Solve 5/6-1/3/frac{5{6}+1/3}a

$$\frac { \frac { 5 } { 6 } - \frac { 1 } { 3 } } { \frac { 5 } { 6 } + \frac { 1 } { 3 } } a$$

Evaluate

$$\frac{3a}{7}$$

Solution Steps

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

$$\frac{\frac{5}{6}-\frac{2}{6}}{\frac{5}{6}+\frac{1}{3}}a$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-2}{6}}{\frac{5}{6}+\frac{1}{3}}a$$

Subtract 2 from 5 to get 3.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{\frac{1}{2}}{\frac{5}{6}+\frac{2}{6}}a$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{5+2}{6}}a$$

Add 5 and 2 to get 7.

$$\frac{\frac{1}{2}}{\frac{7}{6}}a$$

Divide \frac{1}{2} by \frac{7}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{6}.

$$\frac{1}{2}\times \frac{6}{7}a$$

Multiply \frac{1}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{2\times 7}a$$

Do the multiplications in the fraction \frac{1\times 6}{2\times 7}.

$$\frac{6}{14}a$$

Reduce the fraction \frac{6}{14} to lowest terms by extracting and canceling out 2.

$$\frac{3}{7}a$$

Expand

$$\frac{3a}{7}$$

Solution Steps

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

$$\frac{\frac{5}{6}-\frac{2}{6}}{\frac{5}{6}+\frac{1}{3}}a$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-2}{6}}{\frac{5}{6}+\frac{1}{3}}a$$

Subtract 2 from 5 to get 3.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{\frac{1}{2}}{\frac{5}{6}+\frac{2}{6}}a$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{5+2}{6}}a$$

Add 5 and 2 to get 7.

$$\frac{\frac{1}{2}}{\frac{7}{6}}a$$

Divide \frac{1}{2} by \frac{7}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{6}.

$$\frac{1}{2}\times \frac{6}{7}a$$

Multiply \frac{1}{2} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{2\times 7}a$$

Do the multiplications in the fraction \frac{1\times 6}{2\times 7}.

$$\frac{6}{14}a$$

Reduce the fraction \frac{6}{14} to lowest terms by extracting and canceling out 2.

$$\frac{3}{7}a$$