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One-step addition & subtraction equations: fractions & decimals

In this math lesson, we practice solving equations with variables and fractions. We learn to isolate the variable by adding or subtracting terms from both sides of the equation. This helps us find the value of the variable, making the equation true. Keep practicing and have fun!

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Video transcript

- [Voiceover] Let's give ourselves some practice solving equations. So let's say we had the equation 1/3 plus A is equal to 5/3. What is the A that makes this equation true? If I had 1/3 plus this A, what does A need to be in order for 1/3 plus that to be equal to 5/3? So there's a bunch of different ways of doing this, and this is one of the fun things about equations is there's no exactly one right way to do it. But let's think about what at least I think might be the simplest way. And before I work through anything, you should always try to pause the video, and do it on your own. So what I like to think about is can I have just my A on one side of the equation? And since it's already on the left-hand side, let's see if I can keep it on the left-hand side, but get rid of this 1/3 somehow. Well the easiest was I can think of getting rid of this 1/3 is to subtract 1/3 from the left-hand side of the equation. Now I can't just do that from the left-hand side of the equation. If 1/3 plus A is equal to 5/3, and if I just subtract 1/3 from the left-hand side, then they're not going to be equal anymore. Then this thing is going to be 1/3 less, which this thing isn't going to change. So then this thing on the left would become less than 5/3. So in order to hold the equality, whatever I do on the left-hand side I have to do on the right-hand side as well. So I have to subtract 1/3 from both sides. And if I do that, then on the left-hand side, 1/3 minus 1/3, that's the whole reason why I subtracted 1/3 was to get rid of the 1/3, and I am left with A is equal to 5/3 minus 1/3, 5/3 minus 1/3, minus 1/3, and what is that going to be equal to? I have five of something, in this case I have 5/3, and I'm gonna subtract 1/3. So I'm gonna be left with 4/3. So I could write A is equal to 4/3. And you could check to make sure that works. 1/3 plus 4/3 is indeed equal to 5/3. Let's do another one of these. So let's say that we have the equation K minus eight is equal to 11.8. So once again I wanna solve for K. I wanna have just a K on the left-hand side. I don't want this subtracting this eight right over here. So in order to get rid of this eight, let's add eight on the left-hand side. And of course, if I do it on the left-hand side, I have to do it on the right-hand side as well. So we're gonna add eight to both sides. The left-hand side, you are substracting eight and then you're adding eight. That's just going to cancel out, and you're just going to be left with K. And on the right-hand side, 11.8 plus eight. Well, 11 plus eight is 19, so it's going to be 19.8. And we're done, and once again, what's neat about equations, you can always check to see if you got the right answer. 19.8 minus eight is 11.8. Let's do another one, this is too much fun. Alright, so let's say that I had 5/13 is equal to T minus 6/13. Alright, this is interesting 'cause now I have my variable on the right-hand side. But let's just leave it there. Let's just see if we can solve for T by getting rid of everything else on the right-hand side. And like we've done in the past, if I'm subtracting 6/13, so why don't I just add it? Why don't I just add 6/13? I can't just do that on the right-hand side. Then the two sides won't be equal anymore, so I gotta do it on the left-hand side if I wanna hold the equality. So what happens? So what happens? On the left-hand side I have, let me give myself a little bit more space, I have 5/13 plus 6/13, plus 6/13 are equal to, are equal to... Well, I was subtracting 6/13, now I add 6/13. Those are just going to add to zero. 6/13 minus 6/13 is just zero, so you're left with T. So T is equal to this. If I have 5/13 and I add to that 6/13, well I'm gonna have 11/13. So this is going to be 11/13 is equal to T, or I could write that the other way around. I could write T is equal to 11/13.