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

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

Evaluate

$$\frac{5}{13}\approx 0.384615385$$

Solution Steps

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

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

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 9 to get 5.

$$\frac{\frac{5}{12}}{\frac{3}{4}+\frac{1}{3}}$$

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

$$\frac{\frac{5}{12}}{\frac{9}{12}+\frac{4}{12}}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{12}}{\frac{9+4}{12}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{5}{12}}{\frac{13}{12}}$$

Divide \frac{5}{12} by \frac{13}{12} by multiplying \frac{5}{12} by the reciprocal of \frac{13}{12}.

$$\frac{5}{12}\times \frac{12}{13}$$

Multiply \frac{5}{12} times \frac{12}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 12}{12\times 13}$$

Cancel out 12 in both numerator and denominator.

$$\frac{5}{13}$$

Factor

$$\frac{5}{13} = 0.38461538461538464$$