dividing fractions mentally

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Dividing fractions mentally Dividing fractions mentally

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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 :. - PowerPoint PPT Presentation

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Page 1: Dividing fractions mentally

Dividing fractions mentallyDividing fractions mentally

Page 2: Dividing fractions mentally

Mostly, we divide fractions in writing.Mostly, we divide fractions in writing.

However, in some cases we can divide them However, in some cases we can divide them

mentally.mentally.

It can be useful to know how to think in such cases.It can be useful to know how to think in such cases.

Let’s investigate it...Let’s investigate it...

Page 3: Dividing fractions mentally

In this presentation we’ll exercise:In this presentation we’ll exercise:

1st division when the numerator is divisible by 1st division when the numerator is divisible by

numerator and the denominator by denominatornumerator and the denominator by denominator

2nd dividing natural number by natural number,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, 3rd dividing natural number by 2, e.g. 9 : 2,

5th division when the result is natural number,5th division when the result is natural number,

e.g. 5 : 2 .e.g. 5 : 2 .____1122

4th4th dividing natural number by proper fraction with dividing natural number by proper fraction with

numerator equal to 1, npr. 4 : ,numerator equal to 1, npr. 4 : ,____1122

Let’s gooooo…Let’s gooooo…

Page 4: Dividing fractions mentally

DDivision whenivision when the the numerator numerator

is divisible by numeratoris divisible by numerator

and and the the denominator by denominatordenominator by denominator

Page 5: Dividing fractions mentally

1. Calculate:

a) 87

__2435__ : = __3

5

b) 89

__7263__ : = __9

7= 1 __2

7

Can we calculate so in this case:

421__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 onlyfrom the left to the right!In this case we should calculate in writting (not now)…

Page 6: Dividing fractions mentally

a) 87

__2435__ : = __3

5

b) 89

__7263__ : = __9

7= 1 __2

7

c) 29

__89__ : = __4

1= 4

Let’s think: How many times goes into ?__29

__89

__29

+ __29

+ __29

+ __29

= __89

4 times

We can imagine it…

1. Calculate:

Page 7: Dividing fractions mentally

a) 87

__2435__ : = __3

5

b) 89

__7263__ : = __9

7= 1 __2

7

c) 29

__89__ : = __4

1= 4

1. Calculate:

Let’s think: How many times goes into ?__29

__89

Page 8: Dividing fractions mentally

a) 87

__2435__ : = __3

5

b) 89

__7263__ : = __9

7= 1 __2

7

c) 29

__89__ : = __4

1= 4

d) 223__ : =__

1

__13

Imagine…Let’s think:

What part of pizzawill get each girl?

1. Calculate:

Page 9: Dividing fractions mentally

a) 87

__2435__ : = __3

5

b) 89

__7263__ : = __9

7= 1 __2

7

c) 29

__89__ : = __4

1= 4

d) 223__ : = __1

3

e) 489__ : =

Can you say the result?

29

__

Imagine…How much of the cakewill get each kid?

1. Calculate:

Page 10: Dividing fractions mentally

DDividing natural number ividing natural number

by natural numberby natural number

Page 11: Dividing fractions mentally

2. Calculate:

a) 2 : 3 = __23

How much of pizzawill get each boy?

Imagine…

Page 12: Dividing fractions mentally

b) 3 : 2 = __32

= 1 __12

2. Calculate:How much of pizzawill get each girl?

Imagine…

Page 13: Dividing fractions mentally

2. Calculate:

Let’s consider last two examples:

a) 2 : 3 = __23

b) 3 : 2 = __32

= 1 __12

Compare the given numbers in these examples!

They swapped places!

Compare the results?

Results are reciprocal!

In division, if numbers swap places, then we getreciprocal result!

Page 14: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate: How many candieswill get each child?

Imagine…

Page 15: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate:

d) 5 : 15 = __515

= __13

Imagine…

How much of pizzawill get each child?

Page 16: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate:

d) 5 : 15 = __515

= __13

Compare the given numbers and the results again…

Given numbers swapped places,and the results are reciprocal!

Page 17: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate:

d) 5 : 15 = __515

= __13

e) 24 : 4 = 6

d) 4 : 24 = __424

= __16

Compare again…

Page 18: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate:

d) 5 : 15 = __515

= __13

e) 24 : 4 = 6

d) 4 : 24 = __424

= __16

e) 8 : 40 = __15

Say settled solution…

Page 19: Dividing fractions mentally

c) 15 : 5 = 3

2. Calculate:

d) 5 : 15 = __515

= __13

e) 24 : 4 = 6

d) 4 : 24 = __424

= __16

e) 8 : 40 = __15

f) 9 : 72 = __18

g) 3 : 11 = __311

Page 20: Dividing fractions mentally

DDividing natural number by 2ividing natural number by 2

Page 21: Dividing fractions mentally

3. Say the settled solution:

a) 7 : 2 = 3 __12

Imagine…

How much strawberrieswill get each boy?

Page 22: Dividing fractions mentally

a) 7 : 2 = 3 __12

b) 11 : 2 = 5 __12

c) 27 : 2 = 13 __12

d) 40 : 2 = 20

e) 41 : 2 = 20 __12

f) 203 : 2 = 101 __12

3. Say the settled solution:

Page 23: Dividing fractions mentally

DDividing natural number ividing natural number

by proper fraction by proper fraction

withwith numerator equal to 1numerator equal to 1

Page 24: Dividing fractions mentally

4. Calculate:

a) 1 : =__12

Let’s think:

How many times goes into 1 ?__12

2

__12

+ __12

= 1

2 times

1st time 2nd time

Page 25: Dividing fractions mentally

4. Calculate:

b) 2 : =__12 4

__12

+ __12

= 2

4 times

+ __12

+ __12

1st 2nd 3rd 4th

Let’s think:

How many times goes into 2 ?__12

Page 26: Dividing fractions mentally

4. Calculate:

c) 8 : =__12

Just say the solution…

16

What is the question here?

Page 27: Dividing fractions mentally

4. Calculate:

d) 1 : =__13 3

__13

+ __13

= 1

3 times

+ __13

Let’s think:

How many times goes into 1 ?__13

Page 28: Dividing fractions mentally

4. Calculate:

e) 2 : =__13

Just say the solution…

6

What’s the question here?

Or…

Page 29: Dividing fractions mentally

4. Calculate:

f) 1 : =__14

Just say the solution…

4

What’s the question here?

Or…

Page 30: Dividing fractions mentally

4. Calculate:

g) 3 : =__15 15

Just say the solution…What’s the question here?

Page 31: Dividing fractions mentally

DDiviividing fractions and mixed numbersding fractions and mixed numbers

when the result is natural numberwhen the result is natural number

Page 32: Dividing fractions mentally

5. Calculate:

a) 3 : 1 __12 =

Let’s think:

How many times 1 goes into 3 ?__12

1st time 2nd time

2

__12

1 + __12

1 = 3

2 times

Page 33: Dividing fractions mentally

5. Calculate:

b) 4 : 1 __12

__12 =

Let’s think:

How many times 1 goes into 4 ?__12

__12

1st 2nd

3rd

3

__12

1 + __12

1 + __12

1 = __12

4

3 times

Page 34: Dividing fractions mentally

5. Calculate:

c) 10 : 2 __12 =

1st 2nd

3rd 4th

4

__12

2 + __12

2 + __12

2 + __12

2 = 10

4 times

Let’s think:

How many times 2 goes into 10 ?__12

Page 35: Dividing fractions mentally

Is it enough?

Page 36: Dividing fractions mentally

T H E E N D

Page 37: Dividing fractions mentally

Author of presentation:

Antonija HorvatekAntonija HorvatekCroatia , January 2014

Page 38: Dividing fractions mentally

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 Horvatekhttp://public.carnet.hr/[email protected]