Solve 3/5*(5/7+5/24)div9/56

$$\frac { 3 } { 5 } \times ( \frac { 5 } { 7 } + \frac { 5 } { 24 } ) \div \frac { 9 } { 56 }$$

Evaluate

$$\frac{31}{9}\approx 3.444444444$$

Solution Steps

Least common multiple of 7 and 24 is 168. Convert \frac{5}{7} and \frac{5}{24} to fractions with denominator 168.

$$\frac{\frac{3}{5}\left(\frac{120}{168}+\frac{35}{168}\right)}{\frac{9}{56}}$$

Since \frac{120}{168} and \frac{35}{168} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}\times \frac{120+35}{168}}{\frac{9}{56}}$$

Add 120 and 35 to get 155.

$$\frac{\frac{3}{5}\times \frac{155}{168}}{\frac{9}{56}}$$

Multiply \frac{3}{5} times \frac{155}{168} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 155}{5\times 168}}{\frac{9}{56}}$$

Do the multiplications in the fraction \frac{3\times 155}{5\times 168}.

$$\frac{\frac{465}{840}}{\frac{9}{56}}$$

Reduce the fraction \frac{465}{840} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{31}{56}}{\frac{9}{56}}$$

Divide \frac{31}{56} by \frac{9}{56} by multiplying \frac{31}{56} by the reciprocal of \frac{9}{56}.

$$\frac{31}{56}\times \frac{56}{9}$$

Multiply \frac{31}{56} times \frac{56}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 56}{56\times 9}$$

Cancel out 56 in both numerator and denominator.

$$\frac{31}{9}$$

Factor

$$\frac{31}{3 ^ {2}} = 3\frac{4}{9} = 3.4444444444444446$$