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

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

Evaluate

$$\frac{23}{16}=1.4375$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{3}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{18}{30}+\frac{5}{30}}{\frac{1}{3}+\frac{1}{5}}$$

Since \frac{18}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{18+5}{30}}{\frac{1}{3}+\frac{1}{5}}$$

Add 18 and 5 to get 23.

$$\frac{\frac{23}{30}}{\frac{1}{3}+\frac{1}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{\frac{23}{30}}{\frac{5}{15}+\frac{3}{15}}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{30}}{\frac{5+3}{15}}$$

Add 5 and 3 to get 8.

$$\frac{\frac{23}{30}}{\frac{8}{15}}$$

Divide \frac{23}{30} by \frac{8}{15} by multiplying \frac{23}{30} by the reciprocal of \frac{8}{15}.

$$\frac{23}{30}\times \frac{15}{8}$$

Multiply \frac{23}{30} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 15}{30\times 8}$$

Do the multiplications in the fraction \frac{23\times 15}{30\times 8}.

$$\frac{345}{240}$$

Reduce the fraction \frac{345}{240} to lowest terms by extracting and canceling out 15.

$$\frac{23}{16}$$

Factor

$$\frac{23}{2 ^ {4}} = 1\frac{7}{16} = 1.4375$$