Solve 2/3:[5:(2/4+1)-3(1/2-1/4)]

$$\frac { 2 } { 3 } : [ 5 : ( \frac { 2 } { 4 } + 1 ) - 3 ( \frac { 1 } { 2 } - \frac { 1 } { 4 } ) ]$$

Evaluate

$$\frac{8}{31}\approx 0.258064516$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}}{\frac{5}{\frac{1}{2}+1}-3\left(\frac{1}{2}-\frac{1}{4}\right)}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{2}{3}}{\frac{5}{\frac{1}{2}+\frac{2}{2}}-3\left(\frac{1}{2}-\frac{1}{4}\right)}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}}{\frac{5}{\frac{1+2}{2}}-3\left(\frac{1}{2}-\frac{1}{4}\right)}$$

Add 1 and 2 to get 3.

$$\frac{\frac{2}{3}}{\frac{5}{\frac{3}{2}}-3\left(\frac{1}{2}-\frac{1}{4}\right)}$$

Divide 5 by \frac{3}{2} by multiplying 5 by the reciprocal of \frac{3}{2}.

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

Express 5\times \frac{2}{3} as a single fraction.

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

Multiply 5 and 2 to get 10.

$$\frac{\frac{2}{3}}{\frac{10}{3}-3\left(\frac{1}{2}-\frac{1}{4}\right)}$$

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

$$\frac{\frac{2}{3}}{\frac{10}{3}-3\left(\frac{2}{4}-\frac{1}{4}\right)}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\frac{2}{3}}{\frac{10}{3}-\frac{3}{4}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{2}{3}}{\frac{40}{12}-\frac{9}{12}}$$

Since \frac{40}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{3}}{\frac{40-9}{12}}$$

Subtract 9 from 40 to get 31.

$$\frac{\frac{2}{3}}{\frac{31}{12}}$$

Divide \frac{2}{3} by \frac{31}{12} by multiplying \frac{2}{3} by the reciprocal of \frac{31}{12}.

$$\frac{2}{3}\times \frac{12}{31}$$

Multiply \frac{2}{3} times \frac{12}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 12}{3\times 31}$$

Do the multiplications in the fraction \frac{2\times 12}{3\times 31}.

$$\frac{24}{93}$$

Reduce the fraction \frac{24}{93} to lowest terms by extracting and canceling out 3.

$$\frac{8}{31}$$

Factor

$$\frac{2 ^ {3}}{31} = 0.25806451612903225$$