Solve 5/7:3/2+1/6=1/3

$$\frac { 5 } { 7 } : \frac { 3 } { 2 } + \frac { 1 } { 6 } = \frac { 1 } { 3 }$$

Verify

Solution Steps

Divide \frac{5}{7} by \frac{3}{2} by multiplying \frac{5}{7} by the reciprocal of \frac{3}{2}.

$$\frac{5}{7}\times \frac{2}{3}+\frac{1}{6}=\frac{1}{3}$$

Multiply \frac{5}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{7\times 3}+\frac{1}{6}=\frac{1}{3}$$

Do the multiplications in the fraction \frac{5\times 2}{7\times 3}.

$$\frac{10}{21}+\frac{1}{6}=\frac{1}{3}$$

Least common multiple of 21 and 6 is 42. Convert \frac{10}{21} and \frac{1}{6} to fractions with denominator 42.

$$\frac{20}{42}+\frac{7}{42}=\frac{1}{3}$$

Since \frac{20}{42} and \frac{7}{42} have the same denominator, add them by adding their numerators.

$$\frac{20+7}{42}=\frac{1}{3}$$

Add 20 and 7 to get 27.

$$\frac{27}{42}=\frac{1}{3}$$

Reduce the fraction \frac{27}{42} to lowest terms by extracting and canceling out 3.

$$\frac{9}{14}=\frac{1}{3}$$

Least common multiple of 14 and 3 is 42. Convert \frac{9}{14} and \frac{1}{3} to fractions with denominator 42.

$$\frac{27}{42}=\frac{14}{42}$$

Compare \frac{27}{42} and \frac{14}{42}.

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