Solve 5/2div(2/3+3/12)

$$\frac { 5 } { 2 } \div ( \frac { 2 } { 3 } + \frac { 3 } { 12 } )$$

Evaluate

$$\frac{30}{11}\approx 2.727272727$$

Solution Steps

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{\frac{5}{2}}{\frac{8}{12}+\frac{3}{12}}$$

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

$$\frac{\frac{5}{2}}{\frac{8+3}{12}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{5}{2}}{\frac{11}{12}}$$

Divide \frac{5}{2} by \frac{11}{12} by multiplying \frac{5}{2} by the reciprocal of \frac{11}{12}.

$$\frac{5}{2}\times \frac{12}{11}$$

Multiply \frac{5}{2} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 12}{2\times 11}$$

Do the multiplications in the fraction \frac{5\times 12}{2\times 11}.

$$\frac{60}{22}$$

Reduce the fraction \frac{60}{22} to lowest terms by extracting and canceling out 2.

$$\frac{30}{11}$$

Factor

$$\frac{2 \cdot 3 \cdot 5}{11} = 2\frac{8}{11} = 2.727272727272727$$