Solve 1/8(160/17+160/25+36)

$$\frac { 1 } { 8 } ( \frac { 160 } { 17 } + \frac { 160 } { 25 } + 36 )$$

Evaluate

$$\frac{1101}{170}\approx 6.476470588$$

Solution Steps

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

$$\frac{1}{8}\left(\frac{160}{17}+\frac{32}{5}+36\right)$$

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

$$\frac{1}{8}\left(\frac{800}{85}+\frac{544}{85}+36\right)$$

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

$$\frac{1}{8}\left(\frac{800+544}{85}+36\right)$$

Add 800 and 544 to get 1344.

$$\frac{1}{8}\left(\frac{1344}{85}+36\right)$$

Convert 36 to fraction \frac{3060}{85}.

$$\frac{1}{8}\left(\frac{1344}{85}+\frac{3060}{85}\right)$$

Since \frac{1344}{85} and \frac{3060}{85} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\times \frac{1344+3060}{85}$$

Add 1344 and 3060 to get 4404.

$$\frac{1}{8}\times \frac{4404}{85}$$

Multiply \frac{1}{8} times \frac{4404}{85} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4404}{8\times 85}$$

Do the multiplications in the fraction \frac{1\times 4404}{8\times 85}.

$$\frac{4404}{680}$$

Reduce the fraction \frac{4404}{680} to lowest terms by extracting and canceling out 4.

$$\frac{1101}{170}$$

Factor

$$\frac{3 \cdot 367}{2 \cdot 5 \cdot 17} = 6\frac{81}{170} = 6.476470588235294$$