Question

calculate.
(1) $1\frac{13}{72} \div 1\frac{7}{10} - \frac{1}{4} =$
(2) $\left(\frac{1}{5} + 1\frac{7}{15}\
ight) \div 1\frac{1}{6} =$
(3) $\left(1\frac{3}{8} - \frac{2}{5}\
ight) \times \frac{12}{13} =$
(4) $\frac{2}{3} \times 1\frac{1}{4} - 1\frac{1}{5} \div 2 =$

Explanation:

(1)

Step1: Convert mixed numbers to improper fractions

$1\frac{13}{72}=\frac{1\times72 + 13}{72}=\frac{85}{72}$, $1\frac{7}{10}=\frac{1\times10 + 7}{10}=\frac{17}{10}$

Step2: Perform division

$\frac{85}{72}\div\frac{17}{10}=\frac{85}{72}\times\frac{10}{17}=\frac{5\times10}{72}=\frac{50}{72}=\frac{25}{36}$

Step3: Subtract $\frac{1}{4}$

$\frac{25}{36}-\frac{1}{4}=\frac{25}{36}-\frac{9}{36}=\frac{16}{36}=\frac{4}{9}$

Step1: Convert mixed number to improper fraction and add

$\frac{1}{5}+1\frac{7}{15}=\frac{1}{5}+\frac{22}{15}=\frac{3}{15}+\frac{22}{15}=\frac{25}{15}=\frac{5}{3}$

Step2: Convert divisor to improper fraction and divide

$1\frac{1}{6}=\frac{7}{6}$, $\frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\times\frac{6}{7}=\frac{10}{7}=1\frac{3}{7}$

Step1: Convert mixed number to improper fraction and subtract

$1\frac{3}{8}=\frac{11}{8}$, $\frac{11}{8}-\frac{2}{5}=\frac{55 - 16}{40}=\frac{39}{40}$

Step2: Multiply by $\frac{12}{13}$

$\frac{39}{40}\times\frac{12}{13}=\frac{3\times12}{40}=\frac{36}{40}=\frac{9}{10}$

Answer:

$\frac{4}{9}$

(2)