Solve (1/6+3/2+5/4+1/3):frac{1}{12}

$$( \frac { 1 } { 6 } + \frac { 3 } { 2 } + \frac { 5 } { 4 } + \frac { 1 } { 3 } ) : \frac { 1 } { 12 }$$

Evaluate

$$39$$

Solution Steps

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{\frac{1}{6}+\frac{9}{6}+\frac{5}{4}+\frac{1}{3}}{\frac{1}{12}}$$

Since \frac{1}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+9}{6}+\frac{5}{4}+\frac{1}{3}}{\frac{1}{12}}$$

Add 1 and 9 to get 10.

$$\frac{\frac{10}{6}+\frac{5}{4}+\frac{1}{3}}{\frac{1}{12}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{3}+\frac{5}{4}+\frac{1}{3}}{\frac{1}{12}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{20}{12}+\frac{15}{12}+\frac{1}{3}}{\frac{1}{12}}$$

Since \frac{20}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+15}{12}+\frac{1}{3}}{\frac{1}{12}}$$

Add 20 and 15 to get 35.

$$\frac{\frac{35}{12}+\frac{1}{3}}{\frac{1}{12}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{35}{12} and \frac{1}{3} to fractions with denominator 12.

$$\frac{\frac{35}{12}+\frac{4}{12}}{\frac{1}{12}}$$

Since \frac{35}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{35+4}{12}}{\frac{1}{12}}$$

Add 35 and 4 to get 39.

$$\frac{\frac{39}{12}}{\frac{1}{12}}$$

Reduce the fraction \frac{39}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{4}}{\frac{1}{12}}$$

Divide \frac{13}{4} by \frac{1}{12} by multiplying \frac{13}{4} by the reciprocal of \frac{1}{12}.

$$\frac{13}{4}\times 12$$

Express \frac{13}{4}\times 12 as a single fraction.

$$\frac{13\times 12}{4}$$

Multiply 13 and 12 to get 156.

$$\frac{156}{4}$$

Divide 156 by 4 to get 39.

$$39$$

Factor

$$3\times 13$$