1. Multiplying Fractions
Multiply fractions including improper fractions and mixed numbers
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2. Key vocabulary
Numerator Denominator Mixed number Improper fraction 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 fractions
2 1 4
9 4
3 3 7
24 7
1 4 5
9 5
47 9
5 2 9
3 1 4
13 4

5. × × = = = = = How to multiply fractions 4 5 1 6 2 7 3 9 2x3 7x9 4 30
The simplest operation to perform with fractions.
Just multiply across.
4 5
1 6
2 7
3 9 × ×
2x3 7x9
4 30 = =
6 63
2 21
2 15 = = =

6. × × = × = = How to multiply fractions = 6 10 7 21 5 3 5 10 1 2 6 1
We can cross-cancel to make things easier but you do not have to.
We can just multiply the numerators and multiply the denominators. ÷7
10 7
21 5 ×
Look diagonally to spot common factors ÷7
3 5
10 1 × = 2
6 1
3 5
10 1 × = ÷5 =
= 6 1 ÷5

7. × = × = How to multiply fractions – mixed numbers 2 5 4 7 2 2 5 18 7
Convert to improper fraction(s) first.
4 7
2 5 × 2
18 7
2 5 = ×
36 35
1 35 = 1

8. Practice solutions 3 5 × 2 3 = 6 15 = 2 5 1 9 × 4 7 = 4 63
3 5 × 2 3 = 6 15 = 2 5
1 9 × 4 7 = 4 63
7 × = x = =3
4 3 5 × = x =
× = x = =48

9. Problem solving and reasoning
Jane is going to lay laminate flooring in her front room. The length of the room is 2 m and the width is 1.75 m.
What is the area of the floor to be covered?
× 1 3 4
= × =
= m²

10. Problem solving and reasoning
A farm has pigs, cows and sheep are pigs, are sheep, and the rest are cows.
What fraction are cows?
If the farmer has 220 animals, how many of each animal are there?
𝟏 𝟒 + 𝟐 𝟓 = 𝟓 𝟐𝟎 + 𝟖 𝟐𝟎 = 𝟏𝟑 𝟐𝟎
𝟐𝟎 𝟐𝟎 − 𝟏𝟑 𝟐𝟎 = 𝟕 𝟐𝟎 are cows.
𝟐𝟐𝟎× 𝟓 𝟐𝟎 = 𝟏𝟏𝟎𝟎 𝟐𝟎 =𝟓𝟓 are pigs
𝟐𝟐𝟎× 𝟖 𝟐𝟎 = 𝟏𝟕𝟔𝟎 𝟐𝟎 =𝟖𝟖 are sheep
𝟐𝟐𝟎× 𝟕 𝟐𝟎 = 𝟏𝟓𝟒𝟎 𝟐𝟎 =𝟕𝟕 are cows

11. Exam specimen question

12. Exam specimen question

13. Exam specimen question
Sean works for a company.
His normal rate of pay is £12 per hour.
When Sean works more than 8 hours a day, he is paid overtime for each hour he works more than 8 hours.
Sean’s rate of overtime pay per hour is times his normal rate of pay per hour.
On Monday Sean worked for 10 hours.
Work out the total amount of money Sean earned on Monday. £
(4 marks)

14. Exam specimen question