Simplify the following by combining like terms. 1 2 x + 3 4 x − 1 2 y + 1 2 y \frac12x+\frac34x-\frac12y+\frac12y

were asked to simplify the following by combining like terms. Now the algebraic expression we're given here is one half x plus three fourths x minus one half y plus one half y. Now looking to our steps here for simplifying algebraic expressions, the first thing we want to do is distribute any constants or variables into parentheses. Now looking at this particular expressions, there's nothing that needs to get distributed. So I can go ahead and move on to step two, which is to identify my like terms. Those terms that have the same variable raised to the same exponent. So looking at my expression here, my first term is one half x and my very next term is three fourths x. Both of these have that same variable x raised to the same exponent of one. Remember that exponent of one is implied when there is no exponent. So I have those two like terms and then next I have negative one half y and then positive one half y. These two terms have the same variable y raised to the same exponent again of one. So I've identified my like terms. Now let's move on to step three, grouping our like terms by writing them next to each other. Now in this particular expression, our like terms are already grouped. Those first two like terms are right next to each other, as are my second two. So moving on to our final step four, combining our like terms by adding or subtracting their coefficients. Now here, all of our coefficients are fractions. So we need to remember what we know about adding and subtracting fractions. Looking at these first two like terms, one half x plus three fourths x, these do not currently have the same denominator in the fraction. This first fraction has a two in the denominator and the second one has a four. So I need to give these common denominators, which I can easily do by taking that one half and multiplying it by two over two. So effectively just multiplying it by one. I'm not really changing its value. So one times two going across the top there is two. And then on the bottom, two times two is four. So with a like denominator, this becomes two fourths x. So I'm really taking two fourths x and adding it with three fourths x. So now I can go ahead and just add those coefficients by adding those fractions together. So since they have the same denominator, I can add those numerators. Two plus three gives me five. So five over four x. Now looking at my next two terms, I have a negative one half y and positive one half y. Now if I have negative one half and I add positive one half, those are going to actually cancel each other out and just give me a zero y. Now, I don't really need to write this zero y because zero times anything is just zero. So effectively this entire algebraic expression simplifies to just five fourths x. If you have any questions, feel free to let us know in the comments and let's keep going.