Solve 5/2-1/3/frac{7{2}+1/3}

$$\frac { \frac { 5 } { 2 } - \frac { 1 } { 3 } } { \frac { 7 } { 2 } + \frac { 1 } { 3 } }$$

Evaluate

$$\frac{13}{23}\approx 0.565217391$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{15}{6}-\frac{2}{6}}{\frac{7}{2}+\frac{1}{3}}$$

Since \frac{15}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-2}{6}}{\frac{7}{2}+\frac{1}{3}}$$

Subtract 2 from 15 to get 13.

$$\frac{\frac{13}{6}}{\frac{7}{2}+\frac{1}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{13}{6}}{\frac{21}{6}+\frac{2}{6}}$$

Since \frac{21}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{6}}{\frac{21+2}{6}}$$

Add 21 and 2 to get 23.

$$\frac{\frac{13}{6}}{\frac{23}{6}}$$

Divide \frac{13}{6} by \frac{23}{6} by multiplying \frac{13}{6} by the reciprocal of \frac{23}{6}.

$$\frac{13}{6}\times \frac{6}{23}$$

Multiply \frac{13}{6} times \frac{6}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 6}{6\times 23}$$

Cancel out 6 in both numerator and denominator.

$$\frac{13}{23}$$

Factor

$$\frac{13}{23} = 0.5652173913043478$$