Solve [7/20-(4/5-1/2)div13/20]

$$[ \frac { 7 } { 20 } - ( \frac { 4 } { 5 } - \frac { 1 } { 2 } ) \div \frac { 13 } { 20 } ]$$

Evaluate

$$-\frac{29}{260}\approx -0.111538462$$

Solution Steps

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

$$\frac{7}{20}-\frac{\frac{8}{10}-\frac{5}{10}}{\frac{13}{20}}$$

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

$$\frac{7}{20}-\frac{\frac{8-5}{10}}{\frac{13}{20}}$$

Subtract 5 from 8 to get 3.

$$\frac{7}{20}-\frac{\frac{3}{10}}{\frac{13}{20}}$$

Divide \frac{3}{10} by \frac{13}{20} by multiplying \frac{3}{10} by the reciprocal of \frac{13}{20}.

$$\frac{7}{20}-\frac{3}{10}\times \frac{20}{13}$$

Multiply \frac{3}{10} times \frac{20}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{20}-\frac{3\times 20}{10\times 13}$$

Do the multiplications in the fraction \frac{3\times 20}{10\times 13}.

$$\frac{7}{20}-\frac{60}{130}$$

Reduce the fraction \frac{60}{130} to lowest terms by extracting and canceling out 10.

$$\frac{7}{20}-\frac{6}{13}$$

Least common multiple of 20 and 13 is 260. Convert \frac{7}{20} and \frac{6}{13} to fractions with denominator 260.

$$\frac{91}{260}-\frac{120}{260}$$

Since \frac{91}{260} and \frac{120}{260} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-120}{260}$$

Subtract 120 from 91 to get -29.

$$-\frac{29}{260}$$

Factor

$$-\frac{29}{260} = -0.11153846153846154$$