Solve 7/11div(47/11-134/13+94/13)

$$\frac { 7 } { 11 } \div ( 4 \frac { 7 } { 11 } - 13 \frac { 4 } { 13 } + 9 \frac { 4 } { 13 } )$$

Evaluate

$$1$$

Solution Steps

Multiply 4 and 11 to get 44.

$$\frac{\frac{7}{11}}{\frac{44+7}{11}-\frac{13\times 13+4}{13}+\frac{9\times 13+4}{13}}$$

Add 44 and 7 to get 51.

$$\frac{\frac{7}{11}}{\frac{51}{11}-\frac{13\times 13+4}{13}+\frac{9\times 13+4}{13}}$$

Multiply 13 and 13 to get 169.

$$\frac{\frac{7}{11}}{\frac{51}{11}-\frac{169+4}{13}+\frac{9\times 13+4}{13}}$$

Add 169 and 4 to get 173.

$$\frac{\frac{7}{11}}{\frac{51}{11}-\frac{173}{13}+\frac{9\times 13+4}{13}}$$

Least common multiple of 11 and 13 is 143. Convert \frac{51}{11} and \frac{173}{13} to fractions with denominator 143.

$$\frac{\frac{7}{11}}{\frac{663}{143}-\frac{1903}{143}+\frac{9\times 13+4}{13}}$$

Since \frac{663}{143} and \frac{1903}{143} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{11}}{\frac{663-1903}{143}+\frac{9\times 13+4}{13}}$$

Subtract 1903 from 663 to get -1240.

$$\frac{\frac{7}{11}}{-\frac{1240}{143}+\frac{9\times 13+4}{13}}$$

Multiply 9 and 13 to get 117.

$$\frac{\frac{7}{11}}{-\frac{1240}{143}+\frac{117+4}{13}}$$

Add 117 and 4 to get 121.

$$\frac{\frac{7}{11}}{-\frac{1240}{143}+\frac{121}{13}}$$

Least common multiple of 143 and 13 is 143. Convert -\frac{1240}{143} and \frac{121}{13} to fractions with denominator 143.

$$\frac{\frac{7}{11}}{-\frac{1240}{143}+\frac{1331}{143}}$$

Since -\frac{1240}{143} and \frac{1331}{143} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{11}}{\frac{-1240+1331}{143}}$$

Add -1240 and 1331 to get 91.

$$\frac{\frac{7}{11}}{\frac{91}{143}}$$

Reduce the fraction \frac{91}{143} to lowest terms by extracting and canceling out 13.

$$\frac{\frac{7}{11}}{\frac{7}{11}}$$

Divide \frac{7}{11} by \frac{7}{11} to get 1.

$$1$$

Factor

$$1$$