Solve (8/9+6/17)*1/8+15/17

$$( \frac { 8 } { 9 } + \frac { 6 } { 17 } ) \times \frac { 1 } { 8 } + \frac { 15 } { 17 }$$

Evaluate

$$\frac{635}{612}\approx 1.037581699$$

Solution Steps

Least common multiple of 9 and 17 is 153. Convert \frac{8}{9} and \frac{6}{17} to fractions with denominator 153.

$$\left(\frac{136}{153}+\frac{54}{153}\right)\times \frac{1}{8}+\frac{15}{17}$$

Since \frac{136}{153} and \frac{54}{153} have the same denominator, add them by adding their numerators.

$$\frac{136+54}{153}\times \frac{1}{8}+\frac{15}{17}$$

Add 136 and 54 to get 190.

$$\frac{190}{153}\times \frac{1}{8}+\frac{15}{17}$$

Multiply \frac{190}{153} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{190\times 1}{153\times 8}+\frac{15}{17}$$

Do the multiplications in the fraction \frac{190\times 1}{153\times 8}.

$$\frac{190}{1224}+\frac{15}{17}$$

Reduce the fraction \frac{190}{1224} to lowest terms by extracting and canceling out 2.

$$\frac{95}{612}+\frac{15}{17}$$

Least common multiple of 612 and 17 is 612. Convert \frac{95}{612} and \frac{15}{17} to fractions with denominator 612.

$$\frac{95}{612}+\frac{540}{612}$$

Since \frac{95}{612} and \frac{540}{612} have the same denominator, add them by adding their numerators.

$$\frac{95+540}{612}$$

Add 95 and 540 to get 635.

$$\frac{635}{612}$$

Factor

$$\frac{5 \cdot 127}{2 ^ {2} \cdot 3 ^ {2} \cdot 17} = 1\frac{23}{612} = 1.0375816993464053$$