Solve (3/10+12/4)/(frac{13{9}-4/8)}

$$\frac { ( \frac { 3 } { 10 } + \frac { 12 } { 4 } ) } { ( \frac { 13 } { 9 } - \frac { 4 } { 8 } ) }$$

Evaluate

$$\frac{297}{85}\approx 3.494117647$$

Solution Steps

Divide 12 by 4 to get 3.

$$\frac{\frac{3}{10}+3}{\frac{13}{9}-\frac{4}{8}}$$

Convert 3 to fraction \frac{30}{10}.

$$\frac{\frac{3}{10}+\frac{30}{10}}{\frac{13}{9}-\frac{4}{8}}$$

Since \frac{3}{10} and \frac{30}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+30}{10}}{\frac{13}{9}-\frac{4}{8}}$$

Add 3 and 30 to get 33.

$$\frac{\frac{33}{10}}{\frac{13}{9}-\frac{4}{8}}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{33}{10}}{\frac{13}{9}-\frac{1}{2}}$$

Least common multiple of 9 and 2 is 18. Convert \frac{13}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{\frac{33}{10}}{\frac{26}{18}-\frac{9}{18}}$$

Since \frac{26}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{33}{10}}{\frac{26-9}{18}}$$

Subtract 9 from 26 to get 17.

$$\frac{\frac{33}{10}}{\frac{17}{18}}$$

Divide \frac{33}{10} by \frac{17}{18} by multiplying \frac{33}{10} by the reciprocal of \frac{17}{18}.

$$\frac{33}{10}\times \frac{18}{17}$$

Multiply \frac{33}{10} times \frac{18}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 18}{10\times 17}$$

Do the multiplications in the fraction \frac{33\times 18}{10\times 17}.

$$\frac{594}{170}$$

Reduce the fraction \frac{594}{170} to lowest terms by extracting and canceling out 2.

$$\frac{297}{85}$$

Factor

$$\frac{3 ^ {3} \cdot 11}{5 \cdot 17} = 3\frac{42}{85} = 3.4941176470588236$$