Multi digit division strategies for decimals

In a previous video, we started thinking about strategies for dividing numbers where either the numbers or decimals or their quotients are going to be decimals. So now let's continue that. We're going to do slightly more involved examples.

Let's say we want to figure out what 500 divided by 200 is. Pause this video and see if you can figure that out. Well, one strategy for doing this is to just really express this as a fraction and see if you can simplify this fraction in a way that it's straightforward to express it as a decimal.

So, for example, this is going to be the same thing. This is equal to five hundred over two hundred. Now we can simplify this. We could say this is the same thing as five times 100 over two times 100. The reason why that is useful is if you say, "Hey look, I have a hundred in the numerator, I have 100 in the denominator; 100 divided by 100 is just going to be one."

So you could just view this as equal to five halves times 100 over 100. Which is just going to be equal to one. Another way to think about it, you could divide the numerator by 100 and you would have five. And as long as you divide the denominator by the same thing, you're not changing the value of the fraction. So if you divide the denominator by 100, you're going to get two.

So anyway you think about it, this could be simplified as five halves. But we're not done yet. That is what 500 divided by 200 is. But can we express this as a decimal? Well, we can rewrite five halves as a mixed number. So five halves is going to be equal to, well, how many times does 2 go into five? Well, it goes two times and then you have one half left over.

So this is going to be two and 1/2. And now how do we express this right over here as a decimal? Well, you might recognize that 1/2 is the same thing as 5/10. So this is going to be equal to 2 and 5 over 10, which of course we can write as 2.5 or 2 and 5 tenths.

So, 500 divided by 200 is 2.5. Let's do another example. Let's say we wanted to figure out what 0.63 divided by 0.07 is. Pause this video and see if you can come up with a strategy for doing this.

Well, there are multiple ways to tackle it. One way is to think about both of them in terms of hundredths. So for example, this is 63 hundredths and this right over here is seven hundredths. And so, if you have 63 of something and you're dividing that by seven of that same something, what are you going to get? Well, you're going to see that if you took your seven hundredths and you multiply it by nine, you're going to get 63 hundredths.

So, 63 of something divided by seven of that same something is going to be equal to nine. This is going to be equal to 9. Seven times 9 is 63. So, seven hundredths times nine is going to be 63 hundredths.

Another way to think about it is we can express this as a fraction. So, in the numerator, you have 0.63, and in the denominator, you have 0.07. And if the decimals are bothering us, we can multiply both the numerator and the denominator by the same value to get rid of the decimals.

So let's multiply the numerator by 100 and also multiply the denominator by 100. This doesn't change the value of the expression because multiplying by 100 over 100 is just the same thing as multiplying by 1. So this would be equal to 63 over 7. Once again, that is going to be equal to nine.