Solve 41/7+68/11-21/7

$$4 \frac { 1 } { 7 } + 6 \frac { 8 } { 11 } - 2 \frac { 1 } { 7 }$$

Evaluate

$$\frac{96}{11}\approx 8.727272727$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{28+1}{7}+\frac{6\times 11+8}{11}-\frac{2\times 7+1}{7}$$

Add 28 and 1 to get 29.

$$\frac{29}{7}+\frac{6\times 11+8}{11}-\frac{2\times 7+1}{7}$$

Multiply 6 and 11 to get 66.

$$\frac{29}{7}+\frac{66+8}{11}-\frac{2\times 7+1}{7}$$

Add 66 and 8 to get 74.

$$\frac{29}{7}+\frac{74}{11}-\frac{2\times 7+1}{7}$$

Least common multiple of 7 and 11 is 77. Convert \frac{29}{7} and \frac{74}{11} to fractions with denominator 77.

$$\frac{319}{77}+\frac{518}{77}-\frac{2\times 7+1}{7}$$

Since \frac{319}{77} and \frac{518}{77} have the same denominator, add them by adding their numerators.

$$\frac{319+518}{77}-\frac{2\times 7+1}{7}$$

Add 319 and 518 to get 837.

$$\frac{837}{77}-\frac{2\times 7+1}{7}$$

Multiply 2 and 7 to get 14.

$$\frac{837}{77}-\frac{14+1}{7}$$

Add 14 and 1 to get 15.

$$\frac{837}{77}-\frac{15}{7}$$

Least common multiple of 77 and 7 is 77. Convert \frac{837}{77} and \frac{15}{7} to fractions with denominator 77.

$$\frac{837}{77}-\frac{165}{77}$$

Since \frac{837}{77} and \frac{165}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{837-165}{77}$$

Subtract 165 from 837 to get 672.

$$\frac{672}{77}$$

Reduce the fraction \frac{672}{77} to lowest terms by extracting and canceling out 7.

$$\frac{96}{11}$$

Factor

$$\frac{2 ^ {5} \cdot 3}{11} = 8\frac{8}{11} = 8.727272727272727$$