Estimating 2 digit multiplication example

So we are asked, "?" is roughly equal to this squiggly equal sign right over here. This means roughly equal to, so not exactly equal to 44 times 78.

So one way to think about it is 44 times 78 is roughly equal to what? So they're really asking us to estimate. I encourage you to pause this video and try to think through how you would estimate what 44 times 78 is. Once again, you don't have to get it exactly, you just want to get it roughly, and think about which of these choices are closer or closest to that estimation of yours.

All right, now let's work through it together. For me, the best way to estimate is to think about, hey, can I think of these numbers? Can I estimate these numbers or think about what are they roughly equal to? And when I think about what they're roughly equal to, I want to think about numbers that are easy to multiply potentially in my head.

So for example, 44 is reasonably close to 40. So I could say that, hey, this is approximately equal to or roughly equal to 40. So that's my estimate of 44, or 44 is roughly 40. And then 78, I could say, hey, that's pretty close to 80. And so I could say this is roughly equal to 40 times 80.

And this is pretty straightforward. Some of you might already recognize that 4 times 8 is 32, and then we have 4 tens, and then we have 8 tens. So it'd be 4 times 8 times 10 twice. But if what I just said is confusing to you, we could think about it this way: forty times eighty is the same thing as four times ten, that's 40 times 8 times 10, that's 80.

And this is equal to, I'm just going to switch the order here of this multiplication, which we can do. This is equal to 4 times 8 times 10 times 10. 4 times 8 is 32, 10 times 10 is 100. So we could say that this is equal to 32 hundreds, or we could view that as 3200, which you could also view as 32 hundreds. And so that is this choice right over here.

Now, this isn't exactly what 44 times 78 is, but it's roughly, and this is useful. Sometimes in life, you just have to get a rough sense of what something is going to be. Sometimes when you even are trying to find this exact product, you just want your brain to check, does that make sense?

Let's say you went through some process to figure out this, and you got some number that is close to 20, and you're like, "Wait, wait, no, but roughly when I think about 40 times 80, this should be close to 3200." I must have done something wrong. So it also helps you keep a check on yourself.