Solve (15/99+35/3395/11)div(11/99+3frac{1}{33}+9frac{1}{11})=

$$(1 \frac{ 5 }{ 99 } + 3 \frac { 5 } { 33 } 9 \frac { 5 } { 11 } ) \div ( 1 \frac { 1 } { 99 } + 3 \frac { 1 } { 33 } + 9 \frac { 1 } { 11 } )=$$

Evaluate

$$\frac{646}{275}\approx 2.349090909$$

Solution Steps

Multiply 1 and 99 to get 99.

$$\frac{\frac{99+5}{99}+\frac{3\times 33+5}{33}\times \frac{9\times 11+5}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 5 to get 104.

$$\frac{\frac{104}{99}+\frac{3\times 33+5}{33}\times \frac{9\times 11+5}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 3 and 33 to get 99.

$$\frac{\frac{104}{99}+\frac{99+5}{33}\times \frac{9\times 11+5}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 5 to get 104.

$$\frac{\frac{104}{99}+\frac{104}{33}\times \frac{9\times 11+5}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 9 and 11 to get 99.

$$\frac{\frac{104}{99}+\frac{104}{33}\times \frac{99+5}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 5 to get 104.

$$\frac{\frac{104}{99}+\frac{104}{33}\times \frac{104}{11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply \frac{104}{33} times \frac{104}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{104}{99}+\frac{104\times 104}{33\times 11}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Do the multiplications in the fraction \frac{104\times 104}{33\times 11}.

$$\frac{\frac{104}{99}+\frac{10816}{363}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Least common multiple of 99 and 363 is 1089. Convert \frac{104}{99} and \frac{10816}{363} to fractions with denominator 1089.

$$\frac{\frac{1144}{1089}+\frac{32448}{1089}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Since \frac{1144}{1089} and \frac{32448}{1089} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1144+32448}{1089}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 1144 and 32448 to get 33592.

$$\frac{\frac{33592}{1089}}{\frac{1\times 99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 1 and 99 to get 99.

$$\frac{\frac{33592}{1089}}{\frac{99+1}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{33592}{1089}}{\frac{100}{99}+\frac{3\times 33+1}{33}+\frac{9\times 11+1}{11}}$$

Multiply 3 and 33 to get 99.

$$\frac{\frac{33592}{1089}}{\frac{100}{99}+\frac{99+1}{33}+\frac{9\times 11+1}{11}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{33592}{1089}}{\frac{100}{99}+\frac{100}{33}+\frac{9\times 11+1}{11}}$$

Least common multiple of 99 and 33 is 99. Convert \frac{100}{99} and \frac{100}{33} to fractions with denominator 99.

$$\frac{\frac{33592}{1089}}{\frac{100}{99}+\frac{300}{99}+\frac{9\times 11+1}{11}}$$

Since \frac{100}{99} and \frac{300}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{33592}{1089}}{\frac{100+300}{99}+\frac{9\times 11+1}{11}}$$

Add 100 and 300 to get 400.

$$\frac{\frac{33592}{1089}}{\frac{400}{99}+\frac{9\times 11+1}{11}}$$

Multiply 9 and 11 to get 99.

$$\frac{\frac{33592}{1089}}{\frac{400}{99}+\frac{99+1}{11}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{33592}{1089}}{\frac{400}{99}+\frac{100}{11}}$$

Least common multiple of 99 and 11 is 99. Convert \frac{400}{99} and \frac{100}{11} to fractions with denominator 99.

$$\frac{\frac{33592}{1089}}{\frac{400}{99}+\frac{900}{99}}$$

Since \frac{400}{99} and \frac{900}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{33592}{1089}}{\frac{400+900}{99}}$$

Add 400 and 900 to get 1300.

$$\frac{\frac{33592}{1089}}{\frac{1300}{99}}$$

Divide \frac{33592}{1089} by \frac{1300}{99} by multiplying \frac{33592}{1089} by the reciprocal of \frac{1300}{99}.

$$\frac{33592}{1089}\times \frac{99}{1300}$$

Multiply \frac{33592}{1089} times \frac{99}{1300} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33592\times 99}{1089\times 1300}$$

Do the multiplications in the fraction \frac{33592\times 99}{1089\times 1300}.

$$\frac{3325608}{1415700}$$

Reduce the fraction \frac{3325608}{1415700} to lowest terms by extracting and canceling out 5148.

$$\frac{646}{275}$$

Factor

$$\frac{2 \cdot 17 \cdot 19}{5 ^ {2} \cdot 11} = 2\frac{96}{275} = 2.349090909090909$$