Solve (37/11+11/13)-(115/11+10/13)

$$( 3 \frac { 7 } { 11 } + 1 \frac { 1 } { 13 } ) - ( 1 \frac { 15 } { 11 } + \frac { 10 } { 13 } )$$

Evaluate

$$\frac{226}{143}\approx 1.58041958$$

Solution Steps

Multiply 3 and 11 to get 33.

$$\frac{33+7}{11}+\frac{1\times 13+1}{13}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Add 33 and 7 to get 40.

$$\frac{40}{11}+\frac{1\times 13+1}{13}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Multiply 1 and 13 to get 13.

$$\frac{40}{11}+\frac{13+1}{13}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Add 13 and 1 to get 14.

$$\frac{40}{11}+\frac{14}{13}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Least common multiple of 11 and 13 is 143. Convert \frac{40}{11} and \frac{14}{13} to fractions with denominator 143.

$$\frac{520}{143}+\frac{154}{143}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Since \frac{520}{143} and \frac{154}{143} have the same denominator, add them by adding their numerators.

$$\frac{520+154}{143}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Add 520 and 154 to get 674.

$$\frac{674}{143}-\left(\frac{1\times 11+15}{11}+\frac{10}{13}\right)$$

Multiply 1 and 11 to get 11.

$$\frac{674}{143}-\left(\frac{11+15}{11}+\frac{10}{13}\right)$$

Add 11 and 15 to get 26.

$$\frac{674}{143}-\left(\frac{26}{11}+\frac{10}{13}\right)$$

Least common multiple of 11 and 13 is 143. Convert \frac{26}{11} and \frac{10}{13} to fractions with denominator 143.

$$\frac{674}{143}-\left(\frac{338}{143}+\frac{110}{143}\right)$$

Since \frac{338}{143} and \frac{110}{143} have the same denominator, add them by adding their numerators.

$$\frac{674}{143}-\frac{338+110}{143}$$

Add 338 and 110 to get 448.

$$\frac{674}{143}-\frac{448}{143}$$

Since \frac{674}{143} and \frac{448}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{674-448}{143}$$

Subtract 448 from 674 to get 226.

$$\frac{226}{143}$$

Factor

$$\frac{2 \cdot 113}{11 \cdot 13} = 1\frac{83}{143} = 1.5804195804195804$$