 This video we're going to talk about subtracting real numbers. Alright, so let's subtract real numbers. Subtracting real numbers would be a minus b, but you could also write it as a plus a negative b sum. Okay, so you rewrite by adding the opposite of the second number. So let's try that here. We take the first number and we're going to add the opposite of three, which is negative three. Alright, and six plus a negative three if we did the absolute value thing we'd have the absolute value of six minus the absolute value of negative three. That would be six minus three, which is three. And we all know that six minus three is three. So that one checks. Negative seven plus the opposite of five, which is negative five. Okay, now we have the same sign here. So it's really just negative seven plus negative five is equal to negative 12. Same sign, add them, assign the sign. Seven plus five is 12. They're both negative, so it's a negative 12. In this case, we start with negative 2.4. We're going to add the opposite of negative 1.2. The opposite of negative 1.2 is positive 1.2. Again, we have opposite signs. So we can say it's the 2.4 is bigger than 1.2 if we forget about the signs for a second. So we're going to keep this one first. The absolute value of negative 2.4 absolute value minus the absolute value of 1.2. This is going to be positive 2.4 minus 1.2. And if we subtract those we get 1.2 and 2.4 is our larger number. So it's a negative 1.2. And then finally this last problem, we have 1 fourth and then plus the opposite of 3 fourths. So it would be negative 3 fourths. So in this case if we're going to do the absolute value you think about again forget about the sign for a second. 3 fourths is bigger than 1 fourth. Because we know when we take the absolute value they're both going to be positive. So we want the bigger number to come first. So the absolute value of 3 fourths minus the absolute value of 1 fourth, absolute value of 3 fourths is 3 fourths minus the absolute value of 1 fourth which is 1 fourth. So 3 minus 1 over 4 is going to be 2 over 4. And then we go back and look and say okay 3 fourths is bigger or maybe you want to look here and it's a negative. So that means that this is a negative 2 fourths. And finally you got to reduce. Fractions always had to be in reduced form so it's still a negative but it would be negative 1.5. Let's look at these problems again by doing the adding the opposite in a shorthand version instead of using the absolute values. This is a special case here at 6 minus 3 because this is a larger number and minus a smaller number. So we can just subtract. And it's a it was a positive number to begin with so that means things. It was a positive large number minus a smaller number. So we can just subtract. So 6 minus 3 is equal to 3. But most of the time you have something like the rest of these problems. So in that case we want to do that changing the sign. We're going to change the sign and add. And make sure that you know that it takes two strokes. What in the world does she mean by two strokes? Here's what I mean. Negative 7 plus a negative 5. So plus making that negative a positive or minus a plus is one stroke. And then making that 5 a negative 5 is the second stroke. Okay so let me put that in red. Here's my first stroke. Here's my second stroke. So now we have the same signs so we just assign add and assign the sign. So negative 7 plus a negative 5 is equal to negative 12. In the next case we're going to do the same thing. We're going to make our two strokes. So we started out with negative 2.4. And it was a minus. But our first stroke will be to make it a plus. And then it was a negative 1.2. But our second stroke will be to make that a positive 1.2. And then we can just really now we can just subtract and say that's 2.4 minus 1.2 is 1.2. And then assign the sign of the larger which is a negative. So we have a negative 1.2. Now some people might be confused because negative 2.4 is really smaller than negative 1.2. But remember that you when we're subtracting here we drop the signs and subtract. Okay so our last example. We have 1 fourth and it said minus. But we're going to make our first stroke be adding. And then it said it was 3 fourths over here. But our second stroke will be to subtract. And so now again we have we want to drop the signs and subtract and assign the sign of larger. So it's really 3 fourths minus 1 fourth is equal to 2 fourths. 3 minus 1 is 2. And the sign is a negative because 3 fourths is larger. In this case we're assigning a negative. And then of course we have to reduce it so it's a negative 1.2.