Solve 2+3/5-2/3+3/2+frac{1{2}}

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

Evaluate

$$\frac{238}{75}\approx 3.173333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$2+\frac{\frac{9}{15}-\frac{10}{15}+3}{2+\frac{1}{2}}$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{\frac{9-10}{15}+3}{2+\frac{1}{2}}$$

Subtract 10 from 9 to get -1.

$$2+\frac{-\frac{1}{15}+3}{2+\frac{1}{2}}$$

Convert 3 to fraction \frac{45}{15}.

$$2+\frac{-\frac{1}{15}+\frac{45}{15}}{2+\frac{1}{2}}$$

Since -\frac{1}{15} and \frac{45}{15} have the same denominator, add them by adding their numerators.

$$2+\frac{\frac{-1+45}{15}}{2+\frac{1}{2}}$$

Add -1 and 45 to get 44.

$$2+\frac{\frac{44}{15}}{2+\frac{1}{2}}$$

Convert 2 to fraction \frac{4}{2}.

$$2+\frac{\frac{44}{15}}{\frac{4}{2}+\frac{1}{2}}$$

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

$$2+\frac{\frac{44}{15}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$2+\frac{\frac{44}{15}}{\frac{5}{2}}$$

Divide \frac{44}{15} by \frac{5}{2} by multiplying \frac{44}{15} by the reciprocal of \frac{5}{2}.

$$2+\frac{44}{15}\times \frac{2}{5}$$

Multiply \frac{44}{15} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{44\times 2}{15\times 5}$$

Do the multiplications in the fraction \frac{44\times 2}{15\times 5}.

$$2+\frac{88}{75}$$

Convert 2 to fraction \frac{150}{75}.

$$\frac{150}{75}+\frac{88}{75}$$

Since \frac{150}{75} and \frac{88}{75} have the same denominator, add them by adding their numerators.

$$\frac{150+88}{75}$$

Add 150 and 88 to get 238.

$$\frac{238}{75}$$

Factor

$$\frac{2 \cdot 7 \cdot 17}{3 \cdot 5 ^ {2}} = 3\frac{13}{75} = 3.1733333333333333$$