Solve (-1/42)=(1/6-2/7+2/3-frac{3}{14})divfrac{1}{3}

$$( - \frac { 1 } { 42 } ) = ( \frac { 1 } { 6 } - \frac { 2 } { 7 } + \frac { 2 } { 3 } - \frac { 3 } { 14 } ) \div \frac { 1 } { 3 }$$

Verify

Solution Steps

Least common multiple of 6 and 7 is 42. Convert \frac{1}{6} and \frac{2}{7} to fractions with denominator 42.

$$-\frac{1}{42}=\frac{\frac{7}{42}-\frac{12}{42}+\frac{2}{3}-\frac{3}{14}}{\frac{1}{3}}$$

Since \frac{7}{42} and \frac{12}{42} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{42}=\frac{\frac{7-12}{42}+\frac{2}{3}-\frac{3}{14}}{\frac{1}{3}}$$

Subtract 12 from 7 to get -5.

$$-\frac{1}{42}=\frac{-\frac{5}{42}+\frac{2}{3}-\frac{3}{14}}{\frac{1}{3}}$$

Least common multiple of 42 and 3 is 42. Convert -\frac{5}{42} and \frac{2}{3} to fractions with denominator 42.

$$-\frac{1}{42}=\frac{-\frac{5}{42}+\frac{28}{42}-\frac{3}{14}}{\frac{1}{3}}$$

Since -\frac{5}{42} and \frac{28}{42} have the same denominator, add them by adding their numerators.

$$-\frac{1}{42}=\frac{\frac{-5+28}{42}-\frac{3}{14}}{\frac{1}{3}}$$

Add -5 and 28 to get 23.

$$-\frac{1}{42}=\frac{\frac{23}{42}-\frac{3}{14}}{\frac{1}{3}}$$

Least common multiple of 42 and 14 is 42. Convert \frac{23}{42} and \frac{3}{14} to fractions with denominator 42.

$$-\frac{1}{42}=\frac{\frac{23}{42}-\frac{9}{42}}{\frac{1}{3}}$$

Since \frac{23}{42} and \frac{9}{42} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{42}=\frac{\frac{23-9}{42}}{\frac{1}{3}}$$

Subtract 9 from 23 to get 14.

$$-\frac{1}{42}=\frac{\frac{14}{42}}{\frac{1}{3}}$$

Reduce the fraction \frac{14}{42} to lowest terms by extracting and canceling out 14.

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

Divide \frac{1}{3} by \frac{1}{3} to get 1.

$$-\frac{1}{42}=1$$

Convert 1 to fraction \frac{42}{42}.

$$-\frac{1}{42}=\frac{42}{42}$$

Compare -\frac{1}{42} and \frac{42}{42}.

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