Simplify 3/10x + 1/6y + 3/10x + 3/6y. Be sure to reduce any fractions to the lowest terms
To simplify the expression 3/10x + 1/6y + 3/10x + 3/6y, we can combine the like terms.
First, let's look at the terms with x. We have 3/10x + 3/10x. Since the denominators are the same, we can simply add the numerators, which gives us 6/10x.
Next, let's look at the terms with y. We have 1/6y + 3/6y. Again, we can add the numerators since the denominators are the same, giving us 4/6y.
Combining these results, we have 6/10x + 4/6y.
To reduce fractions to the lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
For the fraction 6/10, the GCD of 6 and 10 is 2. Dividing both the numerator and denominator by 2, we get 3/5.
For the fraction 4/6, the GCD of 4 and 6 is 2. Dividing both the numerator and denominator by 2, we get 2/3.
Therefore, the simplified expression is 3/5x + 2/3y.