Approximating dividing by decimals

What we're going to do in this video is get a little bit of practice estimating dividing with decimals.

So, for example, we want to figure out approximately— that's what these kind of squiggly equal sign means; this means approximately equal.

So what is 80 divided by 1.9 approximately equal to?

So we want to estimate what this is. Pause this video and see if you can figure it out.

So, before we even look at these choices, how would we try to do this in our head? Well, we could say 1.9— it's hard to do that in our head to divide it into 80, but it's awfully close to 2.

So we could say this is close to— this is approximately equal to 80 divided by 2.

Because once again, 1.9 is awfully close to 2, and then this is easy to figure out: that is going to be equal to 40.

So our first expression, you could say, is approximately equal to 40.

Is it exactly equal to 40? No, but it's pretty close, so I would select that choice.

Let's do another one.

So pause this video and see if you can figure out the approximation.

What is 209 divided by 3 roughly equal to?

So once again, here we don't have any clear decimals. If we were to divide it out, we would get a decimal answer for our quotient.

But what we could do is— well, is either one of these close to a multiple of 3 that we might recognize?

Well, you might immediately recognize that if you think about multiples of 3, you think in terms of— well, 3 times 6 is 18, 3 times 7 is 21.

Well, this is close to 210, so this is approximately equal to 210 divided by 3.

Now, why is this interesting?

Well, 210 is just 21 times 10, so if 21 divided by 3 is 7, then 210 divided by 3 is going to be equal to 70.

So once again, 209 is pretty close to 210. Remember, we're just estimating, and so 209 divided by 3 would approximately be equal to 70, which is that choice right over there.

Let's do one more example.

So once again, pause the video and figure out what 6.86 divided by 1.12 is approximately equal to.

Alright, so here I would just try to round to the nearest whole number and see if that helps my division in my head.

So 6.86 is approximately 7 if we round up to the nearest whole number.

And if I say 7 divided by— and if we round down 1.12, 7 divided by 1 is much easier for us to do in our head.

So that is going to be 7.

Now, once again, it's very important to realize these are estimations. It's not going to be exactly equal to 7, but it's definitely going to be much closer to 7 than 7,700 or 7,000.