Solve 44/7-17/9+37/11-2frac{14/17}{frac{4}{7}-frac{2}{9}+frac{5}{11}-frac{6}{17}}

$$\frac { 4 \frac { 4 } { 7 } - 1 \frac { 7 } { 9 } + 3 \frac { 7 } { 11 } - 2 \frac { 14 } { 17 } } { \frac { 4 } { 7 } - \frac { 2 } { 9 } + \frac { 5 } { 11 } - \frac { 6 } { 17 } }$$

Evaluate

$$8$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\frac{28+4}{7}-\frac{1\times 9+7}{9}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Add 28 and 4 to get 32.

$$\frac{\frac{32}{7}-\frac{1\times 9+7}{9}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{32}{7}-\frac{9+7}{9}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Add 9 and 7 to get 16.

$$\frac{\frac{32}{7}-\frac{16}{9}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Least common multiple of 7 and 9 is 63. Convert \frac{32}{7} and \frac{16}{9} to fractions with denominator 63.

$$\frac{\frac{288}{63}-\frac{112}{63}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Since \frac{288}{63} and \frac{112}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{288-112}{63}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Subtract 112 from 288 to get 176.

$$\frac{\frac{176}{63}+\frac{3\times 11+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Multiply 3 and 11 to get 33.

$$\frac{\frac{176}{63}+\frac{33+7}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Add 33 and 7 to get 40.

$$\frac{\frac{176}{63}+\frac{40}{11}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Least common multiple of 63 and 11 is 693. Convert \frac{176}{63} and \frac{40}{11} to fractions with denominator 693.

$$\frac{\frac{1936}{693}+\frac{2520}{693}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Since \frac{1936}{693} and \frac{2520}{693} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1936+2520}{693}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Add 1936 and 2520 to get 4456.

$$\frac{\frac{4456}{693}-\frac{2\times 17+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Multiply 2 and 17 to get 34.

$$\frac{\frac{4456}{693}-\frac{34+14}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Add 34 and 14 to get 48.

$$\frac{\frac{4456}{693}-\frac{48}{17}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Least common multiple of 693 and 17 is 11781. Convert \frac{4456}{693} and \frac{48}{17} to fractions with denominator 11781.

$$\frac{\frac{75752}{11781}-\frac{33264}{11781}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Since \frac{75752}{11781} and \frac{33264}{11781} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{75752-33264}{11781}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Subtract 33264 from 75752 to get 42488.

$$\frac{\frac{42488}{11781}}{\frac{4}{7}-\frac{2}{9}+\frac{5}{11}-\frac{6}{17}}$$

Least common multiple of 7 and 9 is 63. Convert \frac{4}{7} and \frac{2}{9} to fractions with denominator 63.

$$\frac{\frac{42488}{11781}}{\frac{36}{63}-\frac{14}{63}+\frac{5}{11}-\frac{6}{17}}$$

Since \frac{36}{63} and \frac{14}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{42488}{11781}}{\frac{36-14}{63}+\frac{5}{11}-\frac{6}{17}}$$

Subtract 14 from 36 to get 22.

$$\frac{\frac{42488}{11781}}{\frac{22}{63}+\frac{5}{11}-\frac{6}{17}}$$

Least common multiple of 63 and 11 is 693. Convert \frac{22}{63} and \frac{5}{11} to fractions with denominator 693.

$$\frac{\frac{42488}{11781}}{\frac{242}{693}+\frac{315}{693}-\frac{6}{17}}$$

Since \frac{242}{693} and \frac{315}{693} have the same denominator, add them by adding their numerators.

$$\frac{\frac{42488}{11781}}{\frac{242+315}{693}-\frac{6}{17}}$$

Add 242 and 315 to get 557.

$$\frac{\frac{42488}{11781}}{\frac{557}{693}-\frac{6}{17}}$$

Least common multiple of 693 and 17 is 11781. Convert \frac{557}{693} and \frac{6}{17} to fractions with denominator 11781.

$$\frac{\frac{42488}{11781}}{\frac{9469}{11781}-\frac{4158}{11781}}$$

Since \frac{9469}{11781} and \frac{4158}{11781} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{42488}{11781}}{\frac{9469-4158}{11781}}$$

Subtract 4158 from 9469 to get 5311.

$$\frac{\frac{42488}{11781}}{\frac{5311}{11781}}$$

Divide \frac{42488}{11781} by \frac{5311}{11781} by multiplying \frac{42488}{11781} by the reciprocal of \frac{5311}{11781}.

$$\frac{42488}{11781}\times \frac{11781}{5311}$$

Multiply \frac{42488}{11781} times \frac{11781}{5311} by multiplying numerator times numerator and denominator times denominator.

$$\frac{42488\times 11781}{11781\times 5311}$$

Cancel out 11781 in both numerator and denominator.

$$\frac{42488}{5311}$$

Divide 42488 by 5311 to get 8.

$$8$$

Factor

$$2^{3}$$