Use the array model to multiply the following fractions. (i) 1
__ 2 × 3
__ 4
(ii) 4
__ 5 × 2
__ 3
(iii) 1
__ 4 × 5
__ 6
(iv) 2
__ 3 × 4
__ 7
Multiplying fractions using fraction strips
A fraction strip is a rectangular piece of paper or plastic that can be used to represent diff erent parts of the same whole. Fraction strips can be used to perform operations on fractions. The fraction strip shown has 4
__ 9 shaded:
2 × 4
_ 9 = 8
1·5 × 4 1 × 4
_ 9
_ 9 = 6
_ 9 = 4
_ 9
Discuss and discover The fraction strip shown represents 2
__ 5
Working with the person beside you, represent the following on separate fraction strips.
(i) 2 × 2
__ 5
(ii) 4 × 2 Multiplication
Multiplication using fraction strips can be very time consuming. It is easier to multiply fractions using the following steps:
__ 5
(iii) 1
__ 2 × 2
__ 5
(iv) 1
__ 4 × 2
__ 5
(v) 1
__ 8 × 2
__ 5
Multipying fractions 1
2 3
Worked example Express the following as a single fraction. (i) 2
__ 7 × 3
__ 5
Solution (ii) 2 3
__ 4 × 5
__ 6
_ 9
_ 2 × 4
1 1
_ 4 × 4
_ 4 × 4
3
_ 9 = 2
_ 9 = 1
_ 9 = 3
_ 9
_ 9
_ 9
(v) 3
__ 8 × 2
__ 3
(vi) 9
__ 6 × 3
__ 4
Multiply the numerators by each other. The result is the numerator of the answer.
Multiply the denominators by each other. The result is the denominator of the answer. Simplify the fraction if necessary.