Solve 9/4*1/4{4-1/3div(12/15-frac{5}{10})*frac{2}{20}}

$$\frac { 9 } { 4 } \times \frac { 1 } { 4 } \{ 4 - \frac { 1 } { 3 } \div ( \frac { 12 } { 15 } - \frac { 5 } { 10 } ) \times \frac { 2 } { 20 } \}$$

Evaluate

$$\frac{35}{16}=2.1875$$

Solution Steps

Multiply \frac{9}{4} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 1}{4\times 4}\left(4-\frac{\frac{1}{3}}{\frac{12}{15}-\frac{5}{10}}\times \frac{2}{20}\right)$$

Do the multiplications in the fraction \frac{9\times 1}{4\times 4}.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{12}{15}-\frac{5}{10}}\times \frac{2}{20}\right)$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{4}{5}-\frac{5}{10}}\times \frac{2}{20}\right)$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{4}{5}-\frac{1}{2}}\times \frac{2}{20}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{8}{10}-\frac{5}{10}}\times \frac{2}{20}\right)$$

Since \frac{8}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{8-5}{10}}\times \frac{2}{20}\right)$$

Subtract 5 from 8 to get 3.

$$\frac{9}{16}\left(4-\frac{\frac{1}{3}}{\frac{3}{10}}\times \frac{2}{20}\right)$$

Divide \frac{1}{3} by \frac{3}{10} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{10}.

$$\frac{9}{16}\left(4-\frac{1}{3}\times \frac{10}{3}\times \frac{2}{20}\right)$$

Multiply \frac{1}{3} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}\left(4-\frac{1\times 10}{3\times 3}\times \frac{2}{20}\right)$$

Do the multiplications in the fraction \frac{1\times 10}{3\times 3}.

$$\frac{9}{16}\left(4-\frac{10}{9}\times \frac{2}{20}\right)$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$\frac{9}{16}\left(4-\frac{10}{9}\times \frac{1}{10}\right)$$

Multiply \frac{10}{9} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}\left(4-\frac{10\times 1}{9\times 10}\right)$$

Cancel out 10 in both numerator and denominator.

$$\frac{9}{16}\left(4-\frac{1}{9}\right)$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{9}{16}\left(\frac{36}{9}-\frac{1}{9}\right)$$

Since \frac{36}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{16}\times \frac{36-1}{9}$$

Subtract 1 from 36 to get 35.

$$\frac{9}{16}\times \frac{35}{9}$$

Multiply \frac{9}{16} times \frac{35}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 35}{16\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{35}{16}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {4}} = 2\frac{3}{16} = 2.1875$$