Solve (1-1/3)/frac{1{6}+1/8}

$$\frac { ( 1 - \frac { 1 } { 3 } ) } { \frac { 1 } { 6 } + \frac { 1 } { 8 } }$$

Evaluate

$$\frac{16}{7}\approx 2.285714286$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{3}{3}-\frac{1}{3}}{\frac{1}{6}+\frac{1}{8}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-1}{3}}{\frac{1}{6}+\frac{1}{8}}$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{2}{3}}{\frac{1}{6}+\frac{1}{8}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{1}{8} to fractions with denominator 24.

$$\frac{\frac{2}{3}}{\frac{4}{24}+\frac{3}{24}}$$

Since \frac{4}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}}{\frac{4+3}{24}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{2}{3}}{\frac{7}{24}}$$

Divide \frac{2}{3} by \frac{7}{24} by multiplying \frac{2}{3} by the reciprocal of \frac{7}{24}.

$$\frac{2}{3}\times \frac{24}{7}$$

Multiply \frac{2}{3} times \frac{24}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 24}{3\times 7}$$

Do the multiplications in the fraction \frac{2\times 24}{3\times 7}.

$$\frac{48}{21}$$

Reduce the fraction \frac{48}{21} to lowest terms by extracting and canceling out 3.

$$\frac{16}{7}$$

Factor

$$\frac{2 ^ {4}}{7} = 2\frac{2}{7} = 2.2857142857142856$$