Examples dividing by tenths and hundredths

Welcome! So let's see if we can figure out what 8 divided by 0.4 is.

Pause this video and see if you can work through that.

All right, so we're trying to figure out what eight ones divided by four tenths is. One way to think about that is to think about everything in terms of tenths. Eight ones, one one is equal to ten tenths, so eight ones is equal to eighty tenths. This is equal to 80 tenths, and I'm dividing it by four tenths.

So, if I have 80 tenths and if I want to divide it into equal groups of four tenths, how many equal groups am I going to have? Well, I am going to have 20 equal groups of four tenths that would make up eighty tenths. Eighty divided by four is twenty, so eight divided by four tenths is equal to 20.

Another way that we could have approached that is we could have thought about it in terms of fractions. We could have said, "Hey, 8 divided by 4 tenths." That's the same thing as 8 divided by 4/10, which is the same thing. When you divide by a fraction, it's the same thing as multiplying by the reciprocal.

So, this is the same thing as 8 times 10 over 4, or you could view it as the same thing as 8 over 1, 8 ones times 10 over 4. In your numerator, you get 8 times 10, so that is going to be equal to, I'll do it in this orange color, 8 times 10 is equal to 80, and then in our denominator we're going to have 1 times 4. I didn't circle the one! Yeah, you're going to have the 1 times the 4, so that's just going to be equal to 4.

So, 80 fourths or 80 divided by 4, once again, that is going to be equal to 20.

Let's do another example. But in this case, let's deal with things in hundredths. Let's draw a line here. So let's say that someone walks up to you on the street and says, "Quick, what is 48 divided by 0.24?"

Pause this video and see if you can figure that out. And I'll give you a little bit of a hint: the techniques we just did might apply, although now we're dealing with hundredths.

All right, now let's work on this together. Well, one way to work on it is you could view this as 48, you could just convert everything to fractions as 48, and actually I can just write it as 48 over 1 divided by 24 hundredths.

This division sign looks a little bit weird; let me make it look a little bit more normal. There you go! So when you divide by a fraction, that's the same thing as multiplying by the reciprocal. We've seen that before.

So this is equal to 48 over 1 times 100 over 24. And so our numerator here is going to be equal to 48 times 100. Actually, I'm just going to write that out as 48 times 100 in the numerator, and then our denominator is going to be 24 times 1. Well, that's just equal to 24.

And so, what is this going to be equal to? 48 times 100 divided by 24. Well, we could divide the numerator and the denominator by 24. If we did that, 48 divided by 24 is 2, and 24 divided by 24 is 1. So we're left with 2 times 100 divided by 1.

Well, 2 times 100 is equal to 200, and then you divide that by 1 and you still get 200. So there you have it, this is equal to 200.

Now, another way that you could have approached this is you could have thought about everything again in terms of hundredths. So, 48 ones is the same thing as 4,800 hundredths. So, it's equal to 4,800 hundredths divided by 24 hundredths.

So if I have 4,800 or 4,800 hundredths and if I want to divide into equal groups of 24 hundredths, how many of those equal groups would I have? Well, you would have 4,800 divided by 24 equal groups.

So this is going to be equal to 4,800 divided by 24. Now, 4,800 is exactly what we had up here, and so we already saw that 4,800 divided by 24 is equal to 200.

And if you just got to this point, and if you said, "Hey, how could I work on this?" you could just say, "Hey, let me divide the numerator and denominator by 24." You could try to re-express 4,800 as 48 times 100, or you could even say that 48 is 24 times 2, and then you're going to multiply that times 100 to get to 4,800.

And then the division is a little bit more straightforward. But the big picture here is to realize that dividing by decimals is not some mysterious thing when you think about it in terms of place value or when you think about it in terms of fractions.