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Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%

Video transcript
So we have 0.79 minus 4/3 minus 1/2 plus 150%. So we have four different numbers written in different formats. Here it's a decimal, here we have two fractions, and then here we have a percentage. So the easiest thing to do would be to write all of these in the same format. And for me, the easiest format to do this computation in would be to write them all as fractions. And the reason why I want to do that, in particular, is because 4/3, when you divide by 3, when you divide 1/3, 2/3, 4/3, you're going to have a repeating decimal. So to avoid that, I want to put all of these-- I want to rewrite all of these as fractions. So let's do them one at a time. So 0.79, this is the same thing as 79/100, so I'll just write it that way. So this is the same thing as 79 over 100. Then of course, we have minus 4/3. Then we have minus 1/2. And then finally, we have-- I don't want to run out of colors here. Finally we have 150%. Well, 150%, percent literally means per cent, per hundred. So this is plus 150 per 100. So now we've written them all as fractions. And in order to do all the subtraction and addition, we have to find a common denominator. So what's the least common multiple of 100, 3, 2, and 100? Well, 100 is divisible by 2, so 100 is actually the least common multiple of 102. So we really have to just find the least common multiple between 100 and 300. And that's just going to be 300. There's no other common factors between 100 and 3. So let's write all of them with 300 as the common denominator. So let me do this in this reddish color. So 79 over 100 is the same thing. If I were to write it over 300, to go from 100 to 300 in the denominator, I'm multiplying by 3, so I have to multiply the numerator by 3 as well. So I'm going to multiply it by 3 as well. Let's see, 80 times 3 would be 240. So it's going to be 3 less than that. So 240 minus 3 is 237. Now 4/3. Well, to get the denominator to be 300, we have to multiply the denominator by 100, so we have to multiply the numerator by 100 as well. 1/2, if our denominator is 300, we multiplied the denominator by 150 to go from 200 to 300, so we have to multiply the numerator by 150. And then finally, 150 over 100, well, we're multiplying the denominator by 3 to get to 300, to go from 100 to 300. So we have to do the same thing in the numerator. So 3 times 150 is 450. So now we have the same denominator, and we can now add our numerators. So this is going to be equal to-- actually, I could just do it right over here on the right-hand side. This is going to be equal to some stuff over 300. So it's going to be 237 minus 400 and minus 150 and-- this actually should be a plus right over here. This should be plus 450. And so let's see if we could simplify this a little bit. We're subtracting 400, and we're subtracting 150. So these two would be the same thing as subtracting 550. And then we have a positive 237, and we're adding it to a positive 450. Or actually, maybe another easier way to think about this is negative 550 plus 450 is going to get us negative 100. And so this simplifies things a good bit. Now we have 237 minus 100 is going to be 137. So it equals 137 in the numerator over 300. And this is about as simplified as I can think of making it. And so this is our final answer, 137/300.