Solve (2/15+15):(12/3-24/5)=

$$( \frac { 2 } { 15 } + 15 ) : ( 1 \frac { 2 } { 3 } - 2 \frac { 4 } { 5 } ) =$$

Evaluate

$$-\frac{227}{17}\approx -13.352941176$$

Solution Steps

Convert 15 to fraction \frac{225}{15}.

$$\frac{\frac{2}{15}+\frac{225}{15}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Since \frac{2}{15} and \frac{225}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+225}{15}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Add 2 and 225 to get 227.

$$\frac{\frac{227}{15}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{227}{15}}{\frac{3+2}{3}-\frac{2\times 5+4}{5}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{227}{15}}{\frac{5}{3}-\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{227}{15}}{\frac{5}{3}-\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$\frac{\frac{227}{15}}{\frac{5}{3}-\frac{14}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{14}{5} to fractions with denominator 15.

$$\frac{\frac{227}{15}}{\frac{25}{15}-\frac{42}{15}}$$

Since \frac{25}{15} and \frac{42}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{227}{15}}{\frac{25-42}{15}}$$

Subtract 42 from 25 to get -17.

$$\frac{\frac{227}{15}}{-\frac{17}{15}}$$

Divide \frac{227}{15} by -\frac{17}{15} by multiplying \frac{227}{15} by the reciprocal of -\frac{17}{15}.

$$\frac{227}{15}\left(-\frac{15}{17}\right)$$

Multiply \frac{227}{15} times -\frac{15}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{227\left(-15\right)}{15\times 17}$$

Do the multiplications in the fraction \frac{227\left(-15\right)}{15\times 17}.

$$\frac{-3405}{255}$$

Reduce the fraction \frac{-3405}{255} to lowest terms by extracting and canceling out 15.

$$-\frac{227}{17}$$

Factor

$$-\frac{227}{17} = -13\frac{6}{17} = -13.352941176470589$$