How To Add Fractions With Variables

okay, in this video, i want to do another example of working with fractions and, what we're gonna do is we're gonna add or subtract some fractions that have different denominators, and also have some variables present. so i think there's two main things that you have to remember when you're adding or subtracting fractions. uh, those two things would be that you have to common denominators; that's the first thing.

How To Add Fractions With Variables, so notice neither of my examples we have common denominators, so we'll have to fix that a little bit. the other thing is once you do have common denominators, the arithmetic occurs in the numerator. it happens in the top part of the fraction, so let's do our first example here. we have 3x/5 minus 2x/15, so definitely different numbers in the denominator.

and, what i first think of is i think what's the greatest, excuse me, what's the least common multiple? what's the least common multiple of 5 and 15? what's the first number that both of those divide into evenly? and the least common multiple of those two numbers would be 15. so, i think well, i want a 15 here in my bottom fraction on the first side, and i think well, how do i do that? the only real way to, to change the denominator is to multiply it by something. so, i think in this case, we would have to multiply the denominator by 3, but remember if you do it to the denominator, you also have to do it to the numerator. and this is all valid because really we're just multiplying by the number 3 over 3 which is 1.

if you multiply something by 1, it doesn't change its value. so we may change how it looks, but numerically we would still, we would still get the same value. okay, so 3 times 3x would be 9x, and hey now i've got my 15 on the bottom.; that's why we did it, minus 2x/15. and now i can just do the arithmetic in the numerator. i do 9x minus 2x. 9x minus 2x would be 7x/15. and if you wanted to, you could, uh, pull the x out to the side and write it as (7/15)x. alrighty, in my next example here we've got 3y/4 and 5y/24, so the first thing i'm gonna have to do again is get common denominators. so i think what's the least common multiple of 4 and 24? and in this case i believe the least common multiple would be 24.

so we would have to multiply the numerator and the denominator by 6. again, the important thing is you gotta multiply the denominator by 6 to get the 24, but as a result we also have to do it to the numerator. so on top, we get, uh, 18y/24 plus 5y/24 if we add 18y and 5y, we simply get 23y/24. and again, we could write this as, we could pull the y out to the side 23/24 times y. and now we have combined our fractions.