Solve (1-3/4)+(3/4-1/6)*[(8/21-frac{1}{3})*frac{28}{5}-frac{4}{15}]

$$( 1 - \frac { 3 } { 4 } ) + ( \frac { 3 } { 4 } - \frac { 1 } { 6 } ) \times [ ( \frac { 8 } { 21 } - \frac { 1 } { 3 } ) \times \frac { 28 } { 5 } - \frac { 4 } { 15 } ]$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}-\frac{3}{4}+\left(\frac{3}{4}-\frac{1}{6}\right)\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{4}+\left(\frac{3}{4}-\frac{1}{6}\right)\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Subtract 3 from 4 to get 1.

$$\frac{1}{4}+\left(\frac{3}{4}-\frac{1}{6}\right)\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{1}{4}+\left(\frac{9}{12}-\frac{2}{12}\right)\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{9-2}{12}\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Subtract 2 from 9 to get 7.

$$\frac{1}{4}+\frac{7}{12}\left(\left(\frac{8}{21}-\frac{1}{3}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Least common multiple of 21 and 3 is 21. Convert \frac{8}{21} and \frac{1}{3} to fractions with denominator 21.

$$\frac{1}{4}+\frac{7}{12}\left(\left(\frac{8}{21}-\frac{7}{21}\right)\times \frac{28}{5}-\frac{4}{15}\right)$$

Since \frac{8}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{7}{12}\left(\frac{8-7}{21}\times \frac{28}{5}-\frac{4}{15}\right)$$

Subtract 7 from 8 to get 1.

$$\frac{1}{4}+\frac{7}{12}\left(\frac{1}{21}\times \frac{28}{5}-\frac{4}{15}\right)$$

Multiply \frac{1}{21} times \frac{28}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}+\frac{7}{12}\left(\frac{1\times 28}{21\times 5}-\frac{4}{15}\right)$$

Do the multiplications in the fraction \frac{1\times 28}{21\times 5}.

$$\frac{1}{4}+\frac{7}{12}\left(\frac{28}{105}-\frac{4}{15}\right)$$

Reduce the fraction \frac{28}{105} to lowest terms by extracting and canceling out 7.

$$\frac{1}{4}+\frac{7}{12}\left(\frac{4}{15}-\frac{4}{15}\right)$$

Subtract \frac{4}{15} from \frac{4}{15} to get 0.

$$\frac{1}{4}+\frac{7}{12}\times 0$$

Multiply \frac{7}{12} and 0 to get 0.

$$\frac{1}{4}+0$$

Add \frac{1}{4} and 0 to get \frac{1}{4}.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$