Question

f95b
(5) $2\frac{1}{5} \times \left(1\frac{1}{4} - \frac{5}{8}\
ight)$
(7) $1\frac{3}{4} \times \frac{3}{5} \div 1\frac{1}{2}$
(6) $\left(1 - \frac{1}{3}\
ight) \div \left(\frac{1}{3} + \frac{1}{4}\
ight)$
(8) $\frac{5}{7} \div \left(5 - 1\frac{1}{4}\
ight)$

Explanation:

(5) Solution:

Step1: Convert mixed numbers to improper fractions

$2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}$, $1\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4}$

Step2: Calculate the subtraction inside the parentheses

$\frac{5}{4}-\frac{5}{8}=\frac{10}{8}-\frac{5}{8}=\frac{5}{8}$

Step3: Multiply the two fractions

$\frac{11}{5}\times\frac{5}{8}=\frac{11\times5}{5\times8}=\frac{11}{8}=1\frac{3}{8}$

Step1: Calculate the operations inside the parentheses

$1 - \frac{1}{3}=\frac{2}{3}$, $\frac{1}{3}+\frac{1}{4}=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}$

Step2: Divide the two results

$\frac{2}{3}\div\frac{7}{12}=\frac{2}{3}\times\frac{12}{7}=\frac{24}{21}=\frac{8}{7}=1\frac{1}{7}$

Step1: Convert mixed numbers to improper fractions

$1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}$, $1\frac{1}{2}=\frac{1\times2+1}{2}=\frac{3}{2}$

Step2: Rewrite division as multiplication

$\frac{7}{4}\times\frac{3}{5}\div\frac{3}{2}=\frac{7}{4}\times\frac{3}{5}\times\frac{2}{3}$

Step3: Simplify and multiply

$\frac{7}{4}\times\frac{3\times2}{5\times3}=\frac{7}{4}\times\frac{2}{5}=\frac{14}{20}=\frac{7}{10}$

Answer:

$1\frac{3}{8}$

(6) Solution: