Solve 13/20div[3/4-(1/6+4/15)]

$$\frac { 13 } { 20 } \div [ \frac { 3 } { 4 } - ( \frac { 1 } { 6 } + \frac { 4 } { 15 } ) ]$$

Evaluate

$$\frac{39}{19}\approx 2.052631579$$

Solution Steps

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{4}{15} to fractions with denominator 30.

$$\frac{\frac{13}{20}}{\frac{3}{4}-\left(\frac{5}{30}+\frac{8}{30}\right)}$$

Since \frac{5}{30} and \frac{8}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{3}{4}-\frac{5+8}{30}}$$

Add 5 and 8 to get 13.

$$\frac{\frac{13}{20}}{\frac{3}{4}-\frac{13}{30}}$$

Least common multiple of 4 and 30 is 60. Convert \frac{3}{4} and \frac{13}{30} to fractions with denominator 60.

$$\frac{\frac{13}{20}}{\frac{45}{60}-\frac{26}{60}}$$

Since \frac{45}{60} and \frac{26}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{20}}{\frac{45-26}{60}}$$

Subtract 26 from 45 to get 19.

$$\frac{\frac{13}{20}}{\frac{19}{60}}$$

Divide \frac{13}{20} by \frac{19}{60} by multiplying \frac{13}{20} by the reciprocal of \frac{19}{60}.

$$\frac{13}{20}\times \frac{60}{19}$$

Multiply \frac{13}{20} times \frac{60}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 60}{20\times 19}$$

Do the multiplications in the fraction \frac{13\times 60}{20\times 19}.

$$\frac{780}{380}$$

Reduce the fraction \frac{780}{380} to lowest terms by extracting and canceling out 20.

$$\frac{39}{19}$$

Factor

$$\frac{3 \cdot 13}{19} = 2\frac{1}{19} = 2.0526315789473686$$