Solve 68div(2/3+3/4)*8/12

$$68 \div ( \frac { 2 } { 3 } + \frac { 3 } { 4 } ) \cdot \frac { 8 } { 12 }$$

Evaluate

$$32$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{68}{\frac{8}{12}+\frac{9}{12}}\times \frac{8}{12}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{68}{\frac{8+9}{12}}\times \frac{8}{12}$$

Add 8 and 9 to get 17.

$$\frac{68}{\frac{17}{12}}\times \frac{8}{12}$$

Divide 68 by \frac{17}{12} by multiplying 68 by the reciprocal of \frac{17}{12}.

$$68\times \frac{12}{17}\times \frac{8}{12}$$

Express 68\times \frac{12}{17} as a single fraction.

$$\frac{68\times 12}{17}\times \frac{8}{12}$$

Multiply 68 and 12 to get 816.

$$\frac{816}{17}\times \frac{8}{12}$$

Divide 816 by 17 to get 48.

$$48\times \frac{8}{12}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$48\times \frac{2}{3}$$

Express 48\times \frac{2}{3} as a single fraction.

$$\frac{48\times 2}{3}$$

Multiply 48 and 2 to get 96.

$$\frac{96}{3}$$

Divide 96 by 3 to get 32.

$$32$$

Factor

$$2^{5}$$