Solve 17/8*23/5+17/8*22/5

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

Evaluate

$$\frac{75}{8}=9.375$$

Solution Steps

Multiply 1 and 8 to get 8.

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

Add 8 and 7 to get 15.

$$\frac{15}{8}\times \frac{2\times 5+3}{5}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{15}{8}\times \frac{10+3}{5}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Add 10 and 3 to get 13.

$$\frac{15}{8}\times \frac{13}{5}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Multiply \frac{15}{8} times \frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 13}{8\times 5}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Do the multiplications in the fraction \frac{15\times 13}{8\times 5}.

$$\frac{195}{40}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Reduce the fraction \frac{195}{40} to lowest terms by extracting and canceling out 5.

$$\frac{39}{8}+\frac{1\times 8+7}{8}\times \frac{2\times 5+2}{5}$$

Multiply 1 and 8 to get 8.

$$\frac{39}{8}+\frac{8+7}{8}\times \frac{2\times 5+2}{5}$$

Add 8 and 7 to get 15.

$$\frac{39}{8}+\frac{15}{8}\times \frac{2\times 5+2}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{39}{8}+\frac{15}{8}\times \frac{10+2}{5}$$

Add 10 and 2 to get 12.

$$\frac{39}{8}+\frac{15}{8}\times \frac{12}{5}$$

Multiply \frac{15}{8} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39}{8}+\frac{15\times 12}{8\times 5}$$

Do the multiplications in the fraction \frac{15\times 12}{8\times 5}.

$$\frac{39}{8}+\frac{180}{40}$$

Reduce the fraction \frac{180}{40} to lowest terms by extracting and canceling out 20.

$$\frac{39}{8}+\frac{9}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{39}{8} and \frac{9}{2} to fractions with denominator 8.

$$\frac{39}{8}+\frac{36}{8}$$

Since \frac{39}{8} and \frac{36}{8} have the same denominator, add them by adding their numerators.

$$\frac{39+36}{8}$$

Add 39 and 36 to get 75.

$$\frac{75}{8}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2 ^ {3}} = 9\frac{3}{8} = 9.375$$