Solve 9/20div[(7/4+1/5)*1/13]=

$$\frac { 9 } { 20 } \div [ ( \frac { 7 } { 4 } + \frac { 1 } { 5 } ) \times \frac { 1 } { 13 } ] =$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{7}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{9}{20}}{\left(\frac{35}{20}+\frac{4}{20}\right)\times \frac{1}{13}}$$

Since \frac{35}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{20}}{\frac{35+4}{20}\times \frac{1}{13}}$$

Add 35 and 4 to get 39.

$$\frac{\frac{9}{20}}{\frac{39}{20}\times \frac{1}{13}}$$

Multiply \frac{39}{20} times \frac{1}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{20}}{\frac{39\times 1}{20\times 13}}$$

Do the multiplications in the fraction \frac{39\times 1}{20\times 13}.

$$\frac{\frac{9}{20}}{\frac{39}{260}}$$

Reduce the fraction \frac{39}{260} to lowest terms by extracting and canceling out 13.

$$\frac{\frac{9}{20}}{\frac{3}{20}}$$

Divide \frac{9}{20} by \frac{3}{20} by multiplying \frac{9}{20} by the reciprocal of \frac{3}{20}.

$$\frac{9}{20}\times \frac{20}{3}$$

Multiply \frac{9}{20} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 20}{20\times 3}$$

Cancel out 20 in both numerator and denominator.

$$\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$3$$

Factor

$$3$$