Solve 3/4-[5/10*(10/7-2/4)]

$$\frac { 3 } { 4 } - [ \frac { 5 } { 10 } \times ( \frac { 10 } { 7 } - \frac { 2 } { 4 } ) ]$$

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

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

$$\frac{3}{4}-\frac{1}{2}\left(\frac{10}{7}-\frac{2}{4}\right)$$

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

$$\frac{3}{4}-\frac{1}{2}\left(\frac{10}{7}-\frac{1}{2}\right)$$

Least common multiple of 7 and 2 is 14. Convert \frac{10}{7} and \frac{1}{2} to fractions with denominator 14.

$$\frac{3}{4}-\frac{1}{2}\left(\frac{20}{14}-\frac{7}{14}\right)$$

Since \frac{20}{14} and \frac{7}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}-\frac{1}{2}\times \frac{20-7}{14}$$

Subtract 7 from 20 to get 13.

$$\frac{3}{4}-\frac{1}{2}\times \frac{13}{14}$$

Multiply \frac{1}{2} times \frac{13}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}-\frac{1\times 13}{2\times 14}$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 14}.

$$\frac{3}{4}-\frac{13}{28}$$

Least common multiple of 4 and 28 is 28. Convert \frac{3}{4} and \frac{13}{28} to fractions with denominator 28.

$$\frac{21}{28}-\frac{13}{28}$$

Since \frac{21}{28} and \frac{13}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-13}{28}$$

Subtract 13 from 21 to get 8.

$$\frac{8}{28}$$

Reduce the fraction \frac{8}{28} to lowest terms by extracting and canceling out 4.

$$\frac{2}{7}$$

Factor

$$\frac{2}{7} = 0.2857142857142857$$