Solve (1/3a+1/6a)*a^2/5

$$( \frac { 1 } { 3 a } + \frac { 1 } { 6 a } ) \cdot \frac { a ^ { 2 } } { 5 }$$

Evaluate

$$\frac{a}{10}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6a is 6a. Multiply \frac{1}{3a} times \frac{2}{2}.

$$\left(\frac{2}{6a}+\frac{1}{6a}\right)\times \frac{a^{2}}{5}$$

Since \frac{2}{6a} and \frac{1}{6a} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{6a}\times \frac{a^{2}}{5}$$

Multiply \frac{3}{6a} times \frac{a^{2}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{2}}{6a\times 5}$$

Cancel out 3a in both numerator and denominator.

$$\frac{a}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{a}{10}$$

Expand

$$\frac{a}{10}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 6a is 6a. Multiply \frac{1}{3a} times \frac{2}{2}.

$$\left(\frac{2}{6a}+\frac{1}{6a}\right)\times \frac{a^{2}}{5}$$

Since \frac{2}{6a} and \frac{1}{6a} have the same denominator, add them by adding their numerators. Add 2 and 1 to get 3.

$$\frac{3}{6a}\times \frac{a^{2}}{5}$$

Multiply \frac{3}{6a} times \frac{a^{2}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3a^{2}}{6a\times 5}$$

Cancel out 3a in both numerator and denominator.

$$\frac{a}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{a}{10}$$