Solve 2-[1/3+3/2-(4/5+3)]=5/3

$$2 - [ \frac { 1 } { 3 } + \frac { 3 } { 2 } - ( \frac { 4 } { 5 } + 3 ) ] = \frac { 5 } { 3 }$$

Verify

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$2-\left(\frac{2}{6}+\frac{9}{6}-\left(\frac{4}{5}+3\right)\right)=\frac{5}{3}$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{2+9}{6}-\left(\frac{4}{5}+3\right)\right)=\frac{5}{3}$$

Add 2 and 9 to get 11.

$$2-\left(\frac{11}{6}-\left(\frac{4}{5}+3\right)\right)=\frac{5}{3}$$

Convert 3 to fraction \frac{15}{5}.

$$2-\left(\frac{11}{6}-\left(\frac{4}{5}+\frac{15}{5}\right)\right)=\frac{5}{3}$$

Since \frac{4}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{11}{6}-\frac{4+15}{5}\right)=\frac{5}{3}$$

Add 4 and 15 to get 19.

$$2-\left(\frac{11}{6}-\frac{19}{5}\right)=\frac{5}{3}$$

Least common multiple of 6 and 5 is 30. Convert \frac{11}{6} and \frac{19}{5} to fractions with denominator 30.

$$2-\left(\frac{55}{30}-\frac{114}{30}\right)=\frac{5}{3}$$

Since \frac{55}{30} and \frac{114}{30} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{55-114}{30}=\frac{5}{3}$$

Subtract 114 from 55 to get -59.

$$2-\left(-\frac{59}{30}\right)=\frac{5}{3}$$

The opposite of -\frac{59}{30} is \frac{59}{30}.

$$2+\frac{59}{30}=\frac{5}{3}$$

Convert 2 to fraction \frac{60}{30}.

$$\frac{60}{30}+\frac{59}{30}=\frac{5}{3}$$

Since \frac{60}{30} and \frac{59}{30} have the same denominator, add them by adding their numerators.

$$\frac{60+59}{30}=\frac{5}{3}$$

Add 60 and 59 to get 119.

$$\frac{119}{30}=\frac{5}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{119}{30} and \frac{5}{3} to fractions with denominator 30.

$$\frac{119}{30}=\frac{50}{30}$$

Compare \frac{119}{30} and \frac{50}{30}.

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