Solve 1/8(320/17+320/25+31)

$$\frac { 1 } { 8 } ( \frac { 320 } { 17 } + \frac { 320 } { 25 } + 31 )$$

Evaluate

$$\frac{5323}{680}\approx 7.827941176$$

Solution Steps

Reduce the fraction \frac{320}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}\left(\frac{320}{17}+\frac{64}{5}+31\right)$$

Least common multiple of 17 and 5 is 85. Convert \frac{320}{17} and \frac{64}{5} to fractions with denominator 85.

$$\frac{1}{8}\left(\frac{1600}{85}+\frac{1088}{85}+31\right)$$

Since \frac{1600}{85} and \frac{1088}{85} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\left(\frac{1600+1088}{85}+31\right)$$

Add 1600 and 1088 to get 2688.

$$\frac{1}{8}\left(\frac{2688}{85}+31\right)$$

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

$$\frac{1}{8}\left(\frac{2688}{85}+\frac{2635}{85}\right)$$

Since \frac{2688}{85} and \frac{2635}{85} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\times \frac{2688+2635}{85}$$

Add 2688 and 2635 to get 5323.

$$\frac{1}{8}\times \frac{5323}{85}$$

Multiply \frac{1}{8} times \frac{5323}{85} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5323}{8\times 85}$$

Do the multiplications in the fraction \frac{1\times 5323}{8\times 85}.

$$\frac{5323}{680}$$

Factor

$$\frac{5323}{2 ^ {3} \cdot 5 \cdot 17} = 7\frac{563}{680} = 7.827941176470588$$