Solve 10011/26-(737/39-6925/26)

$$100 \frac { 11 } { 26 } - ( 73 \frac { 7 } { 39 } - 69 \frac { 25 } { 26 } )$$

Evaluate

$$\frac{3791}{39}\approx 97.205128205$$

Solution Steps

Multiply 100 and 26 to get 2600.

$$\frac{2600+11}{26}-\left(\frac{73\times 39+7}{39}-\frac{69\times 26+25}{26}\right)$$

Add 2600 and 11 to get 2611.

$$\frac{2611}{26}-\left(\frac{73\times 39+7}{39}-\frac{69\times 26+25}{26}\right)$$

Multiply 73 and 39 to get 2847.

$$\frac{2611}{26}-\left(\frac{2847+7}{39}-\frac{69\times 26+25}{26}\right)$$

Add 2847 and 7 to get 2854.

$$\frac{2611}{26}-\left(\frac{2854}{39}-\frac{69\times 26+25}{26}\right)$$

Multiply 69 and 26 to get 1794.

$$\frac{2611}{26}-\left(\frac{2854}{39}-\frac{1794+25}{26}\right)$$

Add 1794 and 25 to get 1819.

$$\frac{2611}{26}-\left(\frac{2854}{39}-\frac{1819}{26}\right)$$

Least common multiple of 39 and 26 is 78. Convert \frac{2854}{39} and \frac{1819}{26} to fractions with denominator 78.

$$\frac{2611}{26}-\left(\frac{5708}{78}-\frac{5457}{78}\right)$$

Since \frac{5708}{78} and \frac{5457}{78} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2611}{26}-\frac{5708-5457}{78}$$

Subtract 5457 from 5708 to get 251.

$$\frac{2611}{26}-\frac{251}{78}$$

Least common multiple of 26 and 78 is 78. Convert \frac{2611}{26} and \frac{251}{78} to fractions with denominator 78.

$$\frac{7833}{78}-\frac{251}{78}$$

Since \frac{7833}{78} and \frac{251}{78} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7833-251}{78}$$

Subtract 251 from 7833 to get 7582.

$$\frac{7582}{78}$$

Reduce the fraction \frac{7582}{78} to lowest terms by extracting and canceling out 2.

$$\frac{3791}{39}$$

Factor

$$\frac{17 \cdot 223}{3 \cdot 13} = 97\frac{8}{39} = 97.2051282051282$$