Solve 1/8(160/17+160/25+31)

$$\frac { 1 } { 8 } ( \frac { 160 } { 17 } + \frac { 160 } { 25 } + 31 )$$

Evaluate

$$\frac{3979}{680}\approx 5.851470588$$

Solution Steps

Reduce the fraction \frac{160}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}\left(\frac{160}{17}+\frac{32}{5}+31\right)$$

Least common multiple of 17 and 5 is 85. Convert \frac{160}{17} and \frac{32}{5} to fractions with denominator 85.

$$\frac{1}{8}\left(\frac{800}{85}+\frac{544}{85}+31\right)$$

Since \frac{800}{85} and \frac{544}{85} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\left(\frac{800+544}{85}+31\right)$$

Add 800 and 544 to get 1344.

$$\frac{1}{8}\left(\frac{1344}{85}+31\right)$$

Convert 31 to fraction \frac{2635}{85}.

$$\frac{1}{8}\left(\frac{1344}{85}+\frac{2635}{85}\right)$$

Since \frac{1344}{85} and \frac{2635}{85} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\times \frac{1344+2635}{85}$$

Add 1344 and 2635 to get 3979.

$$\frac{1}{8}\times \frac{3979}{85}$$

Multiply \frac{1}{8} times \frac{3979}{85} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3979}{8\times 85}$$

Do the multiplications in the fraction \frac{1\times 3979}{8\times 85}.

$$\frac{3979}{680}$$

Factor

$$\frac{23 \cdot 173}{2 ^ {3} \cdot 5 \cdot 17} = 5\frac{579}{680} = 5.851470588235294$$