Simplify 3/10x + 1/6y + 3/10x + 3/6y

Question

. Be sure to reduce any fractions to the lowest term

Answer 1

To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we can first combine like terms.

1. Combine the coefficients of \( x \): \[ \frac{3}{10}x + \frac{3}{10}x = \left( \frac{3}{10} + \frac{3}{10} \right)x = \frac{6}{10}x = \frac{3}{5}x \]

2. Combine the coefficients of \( y \): \[ \frac{1}{6}y + \frac{3}{6}y = \left( \frac{1}{6} + \frac{3}{6} \right)y = \frac{4}{6}y = \frac{2}{3}y \]

Now we put together the simplified terms: \[ \frac{3}{5}x + \frac{2}{3}y \]

Thus, the simplified expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]