Solve 2/3+1/2/frac{5{6}-1/4}

$$\frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 5 } { 6 } - \frac { 1 } { 4 } }$$

Evaluate

$$2$$

Solution Steps

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

$$\frac{\frac{4}{6}+\frac{3}{6}}{\frac{5}{6}-\frac{1}{4}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+3}{6}}{\frac{5}{6}-\frac{1}{4}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{6}}{\frac{5}{6}-\frac{1}{4}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{7}{6}}{\frac{10}{12}-\frac{3}{12}}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{6}}{\frac{10-3}{12}}$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{7}{6}}{\frac{7}{12}}$$

Divide \frac{7}{6} by \frac{7}{12} by multiplying \frac{7}{6} by the reciprocal of \frac{7}{12}.

$$\frac{7}{6}\times \frac{12}{7}$$

Multiply \frac{7}{6} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 12}{6\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$