Question

(5) $1\frac{5}{7} \div \frac{3}{4} \times \frac{7}{10}$
$=$
(7) $1\frac{1}{2} - \frac{3}{10} + \frac{1}{5}$
$=$
(6) $1\frac{2}{5} \div 1\frac{1}{6} \div \frac{8}{25}$
$=$
(8) $3\frac{5}{12} - \frac{1}{6} - \frac{1}{8}$
$=$

Explanation:

(5) Step1: Convert mixed number to improper fraction

$1\frac{5}{7} = \frac{12}{7}$

(5) Step2: Divide by multiplying reciprocal

$\frac{12}{7} \div \frac{3}{4} = \frac{12}{7} \times \frac{4}{3} = \frac{16}{7}$

(5) Step3: Multiply by $\frac{7}{10}$

$\frac{16}{7} \times \frac{7}{10} = \frac{8}{15}$

(7) Step1: Convert mixed number to improper fraction

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

(7) Step2: Find common denominator (10)

$\frac{3}{2} = \frac{15}{10}$, $\frac{1}{5} = \frac{2}{10}$

(7) Step3: Calculate

$\frac{15}{10} - \frac{3}{10} + \frac{2}{10} = \frac{14}{10} = \frac{7}{5}$? Wait correction: $\frac{15-3+2}{10} = \frac{14}{10} = \frac{7}{5}$? No wait original: $1\frac{1}{2} - 3/10 +1/5 = 3/2 -3/10 +2/10 = 3/2 -1/10 = 15/10 -1/10 =14/10=7/5=1.4$. Yes.

(6) Step1: Convert mixed numbers to improper fractions

$1\frac{2}{5} = \frac{7}{5}$, $1\frac{1}{6} = \frac{7}{6}$

(6) Step2: Divide by multiplying reciprocals

$\frac{7}{5} \div \frac{7}{6} = \frac{7}{5} \times \frac{6}{7} = \frac{6}{5}$

(6) Step3: Divide by $\frac{8}{25}$

$\frac{6}{5} \div \frac{8}{25} = \frac{6}{5} \times \frac{25}{8} = \frac{15}{4}$

(8) Step1: Convert mixed number to improper fraction

$3\frac{5}{12} = \frac{41}{12}$

(8) Step2: Find common denominator (24)

$\frac{41}{12} = \frac{82}{24}$, $\frac{1}{6} = \frac{4}{24}$, $\frac{1}{8} = \frac{3}{24}$

(8) Step3: Calculate

$\frac{82}{24} - \frac{4}{24} - \frac{3}{24} = \frac{75}{24} = \frac{25}{8}$? Wait correction: $3\frac{5}{12} = 3 +5/12 = 36/12 +5/12=41/12$. 41/12 -1/6 -1/8 = 41/12 -2/12 -1/8 =39/12 -1/8=13/4 -1/8=26/8 -1/8=25/8=3.125. Yes.

Final answers:
(5) $\frac{8}{15}$
(7) $\frac{7}{5}$
(6) $\frac{15}{4}$
(8) $\frac{25}{8}$

Answer:

$\frac{8}{15}$
$\frac{17}{10}$
$\frac{15}{4}$
$\frac{83}{24}$