Question

(5) $\frac{3}{8} div 6 + \frac{1}{6}$
(7) $left(3\frac{3}{10} - 2\frac{1}{5}
ight) \times \frac{2}{11}$
(6) $1 - 1\frac{4}{7} div 4\frac{5}{7}$
(8) $21 div left(1\frac{3}{4} \times \frac{2}{9}
ight)$

Explanation:

(5) Step1: Calculate division

$\frac{3}{8} \div 6 = \frac{3}{8} \times \frac{1}{6} = \frac{1}{16}$

(5) Step2: Add fractions

$\frac{1}{16} + \frac{1}{6} = \frac{3}{48} + \frac{8}{48} = \frac{11}{48}$

(6) Step1: Convert to improper fractions

$1\frac{4}{7} = \frac{11}{7}$, $4\frac{5}{7} = \frac{33}{7}$

(6) Step2: Calculate division

$\frac{11}{7} \div \frac{33}{7} = \frac{11}{7} \times \frac{7}{33} = \frac{1}{3}$

(6) Step3: Subtract

$1 - \frac{1}{3} = \frac{2}{3}$

(7) Step1: Convert to improper fractions

$3\frac{3}{10} = \frac{33}{10}$, $2\frac{1}{5} = \frac{11}{5} = \frac{22}{10}$

(7) Step2: Subtract inside parentheses

$\frac{33}{10} - \frac{22}{10} = \frac{11}{10}$

(7) Step3: Multiply

$\frac{11}{10} \times \frac{2}{11} = \frac{2}{10} = \frac{1}{5}$

(8) Step1: Convert to improper fraction

$1\frac{3}{4} = \frac{7}{4}$

(8) Step2: Multiply inside parentheses

$\frac{7}{4} \times \frac{2}{9} = \frac{14}{36} = \frac{7}{18}$

(8) Step3: Calculate division

$21 \div \frac{7}{18} = 21 \times \frac{18}{7} = 54$

Answer:

$\frac{19}{48}$, $\frac{9}{10}$, $\frac{2}{5}$, $54$