 1/55 1/3 3/1 or 3 47 1/47

  18. 4 9 ? 1 = x Let’s review what we’ve learned so far. Find the missing fraction for each number sentence. ? 1 13 x =

  19. 1 5 ? 1 = x Let’s review what we’ve learned so far. Find the missing fraction for each number sentence. ? 1 70 x =

  20. reciprocal 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 3 16 16 3 Now FLIP the improper fraction: 5 ⅓ =

  21. Improper Fraction: Reciprocal 2 8 3 Let’s practice finding the refliprocal of some mixed numbers. 10 6 1 7 4 5

  22. Improper Fraction: Reciprocal 2 3 7 Let’s practice finding the refliprocal of some mixed numbers. 30 4 1 20 1 2

  23. 1 5 4 ? 1 = x Let’s review what we’ve learned so far. Find the missing fraction for each number sentence. 3 10 1 ? 7 x =

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