Question

Simplify:

(i) 1 / 4 of $2\frac{2}{7}$ ÷ 3 / 5

(ii) $1\frac{1}{4}$ × 1 / 2 ÷ $1\frac{1}{3}$

(iii) $6\frac{1}{7}$× 0 × $5\frac{3}{8}$

(iv) 3 / 4 × $1\frac{1}{3}$ ÷ 3 / 7 of $2\frac{5}{8}$

(v) $2\frac{1}{4}$ ÷ 2 / 7 of $1\frac{1}{3}$ × 2 / 3

Answer 1

(i) 1 / 4 of
$2\frac{2}{7}$ ÷ 3 / 5

The given expression can be simplified as follows:

1 / 4 × 16 / 7 ÷ 3 / 5 = 4 / 7 ÷ 3 / 5

= (4 × 5) / (7 × 3)

= 20 / 21

Hence, 20 / 21 is the simplified form of the given expression

(ii) $1\frac{1}{4}$ × 1 / 2 ÷ $1\frac{1}{3}$

The given expression can be simplified as follows

$1\frac{1}{4}$ × 1 / 2 ÷ $1\frac{1}{3}$
= 5 / 4 × 1 / 2 × 3 / 4

= 5 / 8 × 3 / 4

= 15 / 32

Hence, 15 / 32 is the simplified form of the given expression

(iii)
$6\frac{1}{7}$ × 0 × $5\frac{3}{8}$

The given expression can be simplified as follows

$6\frac{1}{7}$ × 0 × $5\frac{3}{8}$ = (43 × 0 × 43) / (7 × 0 × 8)

= 0

Hence, 0 is the simplified form of the given expression

(iv) 3 / 4 ×
$1\frac{1}{3}$ ÷ 3 / 7 of $2\frac{5}{8}$

The given expression can be simplified as follows

3 / 4 ×
$1\frac{1}{3}$ ÷ 3 / 7 of
$2\frac{5}{8}$ = 3 / 4 × 4 / 3 ÷ 9 / 8

∵ 3 / 7 of
$2\frac{5}{8}$ = 3 / 7 × 21 / 8 = 9 / 8

= 3 / 4 × 4 / 3 × 8 / 9

= 8 / 9

Hence, 8 / 9 is the simplified form of the given expression

(v)
$2\frac{1}{4}$ ÷ 2 / 7 of

$1\frac{1}{3}$ × 2 / 3

The given expression can be simplified as follows

[2 / 7 of
$1\frac{1}{3}$ = 2 / 7 × 4 / 3 = 8 / 21]

We get

= 9 / 4 ÷ 8 / 21 × 2 / 3

= 9 / 4 × 21 / 8 × 2 / 3

= 63 / 16

= $3\frac{15}{16}$

Hence, $3\frac{15}{16}$ is the simplified form of the given expression