Question

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

Explanation:

(6)

Step1: Calculate division

$\frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Step2: Calculate subtraction

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

Step1: Calculate multiplication

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

Step2: Convert mixed number to improper fraction

$2\frac{2}{3} = \frac{8}{3}$

Step3: Calculate subtraction

$\frac{8}{3} - \frac{3}{2} = \frac{16}{6} - \frac{9}{6} = \frac{7}{6} = 1\frac{1}{6}$

Step1: Convert mixed number to improper fraction

$1\frac{1}{5} = \frac{6}{5}$

Step2: Calculate multiplication

$\frac{6}{5} \times \frac{1}{3} = \frac{2}{5}$

Step3: Calculate addition

$\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$

Answer:

$\frac{1}{4}$

(7)