dividing fractions mentally
DESCRIPTION
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 PresentationTRANSCRIPT
Dividing fractions mentallyDividing 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...
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…
DDivision whenivision when the the numerator numerator
is divisible by numeratoris divisible by numerator
and and the the denominator by denominatordenominator by denominator
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)…
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:
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
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:
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:
DDividing natural number ividing natural number
by natural numberby natural number
2. Calculate:
a) 2 : 3 = __23
How much of pizzawill get each boy?
Imagine…
b) 3 : 2 = __32
= 1 __12
2. Calculate:How much of pizzawill get each girl?
Imagine…
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!
c) 15 : 5 = 3
2. Calculate: How many candieswill get each child?
Imagine…
c) 15 : 5 = 3
2. Calculate:
d) 5 : 15 = __515
= __13
Imagine…
How much of pizzawill get each child?
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!
c) 15 : 5 = 3
2. Calculate:
d) 5 : 15 = __515
= __13
e) 24 : 4 = 6
d) 4 : 24 = __424
= __16
Compare again…
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…
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
DDividing natural number by 2ividing natural number by 2
3. Say the settled solution:
a) 7 : 2 = 3 __12
Imagine…
How much strawberrieswill get each boy?
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:
DDividing natural number ividing natural number
by proper fraction by proper fraction
withwith numerator equal to 1numerator equal to 1
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
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
4. Calculate:
c) 8 : =__12
Just say the solution…
16
What is the question here?
4. Calculate:
d) 1 : =__13 3
__13
+ __13
= 1
3 times
+ __13
Let’s think:
How many times goes into 1 ?__13
4. Calculate:
e) 2 : =__13
Just say the solution…
6
What’s the question here?
Or…
4. Calculate:
f) 1 : =__14
Just say the solution…
4
What’s the question here?
Or…
4. Calculate:
g) 3 : =__15 15
Just say the solution…What’s the question here?
DDiviividing fractions and mixed numbersding fractions and mixed numbers
when the result is natural numberwhen the result is natural number
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
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
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
Is it enough?
T H E E N D
Author of presentation:
Antonija HorvatekAntonija HorvatekCroatia , January 2014
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Antonija Horvatekhttp://public.carnet.hr/[email protected]