Solve .91/frac{1{24}+1/56}

$$.9 \frac { 1 } { \frac { 1 } { 24 } + \frac { 1 } { 56 } }$$

Evaluate

$$15.12$$

Solution Steps

Least common multiple of 24 and 56 is 168. Convert \frac{1}{24} and \frac{1}{56} to fractions with denominator 168.

$$0.9\times \frac{1}{\frac{7}{168}+\frac{3}{168}}$$

Since \frac{7}{168} and \frac{3}{168} have the same denominator, add them by adding their numerators.

$$0.9\times \frac{1}{\frac{7+3}{168}}$$

Add 7 and 3 to get 10.

$$0.9\times \frac{1}{\frac{10}{168}}$$

Reduce the fraction \frac{10}{168} to lowest terms by extracting and canceling out 2.

$$0.9\times \frac{1}{\frac{5}{84}}$$

Divide 1 by \frac{5}{84} by multiplying 1 by the reciprocal of \frac{5}{84}.

$$0.9\times 1\times \frac{84}{5}$$

Multiply 1 and \frac{84}{5} to get \frac{84}{5}.

$$0.9\times \frac{84}{5}$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{9}{10}\times \frac{84}{5}$$

Multiply \frac{9}{10} times \frac{84}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 84}{10\times 5}$$

Do the multiplications in the fraction \frac{9\times 84}{10\times 5}.

$$\frac{756}{50}$$

Reduce the fraction \frac{756}{50} to lowest terms by extracting and canceling out 2.

$$\frac{378}{25}$$

Factor

$$\frac{2 \cdot 7 \cdot 3 ^ {3}}{5 ^ {2}} = 15\frac{3}{25} = 15.12$$