Solve (3/4+1/2)div(5/3+1/6)

$$( \frac { 3 } { 4 } + \frac { 1 } { 2 } ) \div ( \frac { 5 } { 3 } + \frac { 1 } { 6 } )$$

Evaluate

$$\frac{15}{22}\approx 0.681818182$$

Solution Steps

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

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

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

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

$$\frac{\frac{5}{4}}{\frac{10}{6}+\frac{1}{6}}$$

Since \frac{10}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{4}}{\frac{10+1}{6}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{5}{4}}{\frac{11}{6}}$$

Divide \frac{5}{4} by \frac{11}{6} by multiplying \frac{5}{4} by the reciprocal of \frac{11}{6}.

$$\frac{5}{4}\times \frac{6}{11}$$

Multiply \frac{5}{4} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{4\times 11}$$

Do the multiplications in the fraction \frac{5\times 6}{4\times 11}.

$$\frac{30}{44}$$

Reduce the fraction \frac{30}{44} to lowest terms by extracting and canceling out 2.

$$\frac{15}{22}$$

Factor

$$\frac{3 \cdot 5}{2 \cdot 11} = 0.6818181818181818$$