Solve 2/3*3/5+1/6+1/2=frac{1}{3}

$$\frac { 2 } { 3 } \cdot \frac { 3 } { 5 } + \frac { 1 } { 6 } + \frac { 1 } { 2 } = \frac { 1 } { 3 }$$

Verify

Solution Steps

Multiply \frac{2}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Least common multiple of 5 and 6 is 30. Convert \frac{2}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{12}{30}+\frac{5}{30}+\frac{1}{2}=\frac{1}{3}$$

Since \frac{12}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{12+5}{30}+\frac{1}{2}=\frac{1}{3}$$

Add 12 and 5 to get 17.

$$\frac{17}{30}+\frac{1}{2}=\frac{1}{3}$$

Least common multiple of 30 and 2 is 30. Convert \frac{17}{30} and \frac{1}{2} to fractions with denominator 30.

$$\frac{17}{30}+\frac{15}{30}=\frac{1}{3}$$

Since \frac{17}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{17+15}{30}=\frac{1}{3}$$

Add 17 and 15 to get 32.

$$\frac{32}{30}=\frac{1}{3}$$

Reduce the fraction \frac{32}{30} to lowest terms by extracting and canceling out 2.

$$\frac{16}{15}=\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{16}{15} and \frac{1}{3} to fractions with denominator 15.

$$\frac{16}{15}=\frac{5}{15}$$

Compare \frac{16}{15} and \frac{5}{15}.

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