Solve 7/3(1/3+3/5+2/15)

$$\frac { 7 } { 3 } ( \frac { 1 } { 3 } + \frac { 3 } { 5 } + \frac { 2 } { 15 } )$$

Evaluate

$$\frac{112}{45}\approx 2.488888889$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{7}{3}\left(\frac{5}{15}+\frac{9}{15}+\frac{2}{15}\right)$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{7}{3}\left(\frac{5+9}{15}+\frac{2}{15}\right)$$

Add 5 and 9 to get 14.

$$\frac{7}{3}\left(\frac{14}{15}+\frac{2}{15}\right)$$

Since \frac{14}{15} and \frac{2}{15} have the same denominator, add them by adding their numerators.

$$\frac{7}{3}\times \frac{14+2}{15}$$

Add 14 and 2 to get 16.

$$\frac{7}{3}\times \frac{16}{15}$$

Multiply \frac{7}{3} times \frac{16}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 16}{3\times 15}$$

Do the multiplications in the fraction \frac{7\times 16}{3\times 15}.

$$\frac{112}{45}$$

Factor

$$\frac{2 ^ {4} \cdot 7}{3 ^ {2} \cdot 5} = 2\frac{22}{45} = 2.488888888888889$$