Question: 6 4/7 - 3/5 7 1/6 x 4/9 8 5/8 x 2/7 9 2/15 x 3/4 10 8/10 ÷ 5

6 4/7 - 3/5 7 1/6 x 4/9 8 5/8 x 2/7 9 2/15 x 3/4 10 8/10 ÷ 5

Solution

Sure! Let’s solve the problems step by step.

Problem 1:

\(\frac{4}{7} - \frac{3}{5}\)

Find a common denominator. The least common multiple of 7 and 5 is 35.

\[ \frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35} \]

\[ \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \]

Subtract the fractions:

\[ \frac{20}{35} - \frac{21}{35} = \frac{-1}{35} \]
Problem 2:

\(\frac{1}{7} \times \frac{4}{9}\)

Multiply the numerators and denominators:

\[ \frac{1 \times 4}{7 \times 9} = \frac{4}{63} \]
Problem 3:

\(\frac{8}{5} \times \frac{2}{7}\)

Multiply the numerators and denominators:

\[ \frac{8 \times 2}{5 \times 7} = \frac{16}{35} \]
Problem 4:

\(\frac{2}{9} \times \frac{3}{4}\)

Multiply the numerators and denominators:

\[ \frac{2 \times 3}{9 \times 4} = \frac{6}{36} \]

Simplify the fraction:

\[ \frac{6}{36} = \frac{1}{6} \]
Problem 5:

\(\frac{8}{10} \div 5\)

Divide by multiplying by the reciprocal of 5 (\(\frac{1}{5}\)):

\[ \frac{8}{10} \times \frac{1}{5} = \frac{8}{50} \]

Simplify the fraction:

\[ \frac{8}{50} = \frac{4}{25} \]