Dividing fractions mentally Mostly we divide fractions in

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Dividing fractions mentally

Dividing fractions mentally

Mostly, we divide fractions in writing. However, in some cases we can divide them

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: 1 st division when the numerator is divisible by

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

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

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

1. Calculate: a) 8 24 __ : __ 35 7 b) 8 72 __

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

1. Calculate: a) 8 24 __ : __ 35 7 b) 8 72 __

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

1. Calculate: a) 8 24 __ : __ 35 7 b) 8 72 __

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

1. Calculate: a) 8 24 __ : __ 35 7 b) 8 72 __

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

1. Calculate: a) 8 24 __ : __ 35 7 b) 8 72 __

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

Dividing natural number by natural number

Dividing natural number by natural number

2. Calculate: a) 2: 3 = 2 __ 3 Imagine… How much of pizza

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

2. Calculate: b) 1 3 __ __ = 1 3: 2 = 2 2

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

2. Calculate: Let’s consider last two examples: a) 2 __ 2: 3 = 3

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

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

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

2. Calculate: c) d) 15 : 5 = 3 5 : 15 = Imagine…

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

2. Calculate: c) d) 15 : 5 = 3 5 : 15 = 1

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

2. Calculate: c) 15 : 5 = 3 1 5 __ __ = 3

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

2. Calculate: c) 15 : 5 = 3 1 5 __ __ = 3

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

2. Calculate: c) 15 : 5 = 3 1 5 __ __ = 3

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

Dividing natural number by 2

Dividing natural number by 2

3. Say the settled solution: a) 1 __ 7: 2 = 3 2 Imagine…

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

3. Say the settled solution: a) 1 __ 7: 2 = 3 2 b)

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

Dividing natural number by proper fraction with numerator equal to 1

Dividing natural number by proper fraction with numerator equal to 1

4. Calculate: a) 1 __ 1: = 2 2 Let’s think: 1 __ How

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

4. Calculate: b) 1 __ 2: = 4 2 Let’s think: 1 __ How

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

4. Calculate: c) 1 __ 8: = 16 2 Whatsay is the here? Just

4. Calculate: c) 1 __ 8: = 16 2 Whatsay is the here? Just thequestion solution…

4. Calculate: d) 1 __ 1: = 3 3 Let’s think: 1 __ How

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

4. Calculate: e) 1 __ 2: = 6 3 What’s here? Just saythe thequestion

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

4. Calculate: f) 1 __ 1: = 4 4 What’s here? Just saythe thequestion

4. Calculate: f) 1 __ 1: = 4 4 What’s here? Just saythe thequestion solution… Or…

4. Calculate: g) 1 __ 3: = 15 5 What’s here? Just saythe thequestion

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

Dividing fractions and mixed numbers when the result is natural number

Dividing fractions and mixed numbers when the result is natural number

5. Calculate: a) 1 3 : 1 __ = 2 2 Let’s think: 1

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

5. Calculate: b) 1 1 4 __ : 1 __ = 3 2 2

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

5. Calculate: 1 c) 10 : 2 __ = 4 2 Let’s think: 1

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

Is it enoug h?

Is it enoug h?

E E H T D N

E E H T D N

Author of presentation: Antonija Horvatek Croatia , January 2014

Author of presentation: Antonija Horvatek Croatia , January 2014

You are welcome to use this presentation in your teaching. Additionally, you can change

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/~ahorvatek@yahoo. com