Question

calculate. (intermediate steps may be skipped for simple calculations.)
(1) \\(\frac{3}{4} \times \left(1 - \frac{1}{6}\
ight)\\)
\\(= \frac{3}{4} \times \frac{\square}{6}\\)
\\(= \frac{5}{8}\\)
(2) \\(\left(1 - \frac{1}{8}\
ight) \times 3\frac{1}{5}\\)
\\(=\\)
(3) \\(\left(1 - \frac{2}{7}\
ight) \div \frac{5}{6}\\)
(4) \\(2\frac{2}{5} - \left(2 - \frac{7}{8}\
ight)\\)
\\(=\\)
(5) \\(1\frac{5}{7} \times \left(2 - 1\frac{5}{6}\
ight)\\)
\\(=\\)

Explanation:

(1)

Step1: Calculate the bracket

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

Step2: Multiply the fractions

$\frac{3}{4} \times \frac{5}{6} = \frac{15}{24} = \frac{5}{8}$

Step1: Calculate the bracket

$1 - \frac{1}{8} = \frac{7}{8}$

Step2: Convert mixed number to improper fraction

$3\frac{1}{5} = \frac{16}{5}$

Step3: Multiply the fractions

$\frac{7}{8} \times \frac{16}{5} = \frac{112}{40} = \frac{14}{5} = 2\frac{4}{5}$

Step1: Calculate the bracket

$1 - \frac{2}{7} = \frac{5}{7}$

Step2: Divide by fraction (multiply by reciprocal)

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

Answer:

$\frac{5}{8}$

(2)