Solve 2/15*(4/3-3)+2/4*5=

$$\frac { 2 } { 15 } \cdot ( \frac { 4 } { 3 } - 3 ) + \frac { 2 } { 4 } \cdot 5 =$$

Evaluate

$$\frac{41}{18}\approx 2.277777778$$

Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$\frac{2}{15}\left(\frac{4}{3}-\frac{9}{3}\right)+\frac{2}{4}\times 5$$

Since \frac{4}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{15}\times \frac{4-9}{3}+\frac{2}{4}\times 5$$

Subtract 9 from 4 to get -5.

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

Multiply \frac{2}{15} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\left(-5\right)}{15\times 3}.

$$\frac{-10}{45}+\frac{2}{4}\times 5$$

Reduce the fraction \frac{-10}{45} to lowest terms by extracting and canceling out 5.

$$-\frac{2}{9}+\frac{2}{4}\times 5$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{9}+\frac{1}{2}\times 5$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$-\frac{2}{9}+\frac{5}{2}$$

Least common multiple of 9 and 2 is 18. Convert -\frac{2}{9} and \frac{5}{2} to fractions with denominator 18.

$$-\frac{4}{18}+\frac{45}{18}$$

Since -\frac{4}{18} and \frac{45}{18} have the same denominator, add them by adding their numerators.

$$\frac{-4+45}{18}$$

Add -4 and 45 to get 41.

$$\frac{41}{18}$$

Factor

$$\frac{41}{2 \cdot 3 ^ {2}} = 2\frac{5}{18} = 2.2777777777777777$$