1. Chapter 7
Fractions

2. Learning Objectives Work out fractions of a shaded shape
Find equivalent fractions
Simplifying fractions
Writing fractions of 2 quantities
Change improper fractions into mixed numbers
Change mixed numbers into improper fractions
Add/ subtract fractions
Multiply fractions
Divide fractions
Problems involving fractions
Fractions on a calculator
Convert recurring decimals into fractions
Convert fractions to recurring decimals

3. Equivalent Fractions
You must multiply top (numerator) and bottom (denominator) by the same multiply
Examples
Write 3 equivalent fractions to ¾

4. Simplifying Fractions
Divide both top (numerator) and bottom (denominator) by the same number
Examples
Simplify the following
(a) 25/60
(b) 52/90
(c) Write 42 as a fraction of 80

5. Top-Heavy Fractions – Mixed Numbers
A top heavy fraction has the top bigger than the bottom
To convert a top heavy fraction into a mixed number divide the top by the bottom
The answer is the whole number bit
The remainder is the new top
The bottom stays the same

6. Examples Top-Heavy – Mixed Numbers
Change the following into mixed numbers
(a) 13/2
(b) 50/3
(c) 100/7
(d) 32/5

7. Mixed Numbers - Top-Heavy Fractions
A top heavy fraction has the top bigger than the bottom
To convert a mixed number into an improper fraction
New top = whole number × bottom + top
The bottom stays the same

8. Examples Mixed Numbers – Top-Heavy Fractions
Change the following into improper fractions
(a) 41/2
(b) 36/11
(c) 21/7
(d) 83/5

9. Finding Fractions of Quantities
Divide by the bottom and multiply by the top
Examples
2/5 of 60
2/3 of 12
1/5 of 30
8/12 of 24

10. Adding/ Subtracting Fractions
Make all fractions top-heavy (if possible)
Make all bottoms the same by multiply
Add the tops
Do not change the bottoms
Make all answers mixed numbers (if possible)
EXAMPLES
½ + ¾
½ + 1/9
3/8 + ¾

11. More Examples 33/10 – 15/8 ¾ + 2/3 11/10 – 5/6 34/7 – 25/8
33/16 – 25/24

12. Multiplying Fractions
Make all fractions top heavy if possible
Cancel (divide by the same number) any top and bottom
When no more cancelling can be done multiply the tops and multiply the bottoms
EXAMPLES
1. 2/5 × 12/21
2. 23/4 ×12/5
3. 25/8 × 31/3
4. 5/6 of 42/7

13. Dividing Fractions Make all fractions top-heavy if possible
Turn the fraction after the dividing sign up-side-down and multiply
EXAMPLES
13/5 ÷ 4/9
2/3 ÷ 5
22/15 ÷ 13/5
52/5 ÷ 12/3

14. Problems Involving Fractions
Jenny spends 3/5 of her money. If she has £1.40 left how much money did she have to start with?
In an experiment a weight is added to a spring. The spring increases by 2/5. It’s new length is 21 cm, what was it’s length before the weight was added?

15. Decimals to Fractions If 1 decimal place put it over 10
If 2 decimal places put it over 100
EXAMPLES
Change the following into fractions
0.45
0.5
0.81

16. Fractions into Decimals
Divide the top by the bottom
EXAMPLES
Change the following into decimals
4/5
108/200

17. Recurring Decimals Use dots to show recurring EXAMPLES
Change the following into decimals
1/3
1/6
6/13