Solve (1/3-1/5)1/2+1/6=frac{1}{3}

$$( \frac { 1 } { 3 } - \frac { 1 } { 5 } ) \frac { 1 } { 2 } + \frac { 1 } { 6 } = \frac { 1 } { 3 }$$

Verify

Solution Steps

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

$$\left(\frac{5}{15}-\frac{3}{15}\right)\times \frac{1}{2}+\frac{1}{6}=\frac{1}{3}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-3}{15}\times \frac{1}{2}+\frac{1}{6}=\frac{1}{3}$$

Subtract 3 from 5 to get 2.

$$\frac{2}{15}\times \frac{1}{2}+\frac{1}{6}=\frac{1}{3}$$

Multiply \frac{2}{15} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{15\times 2}+\frac{1}{6}=\frac{1}{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{15}+\frac{1}{6}=\frac{1}{3}$$

Least common multiple of 15 and 6 is 30. Convert \frac{1}{15} and \frac{1}{6} to fractions with denominator 30.

$$\frac{2}{30}+\frac{5}{30}=\frac{1}{3}$$

Since \frac{2}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{30}=\frac{1}{3}$$

Add 2 and 5 to get 7.

$$\frac{7}{30}=\frac{1}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{7}{30} and \frac{1}{3} to fractions with denominator 30.

$$\frac{7}{30}=\frac{10}{30}$$

Compare \frac{7}{30} and \frac{10}{30}.

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