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

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

Evaluate

$$\frac{17}{13}\approx 1.307692308$$

Solution Steps

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

$$\frac{\frac{8}{12}+\frac{9}{12}}{\frac{1\times 3+1}{3}-\frac{1}{4}}$$

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

$$\frac{\frac{8+9}{12}}{\frac{1\times 3+1}{3}-\frac{1}{4}}$$

Add 8 and 9 to get 17.

$$\frac{\frac{17}{12}}{\frac{1\times 3+1}{3}-\frac{1}{4}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{17}{12}}{\frac{3+1}{3}-\frac{1}{4}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{17}{12}}{\frac{4}{3}-\frac{1}{4}}$$

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

$$\frac{\frac{17}{12}}{\frac{16}{12}-\frac{3}{12}}$$

Since \frac{16}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17}{12}}{\frac{16-3}{12}}$$

Subtract 3 from 16 to get 13.

$$\frac{\frac{17}{12}}{\frac{13}{12}}$$

Divide \frac{17}{12} by \frac{13}{12} by multiplying \frac{17}{12} by the reciprocal of \frac{13}{12}.

$$\frac{17}{12}\times \frac{12}{13}$$

Multiply \frac{17}{12} times \frac{12}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 12}{12\times 13}$$

Cancel out 12 in both numerator and denominator.

$$\frac{17}{13}$$

Factor

$$\frac{17}{13} = 1\frac{4}{13} = 1.3076923076923077$$