Solve 1/6:5/6-2/3=1

$$\frac { 1 } { 6 } : \frac { 5 } { 6 } - \frac { 2 } { 3 } = 1$$

Verify

Solution Steps

Divide \frac{1}{6} by \frac{5}{6} by multiplying \frac{1}{6} by the reciprocal of \frac{5}{6}.

$$\frac{1}{6}\times \frac{6}{5}-\frac{2}{3}=1$$

Multiply \frac{1}{6} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{6\times 5}-\frac{2}{3}=1$$

Cancel out 6 in both numerator and denominator.

$$\frac{1}{5}-\frac{2}{3}=1$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{15}-\frac{10}{15}=1$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{15}=1$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{15}=1$$

Convert 1 to fraction \frac{15}{15}.

$$-\frac{7}{15}=\frac{15}{15}$$

Compare -\frac{7}{15} and \frac{15}{15}.

$$\text{false}$$