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## Topic A: Use properties of operations to generate equivalent expressions

# Combining like terms with rational coefficients

CCSS.Math:

## Video transcript

- [Voiceover] What I wanna do in this video is get some practice simplifying expressions and have some hairier numbers involved. These numbers are kind of hairy. Like always, try to pause this video and see if you can simplify this expression before I take a stab at it. All right, I'm assuming you have attempted it. Now let's look at it. We have -5.55 minus 8.55c plus 4.35c. So the first thing I wanna do is can I combine these c terms, and I definitely can. We can add -8.55c to 4.35c first, and then that would be, let's see, that would be -8.55 plus 4.35, I'm just adding the coefficients, times c, and of course, we still have that -5.55 out front. -5.55. I'll just put a plus there. Now how do we calculate -8.55 plus 4.35? Well there's a couple of ways to think about it or visualize it. One way is to say well this is the same thing as the negative of 8.55 minus 4.35, and 8.55 minus 4.35, let's see, eight minus four is going to be the negative, eight minus four is four, 55 hundredths minus 35 hundredths is 20 hundredths. So I could write 4.20, which is really just the same thing as 4.2. So all of this can be replaced with a -4.2. So my entire expression has simplified to -5.55, and instead of saying plus -4.2c, I can just write it as minus 4.2c, and we're done. We can't simplify this anymore. We can't add this term that doesn't involve the variable to this term that does involve the variable. So this is about as simple as we're gonna get. So let's do another example. So here I have some more hairy numbers involved. These are all expressed as fractions. And so, let's see, I have 2/5m minus 4/5 minus 3/5m. So how can I simplify? Well I could add all the m terms together. So let me just change the order. I could rewrite this as 2/5m minus 3/5m minus 4/5. All I did was I changed the order. We can see that I have these two m terms. I can add those two together. So this is going to be 2/5 minus 3/5 times m, and then I have the -4/5 still on the right hand side. Now what's 2/5 minus 3/5? Well that's gonna be -1/5. That's gonna be -1/5. So I have -1/5m minus 4/5. Minus 4/5. Now once again, I'm done. I can't simplify it anymore. I can't add this term that involves m somehow to this -4/5. So we are done here. Let's do one more. Let's do one more example. So here, and this is interesting, I have a parentheses and all the rest. Like always, pause the video. See if you can simplify this. All right, let's work through it together. Now the first thing that I want to do is let's distribute this two so that we just have three terms that are just being added and subtracted. So if we distribute this two, we're gonna get two times 1/5m is 2/5m. Let me make sure you see that m. M is right here. Two times -2/5 is -4/5, and then I have plus 3/5. Now how can we simplify this more? Well I have these two terms here that don't involve the variable. Those are just numbers. I can add them to each other. So I have -4/5 plus 3/5. So what's negative four plus three? That's going to be negative one. So this is going to be -1/5, what we have in yellow here. I still have the 2/5m, 2/5m minus 1/5. And we're done. We've simplified that as much as we can.