Equal sign

- When you first learn math, you see things like two plus three is equal to five, or you might see six plus one is equal to seven, or you might see eight minus two is equal to six. And all of these, you might think that the equal sign just says, hey, give me the answer, figure out what two plus three is. Two plus three, well, the answer is five. Six plus one, the answer is seven. Eight minus two, the answer is six. That's not quite right. What the equal sign is saying is that what's on the left side is the same amount, the same quantity, as what is on the right-hand side. It's saying that two plus three is the same thing as five. And you didn't have to write it this way. You could have written, you could have written five is equal to two plus three. You could write that three plus two is equal to two plus three. Notice, here, we're not figuring out the answer, we're just saying that whatever three plus two is, that's going to be the same thing as whatever two plus three is. We know that they both equal five. You could even mix addition and subtraction, you could write, you could write that six plus one is the same thing, is equal to, eight minus one. They are the same amount, the same quantity. What is six plus one, well, that's seven. What's eight minus one, well, that is seven. So the equal sign does not mean just give me the answer or just, you know, add the numbers or subtract the numbers. An equal sign is saying that what's on the left-hand side is the same amount as what's on the right-hand side. So with that in our brain, let's write some statements using equal signs, some equations, you could even say, using equal signs, and figure out which of them are actually true. So if I were to write down, if I were to write down, I won't even read it out, 'cause it might give it away. If I were to write down this, is this true? Well, the number on the left here is 18, the number on the left is 18, the number on the right is a different number, it is 81, it is 81. They swapped, or we swapped (chuckles), the one and the eight, they're in different places. This is a different number, this is 81. These are not equal. These are not, not equal. So this statement is not true. And sometimes you might even see someone do something like this, that means not equal. 18 is not equal to 81. Let's keep going. What if I were to write, what if I were to write nine minus three plus two minus zero is equal to, is equal to... zero plus one minus one plus eight, is this true? Well, let's figure out what the left-hand side is. See, nine minus three is six, plus two is eight, minus zero is eight. So this, this, if I were to, if I were to compute it, that's equal to eight. And then on the right-hand side I have zero plus one minus one, well, one minus one is zero, so this is all going to be eight. So this is, this is true, eight equals eight. This is another way of writing eight, nine minus three plus two minus zero, this is eight. And this is also eight, so once again the equal sign is just saying that this, what we have on the left, is the same as what we have on the right. Let's do another example. Let's do another example, let's do two more examples. If I were to write this, is this true? Well, you might be tempted, hey, if I put a one (chuckles) and a zero together, it's gonna look like a 10, but that's not, this is not how we do mathematics, this is not how we add things. One plus zero is just one, so this would be the same thing as saying that 10 is equal to one, which we know is not true, so this is not equal, this is not equal. Let's do one more. Let's say I had seven plus one is equal to three plus four. Is this equation true? Well, what do we have on the left, seven plus one is eight, three plus four is seven. These are not the same quantity, they're not the same amount, so these are not equal. And we're done.