Solve (192/3+1/4)div(41/5*5/42*frac{1}{6})=

$$( 19 \frac { 2 } { 3 } + \frac { 1 } { 4 } ) \div ( 4 \frac { 1 } { 5 } \times \frac { 5 } { 42 } \times \frac { 1 } { 6 } ) =$$

Evaluate

$$239$$

Solution Steps

Multiply 19 and 3 to get 57.

$$\frac{\frac{57+2}{3}+\frac{1}{4}}{\frac{4\times 5+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Add 57 and 2 to get 59.

$$\frac{\frac{59}{3}+\frac{1}{4}}{\frac{4\times 5+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{59}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{236}{12}+\frac{3}{12}}{\frac{4\times 5+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Since \frac{236}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{236+3}{12}}{\frac{4\times 5+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Add 236 and 3 to get 239.

$$\frac{\frac{239}{12}}{\frac{4\times 5+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{239}{12}}{\frac{20+1}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Add 20 and 1 to get 21.

$$\frac{\frac{239}{12}}{\frac{21}{5}\times \frac{5}{42}\times \frac{1}{6}}$$

Multiply \frac{21}{5} times \frac{5}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{239}{12}}{\frac{21\times 5}{5\times 42}\times \frac{1}{6}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{239}{12}}{\frac{21}{42}\times \frac{1}{6}}$$

Reduce the fraction \frac{21}{42} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{239}{12}}{\frac{1}{2}\times \frac{1}{6}}$$

Multiply \frac{1}{2} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{239}{12}}{\frac{1\times 1}{2\times 6}}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 6}.

$$\frac{\frac{239}{12}}{\frac{1}{12}}$$

Divide \frac{239}{12} by \frac{1}{12} by multiplying \frac{239}{12} by the reciprocal of \frac{1}{12}.

$$\frac{239}{12}\times 12$$

Cancel out 12 and 12.

$$239$$

Factor

$$239$$