Solve 31/3*1.9+19.5div41/2/frac{62{75}-0.16}

$$\frac { 3 \frac { 1 } { 3 } \times 1.9 + 19.5 \div 4 \frac { 1 } { 2 } } { \frac { 62 } { 75 } - 0.16 }$$

Evaluate

$$16$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\frac{\frac{9+1}{3}\times 1.9+\frac{19.5}{\frac{4\times 2+1}{2}}}{\frac{62}{75}-0.16}$$

Add 9 and 1 to get 10.

$$\frac{\frac{10}{3}\times 1.9+\frac{19.5}{\frac{4\times 2+1}{2}}}{\frac{62}{75}-0.16}$$

Convert decimal number 1.9 to fraction \frac{19}{10}.

$$\frac{\frac{10}{3}\times \frac{19}{10}+\frac{19.5}{\frac{4\times 2+1}{2}}}{\frac{62}{75}-0.16}$$

Multiply \frac{10}{3} times \frac{19}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10\times 19}{3\times 10}+\frac{19.5}{\frac{4\times 2+1}{2}}}{\frac{62}{75}-0.16}$$

Cancel out 10 in both numerator and denominator.

$$\frac{\frac{19}{3}+\frac{19.5}{\frac{4\times 2+1}{2}}}{\frac{62}{75}-0.16}$$

Divide 19.5 by \frac{4\times 2+1}{2} by multiplying 19.5 by the reciprocal of \frac{4\times 2+1}{2}.

$$\frac{\frac{19}{3}+\frac{19.5\times 2}{4\times 2+1}}{\frac{62}{75}-0.16}$$

Multiply 19.5 and 2 to get 39.

$$\frac{\frac{19}{3}+\frac{39}{4\times 2+1}}{\frac{62}{75}-0.16}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{19}{3}+\frac{39}{8+1}}{\frac{62}{75}-0.16}$$

Add 8 and 1 to get 9.

$$\frac{\frac{19}{3}+\frac{39}{9}}{\frac{62}{75}-0.16}$$

Reduce the fraction \frac{39}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{19}{3}+\frac{13}{3}}{\frac{62}{75}-0.16}$$

Since \frac{19}{3} and \frac{13}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{19+13}{3}}{\frac{62}{75}-0.16}$$

Add 19 and 13 to get 32.

$$\frac{\frac{32}{3}}{\frac{62}{75}-0.16}$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{32}{3}}{\frac{62}{75}-\frac{4}{25}}$$

Least common multiple of 75 and 25 is 75. Convert \frac{62}{75} and \frac{4}{25} to fractions with denominator 75.

$$\frac{\frac{32}{3}}{\frac{62}{75}-\frac{12}{75}}$$

Since \frac{62}{75} and \frac{12}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{32}{3}}{\frac{62-12}{75}}$$

Subtract 12 from 62 to get 50.

$$\frac{\frac{32}{3}}{\frac{50}{75}}$$

Reduce the fraction \frac{50}{75} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{32}{3}}{\frac{2}{3}}$$

Divide \frac{32}{3} by \frac{2}{3} by multiplying \frac{32}{3} by the reciprocal of \frac{2}{3}.

$$\frac{32}{3}\times \frac{3}{2}$$

Multiply \frac{32}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{32}{2}$$

Divide 32 by 2 to get 16.

$$16$$

Factor

$$2^{4}$$