Question

calculate.
(1) (left(2\frac{5}{8} - 1\frac{4}{5}
ight) \times \frac{10}{11} =)
(2) (left(8\frac{5}{8} - 7\frac{4}{5}
ight) \times 1\frac{1}{3} =)
(3) (left(3\frac{3}{8} - 1\frac{4}{5}
ight) div \frac{9}{10} =)
(4) (left(\frac{1}{7} + \frac{1}{8}
ight) div left(\frac{1}{4} + \frac{2}{7}
ight) =)

Explanation:

(1) Calculation

Step1: Convert mixed numbers to improper fractions

$2\frac{5}{8}=\frac{2\times8 + 5}{8}=\frac{21}{8}$, $1\frac{4}{5}=\frac{1\times5 + 4}{5}=\frac{9}{5}$

Step2: Subtract the two fractions

$\frac{21}{8}-\frac{9}{5}=\frac{21\times5 - 9\times8}{40}=\frac{105 - 72}{40}=\frac{33}{40}$

Step3: Multiply by $\frac{10}{11}$

$\frac{33}{40}\times\frac{10}{11}=\frac{33\times10}{40\times11}=\frac{3}{4}$

Step1: Convert mixed numbers to improper fractions

$8\frac{5}{8}=\frac{8\times8 + 5}{8}=\frac{69}{8}$, $7\frac{4}{5}=\frac{7\times5 + 4}{5}=\frac{39}{5}$

Step2: Subtract the two fractions

$\frac{69}{8}-\frac{39}{5}=\frac{69\times5 - 39\times8}{40}=\frac{345 - 312}{40}=\frac{33}{40}$

Step3: Convert $1\frac{1}{3}$ to improper fraction and multiply

$1\frac{1}{3}=\frac{4}{3}$, $\frac{33}{40}\times\frac{4}{3}=\frac{33\times4}{40\times3}=\frac{11}{10}$

Step1: Convert mixed numbers to improper fractions

$3\frac{3}{8}=\frac{3\times8 + 3}{8}=\frac{27}{8}$, $1\frac{4}{5}=\frac{1\times5 + 4}{5}=\frac{9}{5}$

Step2: Subtract the two fractions

$\frac{27}{8}-\frac{9}{5}=\frac{27\times5 - 9\times8}{40}=\frac{135 - 72}{40}=\frac{63}{40}$

Step3: Divide by $\frac{9}{10}$ (multiply by reciprocal)

$\frac{63}{40}\div\frac{9}{10}=\frac{63}{40}\times\frac{10}{9}=\frac{63\times10}{40\times9}=\frac{7}{4}$

Answer:

$\frac{3}{4}$

(2) Calculation