Mostly, we divide fractions by writing.Mostly, we divide fractions by 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 practice:In this presentation we’ll practice:
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 a natural number by a natural number,2nd dividing a natural number by a natural number,
e.g. 4 ÷ 7,e.g. 4 ÷ 7,
3rd dividing a natural number by 2, e.g. 9 ÷ 2, 3rd dividing a 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 a natural number by a proper fraction dividing a natural number by a proper fraction
with the numerator equal to 1, e.g. 4 ÷ ,with the numerator equal to 1, e.g. 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 left, but onlyfrom the left to right!In this case we should calculate in writing (not now)…
c) 29
__89__ ÷ = __4
1= 4
Let’s think: How many times does go 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
__41
= 4
1. Calculate:
a) 87
__2435__ ÷ = __3
5
b) 89
__7263__ ÷ = __9
7= 1 __2
7
c) 29
__89__ ÷ =
Let’s think: How many times does go into ?__29
__89
d) 223__ ÷ =__
1
__13
Imagine…Let’s think:
What part of the pizzawill each girl get?
1. Calculate:
__41
= 4
a) 87
__2435__ ÷ = __3
5
b) 89
__7263__ ÷ = __9
7= 1 __2
7
c) 29
__89__ ÷ =
__13
e) 489__ ÷ =
Can you say the result?
29
__
Imagine…How much of the cakewill each kid get?
1. Calculate:
__41
= 4
a) 87
__2435__ ÷ = __3
5
b) 89
__7263__ ÷ = __9
7= 1 __2
7
c) 29
__89__ ÷ =
d) 223__ ÷ =
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!
The result is the reciprocal!
In division, if numbers swap places, then we getthe reciprocal!
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 result is the 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
Just give the final answer…
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
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. Give the final answer:
DDividing ividing a a natural number natural number
by by a a proper fraction proper fraction
withwith the the numerator equal to 1numerator equal to 1
4. Calculate:
a) 1 ÷ =__12
Let’s think:
How many times does go into 2 ?__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 does go into 1 ?__12
4. Calculate:
d) 1 ÷ =__13 3
__13
+ __13
= 1
3 times
+ __13
Let’s think:
How many times does go into 1 ?__13
DDiviividing fractions and mixed numbersding fractions and mixed numbers
when the result is when the result is a a natural numbernatural number
5. Calculate:
a) 3 ÷ 1 __12 =
Let’s think:
How many times does 1 go 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 does 1 go 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 does 2 go into 10 ?__12
With thanks to:
Rex BoggsRex Boggsfor support and help with the translation into fluent U.S. idiom (a.k.a. ‘American’).
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Antonija Horvatekhttp://www.antonija-horvatek.from.hr/ [email protected]