Multi-digit division strategies for decimals

- [Instructor] In a previous video we started thinking about strategies for dividing numbers where either the numbers are decimals, or their quotients are going to be decimals. So now let's continue that, and we're gonna do a slightly more involved examples. So let's say we wanna figure out what 500 divided by 200 is. Divided by 200. Pause this video and see if you can figure that out. Well, one strategy for doing this is to just re-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 500, 500 over 200. And now we can simplify this. We can say this is the same thing as five times 100, five times 100, over two times 100. The reason why that is useful is you say, "Hey look, I have a hundred in the numerator, "I have a hundred in the denominator, "a hundred divided by a hundred is just going to be one." So, you could just do this. This is equal to five halves. Five halves times. Times 100 over 100. Times 100 over 100. Which is just going to be equal to, which is just going to be equal to one. Another way to think about it, you could divide the numerator by a hundred. 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 a hundred, you're going to get two. So, any way 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 two go into five? Well it goes two times, and then you have one half left over. So this is going to be two and one half. And now how do we express this right over here as a decimal? Well, you might recognize that one half is the same thing as five tenths. So this is going to be equal to two and five over ten, which of course we can write as 2.5, or two and five 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's 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 hundredths, what are you going to get? Well, you're going to, if you took your seven hundredths, and you multiply it by nine, you're going to get 63 hundredths. And 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 nine. Seven times nine 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 one. So this would be equal to 63 hundredths times 100. Well we would move the decimal two to the right. This is going to be equal to 63 over seven hundredths times 100. Once again we move the decimal two to the right. This is going to be seven. So 63 divided by seven, once again, that is going to be equal to nine.