Solve 2/5=3/4+2/3-1/5

$$\frac { 2 } { 5 } = \frac { 3 } { 4 } + \frac { 2 } { 3 } - \frac { 1 } { 5 }$$

Verify

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{2}{5}=\frac{9}{12}+\frac{8}{12}-\frac{1}{5}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}=\frac{9+8}{12}-\frac{1}{5}$$

Add 9 and 8 to get 17.

$$\frac{2}{5}=\frac{17}{12}-\frac{1}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{17}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{2}{5}=\frac{85}{60}-\frac{12}{60}$$

Since \frac{85}{60} and \frac{12}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}=\frac{85-12}{60}$$

Subtract 12 from 85 to get 73.

$$\frac{2}{5}=\frac{73}{60}$$

Least common multiple of 5 and 60 is 60. Convert \frac{2}{5} and \frac{73}{60} to fractions with denominator 60.

$$\frac{24}{60}=\frac{73}{60}$$

Compare \frac{24}{60} and \frac{73}{60}.

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