Solve 1/frac{144{11}+4+12+15+5}*144/11

$$\frac{ 1 }{ \frac{ 144 }{ 11 } +4+12+15+5 } \times \frac{ 144 }{ 11 }$$

Evaluate

$$\frac{4}{15}\approx 0.266666667$$

Solution Steps

Convert 4 to fraction \frac{44}{11}.

$$\frac{1}{\frac{144}{11}+\frac{44}{11}+12+15+5}\times \frac{144}{11}$$

Since \frac{144}{11} and \frac{44}{11} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{144+44}{11}+12+15+5}\times \frac{144}{11}$$

Add 144 and 44 to get 188.

$$\frac{1}{\frac{188}{11}+12+15+5}\times \frac{144}{11}$$

Convert 12 to fraction \frac{132}{11}.

$$\frac{1}{\frac{188}{11}+\frac{132}{11}+15+5}\times \frac{144}{11}$$

Since \frac{188}{11} and \frac{132}{11} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{188+132}{11}+15+5}\times \frac{144}{11}$$

Add 188 and 132 to get 320.

$$\frac{1}{\frac{320}{11}+15+5}\times \frac{144}{11}$$

Convert 15 to fraction \frac{165}{11}.

$$\frac{1}{\frac{320}{11}+\frac{165}{11}+5}\times \frac{144}{11}$$

Since \frac{320}{11} and \frac{165}{11} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{320+165}{11}+5}\times \frac{144}{11}$$

Add 320 and 165 to get 485.

$$\frac{1}{\frac{485}{11}+5}\times \frac{144}{11}$$

Convert 5 to fraction \frac{55}{11}.

$$\frac{1}{\frac{485}{11}+\frac{55}{11}}\times \frac{144}{11}$$

Since \frac{485}{11} and \frac{55}{11} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{485+55}{11}}\times \frac{144}{11}$$

Add 485 and 55 to get 540.

$$\frac{1}{\frac{540}{11}}\times \frac{144}{11}$$

Divide 1 by \frac{540}{11} by multiplying 1 by the reciprocal of \frac{540}{11}.

$$1\times \frac{11}{540}\times \frac{144}{11}$$

Multiply 1 and \frac{11}{540} to get \frac{11}{540}.

$$\frac{11}{540}\times \frac{144}{11}$$

Multiply \frac{11}{540} times \frac{144}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 144}{540\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{144}{540}$$

Reduce the fraction \frac{144}{540} to lowest terms by extracting and canceling out 36.

$$\frac{4}{15}$$

Factor

$$\frac{2 ^ {2}}{3 \cdot 5} = 0.26666666666666666$$