Solve 8/9+12/11+16/13/frac{2{9}+frac{3}{11}+frac{4}{13}}

$$\frac{ \frac{ 8 }{ 9 } + \frac{ 12 }{ 11 } + \frac{ 16 }{ 13 } }{ \frac{ 2 }{ 9 } + \frac{ 3 }{ 11 } + \frac{ 4 }{ 13 } }$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 9 and 11 is 99. Convert \frac{8}{9} and \frac{12}{11} to fractions with denominator 99.

$$\frac{\frac{88}{99}+\frac{108}{99}+\frac{16}{13}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Since \frac{88}{99} and \frac{108}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{88+108}{99}+\frac{16}{13}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Add 88 and 108 to get 196.

$$\frac{\frac{196}{99}+\frac{16}{13}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Least common multiple of 99 and 13 is 1287. Convert \frac{196}{99} and \frac{16}{13} to fractions with denominator 1287.

$$\frac{\frac{2548}{1287}+\frac{1584}{1287}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Since \frac{2548}{1287} and \frac{1584}{1287} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2548+1584}{1287}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Add 2548 and 1584 to get 4132.

$$\frac{\frac{4132}{1287}}{\frac{2}{9}+\frac{3}{11}+\frac{4}{13}}$$

Least common multiple of 9 and 11 is 99. Convert \frac{2}{9} and \frac{3}{11} to fractions with denominator 99.

$$\frac{\frac{4132}{1287}}{\frac{22}{99}+\frac{27}{99}+\frac{4}{13}}$$

Since \frac{22}{99} and \frac{27}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4132}{1287}}{\frac{22+27}{99}+\frac{4}{13}}$$

Add 22 and 27 to get 49.

$$\frac{\frac{4132}{1287}}{\frac{49}{99}+\frac{4}{13}}$$

Least common multiple of 99 and 13 is 1287. Convert \frac{49}{99} and \frac{4}{13} to fractions with denominator 1287.

$$\frac{\frac{4132}{1287}}{\frac{637}{1287}+\frac{396}{1287}}$$

Since \frac{637}{1287} and \frac{396}{1287} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4132}{1287}}{\frac{637+396}{1287}}$$

Add 637 and 396 to get 1033.

$$\frac{\frac{4132}{1287}}{\frac{1033}{1287}}$$

Divide \frac{4132}{1287} by \frac{1033}{1287} by multiplying \frac{4132}{1287} by the reciprocal of \frac{1033}{1287}.

$$\frac{4132}{1287}\times \frac{1287}{1033}$$

Multiply \frac{4132}{1287} times \frac{1287}{1033} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4132\times 1287}{1287\times 1033}$$

Cancel out 1287 in both numerator and denominator.

$$\frac{4132}{1033}$$

Divide 4132 by 1033 to get 4.

$$4$$

Factor

$$2^{2}$$