1. Dividing fractions mentally

2. Mostly, we divide fractions by 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...

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

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

5. 1. Calculate: a) 8 7 __ 24 35 ÷ = __ 3 5 b) 8 9 __ 72 63 ÷ = __ 9 __ 2 = 1 7 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 left, but only
from the left to right!
In this case we should calculate in writing (not now)…

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

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

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

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

10. Dividing a natural number
by a natural number

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

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

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

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

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

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

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

18. 2. Calculate:
c) ÷ 5 = 3 __ 5 __ 1
d) 5 ÷ 15 = = 15 3
e) ÷ 4 = 6 __ 4 __ 1
d) 4 ÷ 24 = = 24 6 __ 1
e) 8 ÷ 40 = 5
Just give the final answer…

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

20. Dividing a natural number by 2

21. 3. Give the final answer:
How much strawberries
will each boy get? __ 1
a) 7 ÷ 2 = 3 2
Imagine…

22. 3. Give the final answer: __ 1
a) 7 ÷ 2 = 3 2 __ 1
b) ÷ 2 = 5 2 __ 1
c) ÷ 2 = 13 2
d) ÷ 2 = 20 __ 1
e) ÷ 2 = 20 2 __ 1
f) ÷ 2 =
101 2

23. Dividing a natural number with the numerator equal to 1
by a proper fraction
with the numerator equal to 1

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

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

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

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

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

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

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

31. Dividing fractions and mixed numbers
when the result is a natural number

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

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

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

35. Is it enough?

36. T H E E N D

37. for support and help with the translation into fluent U.S. idiom
With thanks to:
Rex Boggs
for support and help with the
translation into fluent U.S. idiom
(a.k.a. ‘American’).

38. Author of presentation:
Antonija Horvatek
Croatia , January 2014

39. 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