Solve 15/8*3.2-31/8div5/16+31/5*7frac{1}{2}

$$1 \frac { 5 } { 8 } \times 3.2 - 3 \frac { 1 } { 8 } \div \frac { 5 } { 16 } + 3 \frac { 1 } { 5 } \times 7 \frac { 1 } { 2 }$$

Evaluate

$$19.2$$

Solution Steps

Multiply 1 and 8 to get 8.

$$\frac{8+5}{8}\times 3.2-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Add 8 and 5 to get 13.

$$\frac{13}{8}\times 3.2-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Convert decimal number 3.2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{13}{8}\times \frac{16}{5}-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Multiply \frac{13}{8} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 16}{8\times 5}-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Do the multiplications in the fraction \frac{13\times 16}{8\times 5}.

$$\frac{208}{40}-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Reduce the fraction \frac{208}{40} to lowest terms by extracting and canceling out 8.

$$\frac{26}{5}-\frac{\frac{3\times 8+1}{8}}{\frac{5}{16}}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Divide \frac{3\times 8+1}{8} by \frac{5}{16} by multiplying \frac{3\times 8+1}{8} by the reciprocal of \frac{5}{16}.

$$\frac{26}{5}-\frac{\left(3\times 8+1\right)\times 16}{8\times 5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Cancel out 8 in both numerator and denominator.

$$\frac{26}{5}-\frac{2\left(1+3\times 8\right)}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Multiply 3 and 8 to get 24.

$$\frac{26}{5}-\frac{2\left(1+24\right)}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Add 1 and 24 to get 25.

$$\frac{26}{5}-\frac{2\times 25}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Multiply 2 and 25 to get 50.

$$\frac{26}{5}-\frac{50}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Since \frac{26}{5} and \frac{50}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-50}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Subtract 50 from 26 to get -24.

$$-\frac{24}{5}+\frac{3\times 5+1}{5}\times \frac{7\times 2+1}{2}$$

Multiply 3 and 5 to get 15.

$$-\frac{24}{5}+\frac{15+1}{5}\times \frac{7\times 2+1}{2}$$

Add 15 and 1 to get 16.

$$-\frac{24}{5}+\frac{16}{5}\times \frac{7\times 2+1}{2}$$

Multiply 7 and 2 to get 14.

$$-\frac{24}{5}+\frac{16}{5}\times \frac{14+1}{2}$$

Add 14 and 1 to get 15.

$$-\frac{24}{5}+\frac{16}{5}\times \frac{15}{2}$$

Multiply \frac{16}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{24}{5}+\frac{16\times 15}{5\times 2}$$

Do the multiplications in the fraction \frac{16\times 15}{5\times 2}.

$$-\frac{24}{5}+\frac{240}{10}$$

Divide 240 by 10 to get 24.

$$-\frac{24}{5}+24$$

Convert 24 to fraction \frac{120}{5}.

$$-\frac{24}{5}+\frac{120}{5}$$

Since -\frac{24}{5} and \frac{120}{5} have the same denominator, add them by adding their numerators.

$$\frac{-24+120}{5}$$

Add -24 and 120 to get 96.

$$\frac{96}{5}$$

Factor

$$\frac{3 \cdot 2 ^ {5}}{5} = 19\frac{1}{5} = 19.2$$