Solve (2/3+1/4)*2/3div1/4

$$( \frac { 2 } { 3 } + \frac { 1 } { 4 } ) \times \frac { 2 } { 3 } \div \frac { 1 } { 4 }$$

Evaluate

$$\frac{22}{9}\approx 2.444444444$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\left(\frac{8}{12}+\frac{3}{12}\right)\times \frac{2}{3}}{\frac{1}{4}}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+3}{12}\times \frac{2}{3}}{\frac{1}{4}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{11}{12}\times \frac{2}{3}}{\frac{1}{4}}$$

Multiply \frac{11}{12} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11\times 2}{12\times 3}}{\frac{1}{4}}$$

Do the multiplications in the fraction \frac{11\times 2}{12\times 3}.

$$\frac{\frac{22}{36}}{\frac{1}{4}}$$

Reduce the fraction \frac{22}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{18}}{\frac{1}{4}}$$

Divide \frac{11}{18} by \frac{1}{4} by multiplying \frac{11}{18} by the reciprocal of \frac{1}{4}.

$$\frac{11}{18}\times 4$$

Express \frac{11}{18}\times 4 as a single fraction.

$$\frac{11\times 4}{18}$$

Multiply 11 and 4 to get 44.

$$\frac{44}{18}$$

Reduce the fraction \frac{44}{18} to lowest terms by extracting and canceling out 2.

$$\frac{22}{9}$$

Factor

$$\frac{2 \cdot 11}{3 ^ {2}} = 2\frac{4}{9} = 2.4444444444444446$$