Solve (2/3+1/2div2/5)+1/3

$$( \frac { 2 } { 3 } + \frac { 1 } { 2 } \div \frac { 2 } { 5 } ) + \frac { 1 } { 3 }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Divide \frac{1}{2} by \frac{2}{5} by multiplying \frac{1}{2} by the reciprocal of \frac{2}{5}.

$$\frac{2}{3}+\frac{1}{2}\times \frac{5}{2}+\frac{1}{3}$$

Multiply \frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{1\times 5}{2\times 2}+\frac{1}{3}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 2}.

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

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{15}{12}+\frac{1}{3}$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+15}{12}+\frac{1}{3}$$

Add 8 and 15 to get 23.

$$\frac{23}{12}+\frac{1}{3}$$

Least common multiple of 12 and 3 is 12. Convert \frac{23}{12} and \frac{1}{3} to fractions with denominator 12.

$$\frac{23}{12}+\frac{4}{12}$$

Since \frac{23}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{23+4}{12}$$

Add 23 and 4 to get 27.

$$\frac{27}{12}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$