Solve 1/8+1/4/frac{1{8}+1/3}=

$$\frac { \frac { 1 } { 8 } + \frac { 1 } { 4 } } { \frac { 1 } { 8 } + \frac { 1 } { 3 } } =$$

Evaluate

$$\frac{9}{11}\approx 0.818181818$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{1}{8}+\frac{2}{8}}{\frac{1}{8}+\frac{1}{3}}$$

Since \frac{1}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+2}{8}}{\frac{1}{8}+\frac{1}{3}}$$

Add 1 and 2 to get 3.

$$\frac{\frac{3}{8}}{\frac{1}{8}+\frac{1}{3}}$$

Least common multiple of 8 and 3 is 24. Convert \frac{1}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{\frac{3}{8}}{\frac{3}{24}+\frac{8}{24}}$$

Since \frac{3}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{8}}{\frac{3+8}{24}}$$

Add 3 and 8 to get 11.

$$\frac{\frac{3}{8}}{\frac{11}{24}}$$

Divide \frac{3}{8} by \frac{11}{24} by multiplying \frac{3}{8} by the reciprocal of \frac{11}{24}.

$$\frac{3}{8}\times \frac{24}{11}$$

Multiply \frac{3}{8} times \frac{24}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 24}{8\times 11}$$

Do the multiplications in the fraction \frac{3\times 24}{8\times 11}.

$$\frac{72}{88}$$

Reduce the fraction \frac{72}{88} to lowest terms by extracting and canceling out 8.

$$\frac{9}{11}$$

Factor

$$\frac{3 ^ {2}}{11} = 0.8181818181818182$$