Solve 1/frac{9{184}+3/68}+4/3

$$\frac{ 1 }{ \frac{ 9 }{ 184 } + \frac{ 3 }{ 68 } } + \frac{ 4 }{ 3 }$$

Evaluate

$$\frac{1172}{97}\approx 12.082474227$$

Solution Steps

Least common multiple of 184 and 68 is 3128. Convert \frac{9}{184} and \frac{3}{68} to fractions with denominator 3128.

$$\frac{1}{\frac{153}{3128}+\frac{138}{3128}}+\frac{4}{3}$$

Since \frac{153}{3128} and \frac{138}{3128} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{153+138}{3128}}+\frac{4}{3}$$

Add 153 and 138 to get 291.

$$\frac{1}{\frac{291}{3128}}+\frac{4}{3}$$

Divide 1 by \frac{291}{3128} by multiplying 1 by the reciprocal of \frac{291}{3128}.

$$1\times \frac{3128}{291}+\frac{4}{3}$$

Multiply 1 and \frac{3128}{291} to get \frac{3128}{291}.

$$\frac{3128}{291}+\frac{4}{3}$$

Least common multiple of 291 and 3 is 291. Convert \frac{3128}{291} and \frac{4}{3} to fractions with denominator 291.

$$\frac{3128}{291}+\frac{388}{291}$$

Since \frac{3128}{291} and \frac{388}{291} have the same denominator, add them by adding their numerators.

$$\frac{3128+388}{291}$$

Add 3128 and 388 to get 3516.

$$\frac{3516}{291}$$

Reduce the fraction \frac{3516}{291} to lowest terms by extracting and canceling out 3.

$$\frac{1172}{97}$$

Factor

$$\frac{2 ^ {2} \cdot 293}{97} = 12\frac{8}{97} = 12.082474226804123$$