Question

(4) $3 - \frac{1}{5} \div \frac{1}{2}$
$= 3 - \frac{2}{5}$
$= 2\frac{3}{5}$
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(6) $\frac{3}{8} \div 2 - \frac{1}{16}$
$=$
(8) $\frac{1}{6} \div \frac{1}{4} + \frac{3}{8}$
$=$
(7) $2\frac{2}{3} - \frac{7}{18} \times 3$
$=$
(9) $1\frac{1}{2} - \frac{3}{4} \div 1\frac{1}{2}$
$=$

Explanation:

(6) $\boldsymbol{\frac{3}{8} \div 2 - \frac{1}{16}}$

Step1: Divide $\frac{3}{8}$ by 2

Dividing by 2 is the same as multiplying by $\frac{1}{2}$, so $\frac{3}{8} \div 2 = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16}$.

Step2: Subtract $\frac{1}{16}$ from the result

$\frac{3}{16} - \frac{1}{16} = \frac{2}{16} = \frac{1}{8}$.

Step1: Multiply $\frac{7}{18}$ by 3

$\frac{7}{18} \times 3 = \frac{7 \times 3}{18} = \frac{21}{18} = \frac{7}{6}$.

Step2: Convert $2\frac{2}{3}$ to an improper fraction

$2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}$.

Step3: Subtract $\frac{7}{6}$ from $\frac{8}{3}$

First, find a common denominator, which is 6. $\frac{8}{3} = \frac{16}{6}$. Then $\frac{16}{6} - \frac{7}{6} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2}$.

Step1: Divide $\frac{1}{6}$ by $\frac{1}{4}$

Dividing by a fraction is multiplying by its reciprocal, so $\frac{1}{6} \div \frac{1}{4} = \frac{1}{6} \times 4 = \frac{4}{6} = \frac{2}{3}$.

Step2: Add $\frac{3}{8}$ to the result

Find a common denominator, which is 24. $\frac{2}{3} = \frac{16}{24}$ and $\frac{3}{8} = \frac{9}{24}$. Then $\frac{16}{24} + \frac{9}{24} = \frac{25}{24} = 1\frac{1}{24}$.

Answer:

$\frac{1}{8}$

(7) $\boldsymbol{2\frac{2}{3} - \frac{7}{18} \times 3}$