1. Fractions, Decimals and Percentages
Interchanging
Fractions, Decimals
and Percentages

2. What area is shaded?

3. 1/2 ? ? 50% 0.5 ? Answers All 3 numbers mean the same thing. Fraction:
Percentage:
Decimal: ?
50%
0.5 ?
All 3 numbers mean the same thing.

4. Interchanging
Fractions, decimals and percentages can all be used to describe parts of a whole.
It is therefore possible to interchange them.

5. More shapes Here are some more shaded shapes.
Can you describe the shaded areas using fractions, percentages and decimals?

6. Can you name the Fraction. Percentage & Decimal?
1/4 ? ?
25%
0.25 ?

7. Can you name the Fraction, Percentage & Decimal?
3/10 ? ?
30%
0.3 ?

8. Missing Pages

9. Can you name the Fraction. Percentage & Decimal?
6/25 ? ?
24%
0.24 ?

10. Interchanging
Without Pictures

11. Interchanging
You don’t need a picture to interchange Fractions, Decimals & Percentages.
There are calculations that will do the job quickly and easily.

12. Decimals & Percentages
Interchanging
Decimals & Percentages

13. Decimals & Percentages
Percentages are a measure out of 100.
Decimals are a measure out of 1.
To change a decimal into a percentage you multiply by 100.
To change a percentage into a decimal you divide by 100.

14. The diagram illustrates this.
Decimals
Percentages
x 100
100

15. Decimals to Percentages
0.45 =
0.67 =
0.12 =
0.30 =
45%
67%
12%
30%

16. Missing Pages

17. Percentages to Decimals
10% =
5% =
11.1% =
888% =
0.1
0.05
0.111
8.88

18. Percentages to Fractions
Interchanging
Percentages to Fractions

19. Percentages to Fractions
A percentage is already a type of fraction.
To be precise, a percentage is a fraction of one hundred.
To change a percentage into a fraction, you first put the percentage over 100, then simplify.

20. Here is an example
60% =
100
20 = 60 ? 3 ?
20 = ? 5

21. Now try this one.
70% =
100
10 = 70 ? ? 7
10 = 10 ?

22. Missing Pages

23. Try working out these. 10% = 80% = 22% = 15% = 7% = 98% = 48% = 1/10
10% =
80% =
22% =
15% =
7% =
98% =
48% =
1/10
4/5
11/50
3/20
7/100
49/50
12/25

24. Interchanging
Fractions to Decimals

25. Fractions to Decimals
You might not realise it, but a fraction is actually a division sum!
For example the fraction ¾ is the division sum 3  4.
When you do the sum you get the decimal.
The only tricky bit is doing the sum.

26. ¾ as a decimal. 3 4 =
4 3

27. So how many 4s go into 3?
0 remainder 3 3
. 0 0 . =
4 3 3 4

28. How many 4’s in 30?
7 remainder 2 3
. 0 0 . 7 =
4 3 3 2 4

29. Missing Pages

30. The answer …
0.75 3 4 = 2
4 3 7 5
. 0 0 .

31. Try these 1/2 = 1/4 = 1/5 = 3/10 = 4/5 = 9/10 = 1/8 = 0.5 0.25 0.2 0.3
1/2 =
1/4 =
1/5 =
3/10 =
4/5 =
9/10 =
1/8 =
0.5
0.25
0.2
0.3
0.8
0.9
0.125

32. Interchanging Fractions, Decimals & Percentages
By S. Howarth
ORB Education
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