Solve 3/25/4/frac{2{9}-3/10}

$$\frac{ \frac{ 3 }{ 2 } \frac{ 5 }{ 4 } }{ \frac{ 2 }{ 9 } - \frac{ 3 }{ 10 } }$$

Evaluate

$$-\frac{675}{28}\approx -24.107142857$$

Solution Steps

Multiply \frac{3}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 5}{2\times 4}}{\frac{2}{9}-\frac{3}{10}}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 4}.

$$\frac{\frac{15}{8}}{\frac{2}{9}-\frac{3}{10}}$$

Least common multiple of 9 and 10 is 90. Convert \frac{2}{9} and \frac{3}{10} to fractions with denominator 90.

$$\frac{\frac{15}{8}}{\frac{20}{90}-\frac{27}{90}}$$

Since \frac{20}{90} and \frac{27}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15}{8}}{\frac{20-27}{90}}$$

Subtract 27 from 20 to get -7.

$$\frac{\frac{15}{8}}{-\frac{7}{90}}$$

Divide \frac{15}{8} by -\frac{7}{90} by multiplying \frac{15}{8} by the reciprocal of -\frac{7}{90}.

$$\frac{15}{8}\left(-\frac{90}{7}\right)$$

Multiply \frac{15}{8} times -\frac{90}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\left(-90\right)}{8\times 7}$$

Do the multiplications in the fraction \frac{15\left(-90\right)}{8\times 7}.

$$\frac{-1350}{56}$$

Reduce the fraction \frac{-1350}{56} to lowest terms by extracting and canceling out 2.

$$-\frac{675}{28}$$

Factor

$$-\frac{675}{28} = -24\frac{3}{28} = -24.107142857142858$$