Simplify 3/10x + 1/6y + 3/10x + 3/6y. Be sure to reduce any fractions to the lowest terms.

Answer 1

To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we can follow these steps:

1. Combine like terms:

   • For the \(x\) terms: \( \frac{3}{10}x + \frac{3}{10}x = \frac{6}{10}x \)
   • For the \(y\) terms: \( \frac{1}{6}y + \frac{3}{6}y = \frac{4}{6}y \)

2. Simplify the fractions:

   • For the \(x\) term: \( \frac{6}{10}x \) can be simplified by dividing the numerator and denominator by 2: \[ \frac{6 \div 2}{10 \div 2}x = \frac{3}{5}x \]
   • For the \(y\) term: \( \frac{4}{6}y \) can be simplified by dividing the numerator and denominator by 2: \[ \frac{4 \div 2}{6 \div 2}y = \frac{2}{3}y \]

3. Combine the simplified terms:

   • The final expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]

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