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Dividing fractions mentally

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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...

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

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Division when the numerator is divisible by numerator and the denominator by denominator and the denominator by denominator

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1. Calculate: a) 8 7 __ 24 35 __ : = 3 5 b) 8 9 __ 72 63 __ : = 9 7 =1 2 7 Can we calculate so in this case: 4 21 __ 32 3 __ : 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)…

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

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

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a) 8 7 __ 24 35 __ : = 3 5 b) 8 9 __ 72 63 __ : = 9 7 =1 2 7 c) 2 9 __ 8 9 : = 4 1 =4 d) 2 2 3 __ : = 1 1 3 Imagine… Let’s think: What part of pizza will get each girl? 1. Calculate:

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

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Dividing natural number by natural number

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

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

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

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

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

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

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

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

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

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Dividing natural number by 2

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

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

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Dividing natural number by proper fraction with numerator equal to 1

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4. Calculate: a) 1 : = __ 1 2 Let’s think: How many times goes into 1 ? __ 1 2 2 1 2 + 1 2 =1 2 times 1st time2nd time

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

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

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

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

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

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

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Dividing fractions and mixed numbers when the result is natural number

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

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5. Calculate: b) 4 : 1 __ 1 2 1 2 = Let’s think: How many times 1 goes into 4 ? __ 1 2 1 2 1st2nd 3rd 3 __ 1 2 1 + 1 2 1 + 1 2 1 = 1 2 4 3 times

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5. Calculate: c) 10 : 2 __ 1 2 = 1st2nd 3rd 4th 4 __ 1 2 2 + 1 2 2 + 1 2 2 + 1 2 2 =10 4 times Let’s think: How many times 2 goes into 10 ? __ 1 2

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Is it enough?

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T H E E N D

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Author of presentation: Antonija Horvatek Croatia, January 2014

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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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Multiplying fractions mentally

Multiplying fractions mentally

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