Solve 3/8*17/20-3/20*375%quad24*13/6divfrac{2}{5}

$$\frac { 3 } { 8 } \times \frac { 17 } { 20 } - \frac { 3 } { 20 } \times 375 \% \quad 24 \times \frac { 13 } { 6 } \div \frac { 2 } { 5 }$$

Evaluate

$$-\frac{11649}{160}=-72.80625$$

Solution Steps

Multiply \frac{3}{8} times \frac{17}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 17}{8\times 20}-\frac{\frac{3}{20}\times \frac{375}{100}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{3\times 17}{8\times 20}.

$$\frac{51}{160}-\frac{\frac{3}{20}\times \frac{375}{100}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Reduce the fraction \frac{375}{100} to lowest terms by extracting and canceling out 25.

$$\frac{51}{160}-\frac{\frac{3}{20}\times \frac{15}{4}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Multiply \frac{3}{20} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{160}-\frac{\frac{3\times 15}{20\times 4}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{3\times 15}{20\times 4}.

$$\frac{51}{160}-\frac{\frac{45}{80}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Reduce the fraction \frac{45}{80} to lowest terms by extracting and canceling out 5.

$$\frac{51}{160}-\frac{\frac{9}{16}\times 24\times \frac{13}{6}}{\frac{2}{5}}$$

Express \frac{9}{16}\times 24 as a single fraction.

$$\frac{51}{160}-\frac{\frac{9\times 24}{16}\times \frac{13}{6}}{\frac{2}{5}}$$

Multiply 9 and 24 to get 216.

$$\frac{51}{160}-\frac{\frac{216}{16}\times \frac{13}{6}}{\frac{2}{5}}$$

Reduce the fraction \frac{216}{16} to lowest terms by extracting and canceling out 8.

$$\frac{51}{160}-\frac{\frac{27}{2}\times \frac{13}{6}}{\frac{2}{5}}$$

Multiply \frac{27}{2} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{160}-\frac{\frac{27\times 13}{2\times 6}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{27\times 13}{2\times 6}.

$$\frac{51}{160}-\frac{\frac{351}{12}}{\frac{2}{5}}$$

Reduce the fraction \frac{351}{12} to lowest terms by extracting and canceling out 3.

$$\frac{51}{160}-\frac{\frac{117}{4}}{\frac{2}{5}}$$

Divide \frac{117}{4} by \frac{2}{5} by multiplying \frac{117}{4} by the reciprocal of \frac{2}{5}.

$$\frac{51}{160}-\frac{117}{4}\times \frac{5}{2}$$

Multiply \frac{117}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{160}-\frac{117\times 5}{4\times 2}$$

Do the multiplications in the fraction \frac{117\times 5}{4\times 2}.

$$\frac{51}{160}-\frac{585}{8}$$

Least common multiple of 160 and 8 is 160. Convert \frac{51}{160} and \frac{585}{8} to fractions with denominator 160.

$$\frac{51}{160}-\frac{11700}{160}$$

Since \frac{51}{160} and \frac{11700}{160} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-11700}{160}$$

Subtract 11700 from 51 to get -11649.

$$-\frac{11649}{160}$$

Factor

$$-\frac{11649}{160} = -72\frac{129}{160} = -72.80625$$