Solve (7/2-1/5):(4/5-7/3)

$$( \frac { 7 } { 2 } - \frac { 1 } { 5 } ) : ( \frac { 4 } { 5 } - \frac { 7 } { 3 } )$$

Evaluate

$$-\frac{99}{46}\approx -2.152173913$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{7}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{35}{10}-\frac{2}{10}}{\frac{4}{5}-\frac{7}{3}}$$

Since \frac{35}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35-2}{10}}{\frac{4}{5}-\frac{7}{3}}$$

Subtract 2 from 35 to get 33.

$$\frac{\frac{33}{10}}{\frac{4}{5}-\frac{7}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{7}{3} to fractions with denominator 15.

$$\frac{\frac{33}{10}}{\frac{12}{15}-\frac{35}{15}}$$

Since \frac{12}{15} and \frac{35}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{33}{10}}{\frac{12-35}{15}}$$

Subtract 35 from 12 to get -23.

$$\frac{\frac{33}{10}}{-\frac{23}{15}}$$

Divide \frac{33}{10} by -\frac{23}{15} by multiplying \frac{33}{10} by the reciprocal of -\frac{23}{15}.

$$\frac{33}{10}\left(-\frac{15}{23}\right)$$

Multiply \frac{33}{10} times -\frac{15}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\left(-15\right)}{10\times 23}$$

Do the multiplications in the fraction \frac{33\left(-15\right)}{10\times 23}.

$$\frac{-495}{230}$$

Reduce the fraction \frac{-495}{230} to lowest terms by extracting and canceling out 5.

$$-\frac{99}{46}$$

Factor

$$-\frac{99}{46} = -2\frac{7}{46} = -2.152173913043478$$