Solve 1/3div(1/60+1/90+1/40)

$$\frac { 1 } { 3 } \div ( \frac { 1 } { 60 } + \frac { 1 } { 90 } + \frac { 1 } { 40 } )$$

Evaluate

$$\frac{120}{19}\approx 6.315789474$$

Solution Steps

Least common multiple of 60 and 90 is 180. Convert \frac{1}{60} and \frac{1}{90} to fractions with denominator 180.

$$\frac{\frac{1}{3}}{\frac{3}{180}+\frac{2}{180}+\frac{1}{40}}$$

Since \frac{3}{180} and \frac{2}{180} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{3+2}{180}+\frac{1}{40}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{1}{3}}{\frac{5}{180}+\frac{1}{40}}$$

Reduce the fraction \frac{5}{180} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{3}}{\frac{1}{36}+\frac{1}{40}}$$

Least common multiple of 36 and 40 is 360. Convert \frac{1}{36} and \frac{1}{40} to fractions with denominator 360.

$$\frac{\frac{1}{3}}{\frac{10}{360}+\frac{9}{360}}$$

Since \frac{10}{360} and \frac{9}{360} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{10+9}{360}}$$

Add 10 and 9 to get 19.

$$\frac{\frac{1}{3}}{\frac{19}{360}}$$

Divide \frac{1}{3} by \frac{19}{360} by multiplying \frac{1}{3} by the reciprocal of \frac{19}{360}.

$$\frac{1}{3}\times \frac{360}{19}$$

Multiply \frac{1}{3} times \frac{360}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 360}{3\times 19}$$

Do the multiplications in the fraction \frac{1\times 360}{3\times 19}.

$$\frac{360}{57}$$

Reduce the fraction \frac{360}{57} to lowest terms by extracting and canceling out 3.

$$\frac{120}{19}$$

Factor

$$\frac{2 ^ {3} \cdot 3 \cdot 5}{19} = 6\frac{6}{19} = 6.315789473684211$$