1. Whole Number 5 x 3 3 4 = 15 4 = Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 3 4
5 x =
Example 1: 15 4 3 =
To see why this works consider the diagrams below.

2. 5 x 3 1 3 4 = 15 4 = Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 3 4
5 x =
Example 1: 15 4 3 =
To see why this works consider the diagrams below. 1

3. 5 x 3 1 2 3 4 = 15 4 = Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 3 4
5 x =
Example 1: 15 4 3 =
To see why this works consider the diagrams below. 1 2

4. 5 x 3 = 3 1 2 3 3 4 = 15 4 = 3 4 3 4 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 3 4
5 x =
Example 1: 15 4 3 =
To see why this works consider the diagrams below. 3 4
= 3 3 4 1 2 3

5. 8 x 5 2 3 = 16 3 = 1 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below.

6. 8 x 5 1 2 3 = 16 3 = 1 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below. 1

7. 8 x 5 1 2 2 3 = 16 3 = 1 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below. 1 2

8. 8 x 5 1 2 3 2 3 = 16 3 = 1 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below. 1 2 3

9. 8 x 5 1 2 3 4 2 3 = 16 3 = 1 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below. 1 2 3 4

10. 8 x 5 = 5 1 2 3 4 5 2 3 = 16 3 = 1 1 3 1 3 Multiplication of Fractions
Multiplying by a whole number.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary. 2 3
8 x =
Example 2: 16 3 5 = 1
To see why this works consider the diagrams below. 1 3
= 5 1 3 1 2 3 4 5

11. 3 x 2 x 5 x 4 x 6 x 8 x Questions1 9 x 12 x 15 x 3 4 = 2 3 = 3 5 = 5 6
Answer the following questions: a b c 3 4
3 x = 2 3
2 x = 3 5
5 x = 1 4 2 1 3 3 d e f 5 6
4 x = 4 5
6 x = 1 7
8 x =
Questions1 2 6 3 1
= 3 4 5 1 7 g h i 3 10
9 x = 4 5
12 x = 2 3
15 x = 7 10 2 3 5 9 10

12. Unit Fraction Multiplication of Fractions = 12 2 x = 12 2 of
Multiplying by a unit fraction.
Before considering multiplication of fractions it is important for you to understand that in mathematics of and x (multiplication) mean the same thing.
To see why this is the case consider the set of 6 discs shown below:
If you had this set of discs 2 times you would have a total of 12 discs.
= 12
2 x
Or to rephrase this if you had 2 of these sets of discs you would have 12 discs
2 of
= 12

13. Taking a ¼ of 2/5 by dividing it by 4
Multiplication of Fractions
Multiplying by a unit fraction.
To multiply a fraction by a unit fraction simply multiply out the numerators and denominators then simplify the resulting fraction if necessary 2 5
Example 1: 1 4 x = 2 20 = 1 10
To see why this is using a diagram consider the following: 2 5 2 20 1 10
Taking a ¼ of 2/5 by dividing it by 4

14. Taking a 1/3 of 5/8 by dividing it by 3
Multiplication of Fractions
Multiplying by a unit fraction.
To multiply a fraction by a unit fraction simply multiply out the numerators and denominators then simplify the resulting fraction if necessary 5 8
Example 2: 1 3 x = 5 24
To see why this is using a diagram consider the following: 5 8 5 24
Taking a 1/3 of 5/8 by dividing it by 3

15. Answer the following questions:b c 1 2 = 3 x 2 3 = 1 4 x 5 7 = 1 2 x 1 6 2 12 = 1 6 5 14 d e f 3 4 = 1 5 of 1 6 = x 1 4 = 2 of
Questions2 3 20 1 36 1 8 g h i 4 5 = 1 x 3 8 = 1 of 2 3 = 1 10 x 4 20 = 1 5 3 64 2 30 = 1 15

16. General Fraction 3 4 2 = 6 12 = 1 2 = 3 4 2 1 2 x x
Multiplication of Fractions
Multiplying by a general fraction.
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary 3 4
Example 1: 2 x = 6 12 = 1 2
It is often more efficient to cancel highest common factors “top and bottom” and then “multiply out” to arrive at the answer directly. 1 = 3 4 2 x 1 1 2 1 2

17. Taking 2/3 of 3/4 by dividing it into thirds
Multiplication of Fractions
Multiplying by a general fraction.
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary 3 4
Example 1: 2 x = 6 12 = 1 2
To see why this works consider the diagram below. { 3 4 2 of = 6 12 1 2 3 4
Taking 2/3 of 3/4 by dividing it into thirds

18. Multiplication of Fractions
Multiplying by a general fraction.
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary 8 15
Example 2: 5 12 x = 40
180 = 2 9
Using the method of cancelling highest common factors is very useful in this more awkward case. 1 2 8 15 5 12 x = 2 9 3 3

19. 3 Fractions
Multiplication of Fractions
Multiplying more than two fractions.
To multiply more than two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary. Cancelling common factors “top and bottom” is advisable. 1 1 4 9 3 10
Example 1: 5 8 x 1 12 = 1 2 2 3 1 8 9 7 12
Example 2: 3 5 of 2 14 45 = 3 3

20. Answer the following questions: (cancelling is strongly advisable!)5 6 2 3 x 4 b 4 9 5 8 x 3 10 4 9 1 12 c 5 6 3 4 of 8 9 d 3 20 7 8 x 5 6
Questions3 5 9 7 64 e 7 8 6 x 9 f 5 6 14 15 of 9 28 2 3 1 4

21. Mixed Numbers
Multiplication of Fractions
Multiplying mixed numbers.
To multiply fractions involving mixed numbers, re-write the mixed numbers as improper fractions and proceed as usual.
Example 1: 5 8 x 2 6 7 = 21 8 x 6 7 3 3 = 9 4 1 4 2 = 4 1
Example 2: 2 3 x 6 1 4 = 20 3 x 9 2 10 3 30 = 1 1

22. Answer the following questions:2 3 x 8 b 1 2 x 4 3 8 9
Question4 c 1 6 x 5 4 3 d 3 4 2 3 6 of 1 3 13 1 2 4 3 5 of 18 9 e 1 10 x 2 9 8 f 2 3 50 9 10

23. Worksheet 1 3 x 2 x 5 x 4 x 6 x 8 x 9 x 12 x 15 x 3 4 = 2 3 = 3 5 = 5
Answer the following questions: a b c 3 4
3 x = 2 3
2 x = 3 5
5 x = d e f 5 6
4 x = 4 5
6 x = 1 7
8 x = g h i 3 10
9 x = 4 5
12 x = 2 3
15 x =
Worksheet 1

24. Answer the following questions:b c 1 2 = 3 x 2 3 = 1 4 x 5 7 = 1 2 x d e f 3 4 = 1 5 of 1 6 = x 1 4 = 2 of g h i 4 5 = 1 x 3 8 = 1 of 2 3 = 1 10 x
Worksheet 2

25. Answer the following questions: (cancelling is strongly advisable!)5 6 2 3 x 4 b 4 9 5 8 x 3 10 c 5 6 3 4 of 8 9 d 3 20 7 8 x 5 6 e 7 8 6 x 9 f 5 6 14 15 of 9 28
Worksheet 3

26. Answer the following questions:2 3 x 8 b 1 2 x 4 c 1 6 x 5 4 3 d 3 4 2 3 6 of 3 5 of 18 9 e 1 10 x 2 9 8 f
Worksheet 4