Question

a) Convert the following mixed fractions to improper fractions.

$12\frac{2}{3}$; $8\frac{4}{9}$; $4\frac{6}{11}$
b) Reduce the following fractions into their simplest form: -

$\frac{36}{48}$; $\frac{39}{65}$

c) Convert the following improper fractions to mixed fractions.
$\frac{43}{7}$; $\frac{93}{11}$; $\frac{57}{9}$

[8 marks]

Answer 1

a) $12\frac{2}{3}=\frac{12\times 3+2}{3}=\frac{38}{3}$ (1 mark)

$8\frac{4}{9}=\frac{8\times 9+4}{9}=\frac{76}{9}$ (1 mark)

$4\frac{6}{11}=\frac{4\times 11+6}{11}=\frac{50}{11}$(1 mark)

b) In $\frac{36}{48}$, we can identify multiples of 12
So, $\frac{36}{48}$ = $\frac{3\times 12}{4\times 12}$ = $\frac{3}{4}$ (1 mark)

In $\frac{39}{65}$, we can identify multiples of 13.
So, $\frac{39}{65}$ = $\frac{3\times 13}{5\times 13}$ = $\frac{3}{5}$ (1 mark)

c)
______
7 | 43 | 6
42 $\frac{43}{7}=6\frac{1}{7}$
______
1
(1 mark)
______
11 | 93 | 8
88 $\frac{93}{11}=8\frac{5}{11}$
______
5
(1 mark)
______
9 | 57 | 6
54 $\frac{57}{9}=6\frac{3}{9}=6\frac{1}{3}\left(\frac{3}{9}=\frac{1\times 3}{3\times 3}=\frac{1}{3}\right)$
______
3
(1 mark)