Solve 2/5=(1/5-7/10)+(1/4-frac{1}{2})

$$\frac { 2 } { 5 } = ( \frac { 1 } { 5 } - \frac { 7 } { 10 } ) + ( \frac { 1 } { 4 } - \frac { 1 } { 2 } )$$

Verify

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{7}{10} to fractions with denominator 10.

$$\frac{2}{5}=\frac{2}{10}-\frac{7}{10}+\frac{1}{4}-\frac{1}{2}$$

Since \frac{2}{10} and \frac{7}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}=\frac{2-7}{10}+\frac{1}{4}-\frac{1}{2}$$

Subtract 7 from 2 to get -5.

$$\frac{2}{5}=\frac{-5}{10}+\frac{1}{4}-\frac{1}{2}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{2}{5}=-\frac{1}{2}+\frac{1}{4}-\frac{1}{2}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{2}{5}=-\frac{2}{4}+\frac{1}{4}-\frac{1}{2}$$

Since -\frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}=\frac{-2+1}{4}-\frac{1}{2}$$

Add -2 and 1 to get -1.

$$\frac{2}{5}=-\frac{1}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{2}{5}=-\frac{1}{4}-\frac{2}{4}$$

Since -\frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}=\frac{-1-2}{4}$$

Subtract 2 from -1 to get -3.

$$\frac{2}{5}=-\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and -\frac{3}{4} to fractions with denominator 20.

$$\frac{8}{20}=-\frac{15}{20}$$

Compare \frac{8}{20} and -\frac{15}{20}.

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