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Dividing fractions mentally

Dividing fractions mentally. Mostly , we divide fractions in writing. However , in some cases we can divide them mentally. It can be useful to know how to think in such cases. Let’s investigate it. In this presentation we ’ll exercise :.

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Dividing fractions mentally

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  1. Dividingfractionsmentally

  2. Mostly, wedividefractionsinwriting. However, in some caseswecandividethem mentally. Itcanbeuseful to know how to thinkinsuchcases. Let’s investigateit...

  3. Inthispresentationwe’ll exercise: 1st division when the numerator is divisible by numerator and the denominator by denominator 2nd dividing natural number by natural number, e.g. 4 : 7, 3rd dividing natural number by 2, e.g. 9 : 2, 4thdividingnaturalnumberbyproperfractionwith numerator equal to 1, npr. 4 : , 1 __ 2 5th division when the result is natural number, 1 __ e.g. 5 : 2 . Let’s gooooo… 2

  4. Division whenthenumerator is divisible by numerator and thedenominator by denominator

  5. 72 32 24 8 4 8 __ __ __ __ __ __ 35 63 21 3 7 9 1. Calculate: 3 __ : : : a) b) = = 5 9 2 __ __ = 1 7 7 Can we calculate so in this case: ? No, because 3 is not divisible by 21 ! (21 is divisible by 3) It’s not allowed to divide from right to the left, but only from the left to the right! In this case we should calculate in writting (not now)…

  6. 24 72 8 8 8 2 __ __ __ __ __ __ 35 63 9 9 7 9 1. Calculate: 3 __ : : : c) b) a) = = = 5 9 2 __ __ = 1 7 7 4 __ = 4 1 We can imagine it… 8 2 __ __ Let’s think: Howmanytimesgoesinto ? 9 9 + + + = 2 2 2 2 8 __ __ __ __ __ 9 9 9 9 9 4 times

  7. 24 72 8 8 2 8 __ __ __ __ __ __ 35 63 9 7 9 9 1. Calculate: 3 __ : : : c) b) a) = = = 5 9 2 __ __ = 1 7 7 4 __ = 4 1 8 2 __ __ Let’s think: Howmanytimesgoesinto ? 9 9

  8. 24 72 8 2 2 8 8 __ __ __ __ __ __ __ 35 63 3 9 9 7 9 1. Calculate: 3 __ : : : : c) b) d) a) = = = = 2 5 9 2 __ __ = 1 7 7 4 __ = 4 1 1 __ __ 3 1 Let’s think: Whatpartofpizza willgeteachgirl? Imagine…

  9. 72 24 8 2 8 8 2 8 __ __ __ __ __ __ __ __ 35 63 9 9 3 9 9 7 1. Calculate: 3 __ : : : : : c) a) e) b) d) 4 = = = = = 2 5 9 2 __ __ = 1 7 7 4 __ = 4 1 1 __ 3 2 __ 9 How much of the cake will get each kid? Can you say the result? Imagine…

  10. Dividingnatural number by natural number

  11. 2. Calculate: 2 __ a) 2 : 3 = 3 Imagine… How much of pizza will get each boy?

  12. 2. Calculate: How much of pizza will get each girl? 1 3 __ __ = 1 b) 3 : 2 = 2 2 Imagine…

  13. 2. Calculate: Let’s consider last two examples: 2 __ a) 2 : 3 = 3 1 3 __ __ = 1 b) 3 : 2 = 2 2 Compare the given numbers in these examples! In division, if numbers swap places, then we get reciprocal result! They swapped places! Compare the results? Results are reciprocal!

  14. 2. Calculate: How many candies will get each child? c) 15 : 5 = 3 Imagine…

  15. 2. Calculate: How much of pizza will get each child? c) 15 : 5 = 3 1 5 __ __ = d) 5 : 15 = 3 15 Imagine…

  16. 2. Calculate: c) 15 : 5 = 3 1 5 __ __ = d) 5 : 15 = 3 15 Compare the given numbers and the results again… Given numbers swapped places, and the results are reciprocal!

  17. 2. Calculate: c) 15 : 5 = 3 1 5 __ __ = d) 5 : 15 = 3 15 e) 24 : 4 = 6 1 4 __ __ = d) 4 : 24 = 6 24 Compare again…

  18. 2. Calculate: c) 15 : 5 = 3 1 5 __ __ = d) 5 : 15 = 3 15 e) 24 : 4 = 6 1 4 __ __ = d) 4 : 24 = 6 24 1 __ e) 8 : 40 = 5 Say settled solution…

  19. 2. Calculate: c) 15 : 5 = 3 1 5 __ __ = d) 5 : 15 = 3 15 e) 24 : 4 = 6 1 4 __ __ = d) 4 : 24 = 6 24 1 __ e) 8 : 40 = 5 1 __ f) 9 : 72 = 8 3 __ g) 3 : 11 = 11

  20. Dividingnatural number by 2

  21. 3. Say the settled solution: How much strawberries will get each boy? 1 __ a) 7 : 2 = 3 2 Imagine…

  22. 3. Say the settled solution: 1 __ a) 7 : 2 = 3 2 1 __ b) 11 : 2 = 5 2 1 __ c) 27 : 2 = 13 2 d) 40 : 2 = 20 1 __ e) 41 : 2 = 20 2 1 __ f) 203 : 2 = 101 2

  23. Dividingnatural number by proper fraction withnumerator equal to 1

  24. 4. Calculate: Let’s think: How many times goes into 1 ? 1 __ 1 __ a) 1 : = 2 2 2 1st time 2nd time 1 1 __ __ + = 1 2 2 2 times

  25. 4. Calculate: Let’s think: How many times goes into 2 ? 1 __ 1 __ b) 2 : = 2 4 2 2nd 4th 1st 3rd 1 1 1 1 __ __ __ __ + + + = 2 2 2 2 2 4 times

  26. 4. Calculate: 1 __ c) 8 : = 16 2 What is the question here? Just say the solution…

  27. 4. Calculate: Let’s think: How many times goes into 1 ? 1 __ 1 __ d) 1 : = 3 3 3 1 1 1 __ __ __ 3 3 3 + + = 1 3 times

  28. 4. Calculate: 1 __ e) 2 : = 6 3 What’s the question here? Just say the solution… Or…

  29. 4. Calculate: 1 __ f) 1 : = 4 4 What’s the question here? Just say the solution… Or…

  30. 4. Calculate: 1 __ g) 3 : = 15 5 What’s the question here? Just say the solution…

  31. Dividingfractionsandmixednumbers when the result is natural number

  32. 5. Calculate: Let’s think: How many times 1 goes into 3 ? 1 __ a) 3 : 1 2 2 = 1st time 2nd time 1 1 1 __ __ __ + = 3 1 1 2 2 2 2 times

  33. 5. Calculate: Let’s think: How many times 1 goes into 4 ? 1 __ 1 __ b) 4 : 1 2 3 = 2 1st 2nd 3rd 1 1 1 1 1 1 __ __ __ __ __ __ 1 4 1 1 2 2 2 2 2 2 + + = 3 times

  34. 5. Calculate: Let’s think: How many times 2 goes into 10 ? 1 __ c) 10 : 2 2 4 = 1st 2nd 1 1 1 1 1 __ __ __ __ __ 3rd 4th 2 2 2 2 2 2 2 2 2 + + + = 10 4 times

  35. Is it enough?

  36. T H E E N D

  37. Authorofpresentation: Antonija Horvatek Croatia, January 2014

  38. You are welcome to use this presentation in your teaching. Additionally, you can change some parts of it if used solely for teaching. However, if you want to use it in public lectures, workshops, websites,in writing books, articles, on CDs or any public forum or for any commercial purpose, please ask for specific permission from the author. Antonija Horvatek http://public.carnet.hr/~ahorvate ahorvatek@yahoo.com

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