Solve {2/3-(0.25div5/8)div3}div31/4

$$\{ \frac { 2 } { 3 } - ( 0.25 \div \frac { 5 } { 8 } ) \div 3 \} \div 3 \frac { 1 } { 4 }$$

Evaluate

$$\frac{32}{195}\approx 0.164102564$$

Solution Steps

Express \frac{\frac{0.25}{\frac{5}{8}}}{3} as a single fraction.

$$\frac{\frac{2}{3}-\frac{0.25}{\frac{5}{8}\times 3}}{\frac{3\times 4+1}{4}}$$

Express \frac{5}{8}\times 3 as a single fraction.

$$\frac{\frac{2}{3}-\frac{0.25}{\frac{5\times 3}{8}}}{\frac{3\times 4+1}{4}}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{2}{3}-\frac{0.25}{\frac{15}{8}}}{\frac{3\times 4+1}{4}}$$

Divide 0.25 by \frac{15}{8} by multiplying 0.25 by the reciprocal of \frac{15}{8}.

$$\frac{\frac{2}{3}-0.25\times \frac{8}{15}}{\frac{3\times 4+1}{4}}$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{2}{3}-\frac{1}{4}\times \frac{8}{15}}{\frac{3\times 4+1}{4}}$$

Multiply \frac{1}{4} times \frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{3}-\frac{1\times 8}{4\times 15}}{\frac{3\times 4+1}{4}}$$

Do the multiplications in the fraction \frac{1\times 8}{4\times 15}.

$$\frac{\frac{2}{3}-\frac{8}{60}}{\frac{3\times 4+1}{4}}$$

Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{2}{3}-\frac{2}{15}}{\frac{3\times 4+1}{4}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{2}{3} and \frac{2}{15} to fractions with denominator 15.

$$\frac{\frac{10}{15}-\frac{2}{15}}{\frac{3\times 4+1}{4}}$$

Since \frac{10}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-2}{15}}{\frac{3\times 4+1}{4}}$$

Subtract 2 from 10 to get 8.

$$\frac{\frac{8}{15}}{\frac{3\times 4+1}{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{8}{15}}{\frac{12+1}{4}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{8}{15}}{\frac{13}{4}}$$

Divide \frac{8}{15} by \frac{13}{4} by multiplying \frac{8}{15} by the reciprocal of \frac{13}{4}.

$$\frac{8}{15}\times \frac{4}{13}$$

Multiply \frac{8}{15} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 4}{15\times 13}$$

Do the multiplications in the fraction \frac{8\times 4}{15\times 13}.

$$\frac{32}{195}$$

Factor

$$\frac{2 ^ {5}}{3 \cdot 5 \cdot 13} = 0.1641025641025641$$