1. Calculate with Fractions
Calculate with fractions including problem solving
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2. Key vocabulary
Numerator Denominator Equivalent Improper Fraction Mixed Number Simplify

3. Fractions - introduction
Which fraction is not equivalent to ¼
There are only black and green pens in a box. The ratio of the number of black to green is 2 : 5. What fraction of the pens are black?
What fraction of the students in the class 11A are girls? 2 7 15 29
ABCD is a square drawn accurately. What fraction of the square is shaded? + + 1 64
Write as a fraction in its simplest form. 3 4 1 16 = 75
1000 3 40 = 1 4 × 1 4 1 16
There are 35 pens in a box. 15 are green and the rest are red. What fraction of the pens in the box are red? = 1 16 1 64 = + + × 1 4 20 35 4 7 = 48 64 4 64 1 64 53 64

4. Convert mixed / improper
1 4
9 4 2
3 7
24 7 3
4 5
9 5 1
2 9
47 9 5
1 4
13 4 3

5. Mixed fractions practice
=1 6 35
(a)
(b) 7 9 − 2 5
(c)
(d) −3 2 7
(e)
(f) 2 3 − 1 4
(g) 4 7 × 3 5
(h) 7 9 ÷ 2 5
(i) ÷ 2 5
(j) × 5 27
(k) ÷ 6 18
(l) 2 3 ÷ 1 7 = = = =
= 6 3 7 =
= 1 6 =
= 2 2 5
= 5 12
= 4 2 3

6. Calculating with fractions (1)
Austin has gone shopping. He spends minutes walking from the bus into the town. He then spends minutes in ‘supersaves’, minutes in ‘station fun’ and then another minutes walking back to the bus stop.
What is the total time he spent in town?
= = around 45 minutes

7. Calculating with fractions (2)
Jim gave his DVDs away to 3 of his friends.
Archie received of them, and Bert received of them. Charlie received the rest.
(a) What fraction of the games did Charlie receive?
(b) How many games could Jim have had altogether?
(c) Is this the only number Jim could have had?
(a) 𝟑 𝟕 + 𝟐 𝟗 =
𝟐𝟕 𝟔𝟑 + 𝟏𝟒 𝟔𝟑 = 𝟒𝟏 𝟔𝟑
𝟔𝟑 𝟔𝟑 − 𝟒𝟏 𝟔𝟑 = 𝟐𝟐 𝟔𝟑 were Charlie’s
(b) 63
(c) No, he could have any multiple of 63 games ie. 126, 189…

8. Calculating with fractions (3)
Colin drinks of a litre of milk each day. Milk costs 89p for a 2-litre carton and 49p for a 1-litre carton. What is the smallest amount that Colin would have to spend to buy milk for one week? Show your working.
7 x 3 8
7 1 x 3 8 = 21 8
= litres per week
2 litre carton 89p + 1 litre carton 49p
= 138p
= £1.38

9. Calculating with fractions (4)
A rectangle has an area of cm2. If the width is cm, calculate the length. ÷
51 2 ÷ 9 2
51 2 x 2 9 = =
= cm
m𝑐𝑚𝑐