Solve -115^2/10026+727*115/10626+660/161

$$- \frac { 115 ^ { 2 } } { 10026 } + \frac { 727 \times 115 } { 10626 } + \frac { 660 } { 161 }$$

Evaluate

$$\frac{94535620}{8878023}\approx 10.648273833$$

Solution Steps

Calculate 115 to the power of 2 and get 13225.

$$-\frac{13225}{10026}+\frac{727\times 115}{10626}+\frac{660}{161}$$

Multiply 727 and 115 to get 83605.

$$-\frac{13225}{10026}+\frac{83605}{10626}+\frac{660}{161}$$

Reduce the fraction \frac{83605}{10626} to lowest terms by extracting and canceling out 23.

$$-\frac{13225}{10026}+\frac{3635}{462}+\frac{660}{161}$$

Least common multiple of 10026 and 462 is 772002. Convert -\frac{13225}{10026} and \frac{3635}{462} to fractions with denominator 772002.

$$-\frac{1018325}{772002}+\frac{6074085}{772002}+\frac{660}{161}$$

Since -\frac{1018325}{772002} and \frac{6074085}{772002} have the same denominator, add them by adding their numerators.

$$\frac{-1018325+6074085}{772002}+\frac{660}{161}$$

Add -1018325 and 6074085 to get 5055760.

$$\frac{5055760}{772002}+\frac{660}{161}$$

Reduce the fraction \frac{5055760}{772002} to lowest terms by extracting and canceling out 2.

$$\frac{2527880}{386001}+\frac{660}{161}$$

Least common multiple of 386001 and 161 is 8878023. Convert \frac{2527880}{386001} and \frac{660}{161} to fractions with denominator 8878023.

$$\frac{58141240}{8878023}+\frac{36394380}{8878023}$$

Since \frac{58141240}{8878023} and \frac{36394380}{8878023} have the same denominator, add them by adding their numerators.

$$\frac{58141240+36394380}{8878023}$$

Add 58141240 and 36394380 to get 94535620.

$$\frac{94535620}{8878023}$$

Factor

$$\frac{2 ^ {2} \cdot 5 \cdot 2113 \cdot 2237}{3 ^ {2} \cdot 7 \cdot 11 \cdot 23 \cdot 557} = 10\frac{5755390}{8878023} = 10.648273833036928$$