Solve 27/20div[3/4+9/2*1/15]

$$2 \frac { 7 } { 20 } \div [ \frac { 3 } { 4 } + \frac { 9 } { 2 } \times \frac { 1 } { 15 } ]$$

Evaluate

$$\frac{47}{21}\approx 2.238095238$$

Solution Steps

Multiply 2 and 20 to get 40.

$$\frac{\frac{40+7}{20}}{\frac{3}{4}+\frac{9}{2}\times \frac{1}{15}}$$

Add 40 and 7 to get 47.

$$\frac{\frac{47}{20}}{\frac{3}{4}+\frac{9}{2}\times \frac{1}{15}}$$

Multiply \frac{9}{2} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{47}{20}}{\frac{3}{4}+\frac{9\times 1}{2\times 15}}$$

Do the multiplications in the fraction \frac{9\times 1}{2\times 15}.

$$\frac{\frac{47}{20}}{\frac{3}{4}+\frac{9}{30}}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{47}{20}}{\frac{3}{4}+\frac{3}{10}}$$

Least common multiple of 4 and 10 is 20. Convert \frac{3}{4} and \frac{3}{10} to fractions with denominator 20.

$$\frac{\frac{47}{20}}{\frac{15}{20}+\frac{6}{20}}$$

Since \frac{15}{20} and \frac{6}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{47}{20}}{\frac{15+6}{20}}$$

Add 15 and 6 to get 21.

$$\frac{\frac{47}{20}}{\frac{21}{20}}$$

Divide \frac{47}{20} by \frac{21}{20} by multiplying \frac{47}{20} by the reciprocal of \frac{21}{20}.

$$\frac{47}{20}\times \frac{20}{21}$$

Multiply \frac{47}{20} times \frac{20}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{47\times 20}{20\times 21}$$

Cancel out 20 in both numerator and denominator.

$$\frac{47}{21}$$

Factor

$$\frac{47}{3 \cdot 7} = 2\frac{5}{21} = 2.238095238095238$$