Question

f90b
(5) $10\frac{5}{6} - 8\frac{3}{4} - 1\frac{1}{20}$
$=$
(7) $(3\frac{2}{7} - 2\frac{3}{14}) \div \frac{15}{16}$
$=$
(6) $2\frac{5}{14} \div (2 - \frac{5}{8})$
$=$

Explanation:

Problem (5)

Step1: Find a common denominator (60)

Convert mixed numbers to improper fractions with denominator 60:
$10\frac{5}{6} = \frac{65}{6} = \frac{650}{60}$, $8\frac{3}{4} = \frac{35}{4} = \frac{525}{60}$, $1\frac{1}{20} = \frac{21}{20} = \frac{63}{60}$

Step2: Subtract sequentially

$\frac{650}{60} - \frac{525}{60} - \frac{63}{60} = \frac{650 - 525 - 63}{60} = \frac{62}{60} = \frac{31}{30} = 1\frac{1}{30}$

Problem (6)

Step1: Simplify the denominator

Calculate $2 - \frac{5}{8} = \frac{16}{8} - \frac{5}{8} = \frac{11}{8}$

Step2: Convert mixed number to improper fraction

$2\frac{5}{14} = \frac{33}{14}$

Step3: Divide by multiplying reciprocal

$\frac{33}{14} \div \frac{11}{8} = \frac{33}{14} \times \frac{8}{11} = \frac{24}{14} = \frac{12}{7} = 1\frac{5}{7}$

Problem (7)

Step1: Simplify the numerator

Convert mixed numbers to improper fractions: $3\frac{2}{7} = \frac{23}{7}$, $2\frac{3}{14} = \frac{31}{14}$
Subtract: $\frac{23}{7} - \frac{31}{14} = \frac{46}{14} - \frac{31}{14} = \frac{15}{14}$

Step2: Divide by multiplying reciprocal

$\frac{15}{14} \div \frac{15}{16} = \frac{15}{14} \times \frac{16}{15} = \frac{16}{14} = \frac{8}{7} = 1\frac{1}{7}$

Answer:

s:
(5) $\boldsymbol{1\frac{1}{30}}$
(6) $\boldsymbol{1\frac{5}{7}}$
(7) $\boldsymbol{1\frac{1}{7}}$