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Whole Number 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 = 3 4 To see why this works consider the diagrams below.

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Whole NumberMultiplication 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.

34

5 x =Example 1:

154

3=34

To see why this works consider the diagrams below.

Multiplication of Fractions

Multiplying by a whole number.

34

5 x =Example 1:

154

3=34

To see why this works consider the diagrams below.

1

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

34

5 x =Example 1:

154

3=34

To see why this works consider the diagrams below.

1 2

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

154

3=34

1 2 3 = 3 34

34

To see why this works consider the diagrams below.

34

5 x =Example 1:

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

1

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

1 2

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

1 2 3

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

1 2 3 4

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Multiplication of Fractions

Multiplying by a whole number.

23

8 x =Example 2:

163

5=13

To see why this works consider the diagrams below.

1 2 3 = 5 13

134 5

To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.

Questions1

34

3 x =23

2 x =35

5 x =

56

4 x =45

6 x =17

8 x =

310

9 x =45

12 x =23

15 x =

142 1

31 3

4 54

171

7102 3

59 10

263

13= 3

a b c

d e f

g h i

Unit FractionMultiplication of FractionsMultiplying 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:

2 x

If you had this set of discs 2 times you would have a total of 12 discs.

= 12

Or to rephrase this if you had 2 of these sets of discs you would have 12 discs

2 of = 12

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

= 220

=1

1025

Example 1:

14

x

To see why this is using a diagram consider the following:

25

Taking a ¼ of 2/5 by dividing it by 4

220

110

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

= 524

58

Example 2:

13

x

To see why this is using a diagram consider the following:

58

Taking a 1/3 of 5/8 by dividing it

by 3

524

Questions2

16

12

=13

x 23

=14

x 57

=12

x

34

=15

of 16

=16

x 14

=12

of

45

=14

x 38

=18

of 23

=110

x

212

=16

514

320

136

18

420

=15

364

230

=1

15

a b c

d e f

g h i

General FractionMultiplication 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

= 612

=12

34

Example 1:

23

x

It is often more efficient to cancel highest common factors “top and bottom” and then “multiply out” to arrive at the answer directly.

12

=34

23

x1

21

1

Multiplication of Fractions

To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary

= 612

=12

34

Example 1:

23

x

To see why this works consider the diagram below.

Taking 2/3 of 3/4 by dividing it into thirds

34

{34

23

of = 612

=12

Multiplying by a general fraction.

Multiplication of Fractions

To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary

= 40180

=29

815

Example 2:

512

x

Using the method of cancelling highest common factors is very useful in this more awkward case.

29

1

33

28

155

12x =

Multiplying by a general fraction.

3 FractionsMultiplication of 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

2

1

2

Multiplying more than two fractions.

49

310

Example 1:

58

x x1

3

112

=

89

712

Example 2:

35

of of1445

=1

3

2

3

Questions3

49

56

23

x 45

x 49

58

x 310

x

56

34

of 89

of 320

78

x 56

x

78

67

x 89

x 56

1415

of 928

of

112

59

764

23

14

a b

c d

e f

Mixed NumbersMultiplication of Fractions

To multiply fractions involving mixed numbers, re-write the mixed numbers as improper fractions and proceed as usual.

Multiplying mixed numbers.

Example 1:

58

x2 67

=218

x 67

= 94

14

2=1

3 3

4

Example 2:

=203

x 92 30=

1

10 3

1

23

x6 12

4

Question4

a b

c d

e f

23

x 38

2 3 12

x 14

1 2

9

16

x 15

4 3 34

of 23

6

35

of 518

9 5 110

x 29

8 1

13

13 12

4

910

9

38

3

23

50

Worksheet 1

34

3 x =23

2 x =35

5 x =

56

4 x =45

6 x =17

8 x =

310

9 x =45

12 x =23

15 x =

a b c

d e f

g h i

Worksheet 2

12

=13

x 23

=14

x 57

=12

x

34

=15

of 16

=16

x 14

=12

of

45

=14

x 38

=18

of 23

=110

x

a b c

d e f

g h i

Worksheet 3

56

23

x 45

x 49

58

x 310

x

56

34

of 89

of 320

78

x 56

x

78

67

x 89

x 56

1415

of 928

of

a b

c d

e f

Worksheet 4

a b

c d

e f

23

x 38

2 3 12

x 14

1 2

16

x 15

4 3 34

of 23

6

35

of 518

9 5 110

x 29

8 1