Solve 3.75*(23/5-12/3)*0.85div32/5

$$3.75 \times (2 \frac{ 3 }{ 5 } -1 \frac{ 2 }{ 3 } ) \times 0.85 \div 3 \frac{ 2 }{ 5 }$$

Evaluate

$$0.875$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{3.75\left(\frac{10+3}{5}-\frac{1\times 3+2}{3}\right)\times 0.85}{\frac{3\times 5+2}{5}}$$

Add 10 and 3 to get 13.

$$\frac{3.75\left(\frac{13}{5}-\frac{1\times 3+2}{3}\right)\times 0.85}{\frac{3\times 5+2}{5}}$$

Multiply 1 and 3 to get 3.

$$\frac{3.75\left(\frac{13}{5}-\frac{3+2}{3}\right)\times 0.85}{\frac{3\times 5+2}{5}}$$

Add 3 and 2 to get 5.

$$\frac{3.75\left(\frac{13}{5}-\frac{5}{3}\right)\times 0.85}{\frac{3\times 5+2}{5}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{13}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{3.75\left(\frac{39}{15}-\frac{25}{15}\right)\times 0.85}{\frac{3\times 5+2}{5}}$$

Since \frac{39}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3.75\times \frac{39-25}{15}\times 0.85}{\frac{3\times 5+2}{5}}$$

Subtract 25 from 39 to get 14.

$$\frac{3.75\times \frac{14}{15}\times 0.85}{\frac{3\times 5+2}{5}}$$

Convert decimal number 3.75 to fraction \frac{375}{100}. Reduce the fraction \frac{375}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{15}{4}\times \frac{14}{15}\times 0.85}{\frac{3\times 5+2}{5}}$$

Multiply \frac{15}{4} times \frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15\times 14}{4\times 15}\times 0.85}{\frac{3\times 5+2}{5}}$$

Cancel out 15 in both numerator and denominator.

$$\frac{\frac{14}{4}\times 0.85}{\frac{3\times 5+2}{5}}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{2}\times 0.85}{\frac{3\times 5+2}{5}}$$

Convert decimal number 0.85 to fraction \frac{85}{100}. Reduce the fraction \frac{85}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{2}\times \frac{17}{20}}{\frac{3\times 5+2}{5}}$$

Multiply \frac{7}{2} times \frac{17}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 17}{2\times 20}}{\frac{3\times 5+2}{5}}$$

Do the multiplications in the fraction \frac{7\times 17}{2\times 20}.

$$\frac{\frac{119}{40}}{\frac{3\times 5+2}{5}}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{119}{40}}{\frac{15+2}{5}}$$

Add 15 and 2 to get 17.

$$\frac{\frac{119}{40}}{\frac{17}{5}}$$

Divide \frac{119}{40} by \frac{17}{5} by multiplying \frac{119}{40} by the reciprocal of \frac{17}{5}.

$$\frac{119}{40}\times \frac{5}{17}$$

Multiply \frac{119}{40} times \frac{5}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{119\times 5}{40\times 17}$$

Do the multiplications in the fraction \frac{119\times 5}{40\times 17}.

$$\frac{595}{680}$$

Reduce the fraction \frac{595}{680} to lowest terms by extracting and canceling out 85.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$