Solve (1-1/3)div(1/3+1/4)

$$( 1 - \frac { 1 } { 3 } ) \div ( \frac { 1 } { 3 } + \frac { 1 } { 4 } )$$

Evaluate

$$\frac{8}{7}\approx 1.142857143$$

Solution Steps

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

$$\frac{\frac{3}{3}-\frac{1}{3}}{\frac{1}{3}+\frac{1}{4}}$$

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

$$\frac{\frac{3-1}{3}}{\frac{1}{3}+\frac{1}{4}}$$

Subtract 1 from 3 to get 2.

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

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

$$\frac{\frac{2}{3}}{\frac{4}{12}+\frac{3}{12}}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}}{\frac{4+3}{12}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{2}{3}}{\frac{7}{12}}$$

Divide \frac{2}{3} by \frac{7}{12} by multiplying \frac{2}{3} by the reciprocal of \frac{7}{12}.

$$\frac{2}{3}\times \frac{12}{7}$$

Multiply \frac{2}{3} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 12}{3\times 7}$$

Do the multiplications in the fraction \frac{2\times 12}{3\times 7}.

$$\frac{24}{21}$$

Reduce the fraction \frac{24}{21} to lowest terms by extracting and canceling out 3.

$$\frac{8}{7}$$

Factor

$$\frac{2 ^ {3}}{7} = 1\frac{1}{7} = 1.1428571428571428$$