Mental Math: Dividing by 5

Mike McGarry
Lesson by Mike McGarry
Magoosh Expert
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One small trick of mental math involves a quick way to divide a number by 5. Suppose we had to divide 630 by 5. And we're gonna do this entirely without even touching a calculator. Well, whatever our answer is, 630 is five times too big. Notice that if we double 630, that will be ten times too big. You see, it's usually relatively easy to double a number, even in your head.

So 630 doubled, well this, we know how to double 6. 6 doubled is 12. 30 doubled is 60. So when we double it we're gonna get 1260. Well that's ten times too big now, so all we're gonna do is divide by 10, and of course that's the easiest thing in the world, because we just remove a 0, 126.

We divided by 10. So that is 630 divided by 5. That's a very easy way to get it. When we need to divide by 5, we can double N and then divide the doubled number by 10. And in fact, we don't even need to do things in that order we can do them either order.

We could divide by ten first and then double or we could double first and divide by ten, whichever seems easier. So, pause the video, practice dividing that by five in your head. Okay, so I'm gonna choose to double it first because then i'll get something that is divisible by ten. So of course, 200 doubled is 400, and 35 doubled is 70.

So when that's doubled it's 470. And then when we divide by 10 we just remove a 0, 47. So 235 divided by 5 is 47. Here's another one. Divide 1140 by 5. Pause the video and do this in your head.

Okay. Here what I'm gonna choose to do first is because it's divisible by 10 already I'm just gonna divide by 10, just to get a smaller number. So I divide this by 10 and I get 114. Now I'm gonna double. Well, 100 doubled is 200, 14 doubled is 28.

So it's gonna be 228, and that is the answer. 1140 divided by 5 is 228, very easy to do this in your head without even touching a calculator. To divide any number by 5, we can simply double it and divide it by ten. We don't even have to do the steps in that order. We can either divide by ten first or double it.

We just have to do those two simple steps in our head.

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