Solve 3/frac{1{60}+1/120+1/110}

$$\frac{ 3 }{ \frac{ 1 }{ 60 } + \frac{ 1 }{ 120 } + \frac{ 1 }{ 110 } }$$

Evaluate

$$88$$

Solution Steps

Least common multiple of 60 and 120 is 120. Convert \frac{1}{60} and \frac{1}{120} to fractions with denominator 120.

$$\frac{3}{\frac{2}{120}+\frac{1}{120}+\frac{1}{110}}$$

Since \frac{2}{120} and \frac{1}{120} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{2+1}{120}+\frac{1}{110}}$$

Add 2 and 1 to get 3.

$$\frac{3}{\frac{3}{120}+\frac{1}{110}}$$

Reduce the fraction \frac{3}{120} to lowest terms by extracting and canceling out 3.

$$\frac{3}{\frac{1}{40}+\frac{1}{110}}$$

Least common multiple of 40 and 110 is 440. Convert \frac{1}{40} and \frac{1}{110} to fractions with denominator 440.

$$\frac{3}{\frac{11}{440}+\frac{4}{440}}$$

Since \frac{11}{440} and \frac{4}{440} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{11+4}{440}}$$

Add 11 and 4 to get 15.

$$\frac{3}{\frac{15}{440}}$$

Reduce the fraction \frac{15}{440} to lowest terms by extracting and canceling out 5.

$$\frac{3}{\frac{3}{88}}$$

Divide 3 by \frac{3}{88} by multiplying 3 by the reciprocal of \frac{3}{88}.

$$3\times \frac{88}{3}$$

Cancel out 3 and 3.

$$88$$

Factor

$$2^{3}\times 11$$