Dividing whole numbers by decimals (tenths)

0:00- [Instructor] We're told, "The 6th-grade class is selling cookies for $0.40 each to raise money for a trip. After a few days, they have $96. How many cookies were sold?" Pause this video and see if you can figure that out. All right. So you might already be realizing, if I take the total amount earned, so $96.

0:22And if I were to divide it by the cost of each cookie, how much they sold each cookie for. So if I were to divide it by $0.40 or 40 cents, then this would be equal to the number of cookies sold. So it all boils down to what is $96 divided by $0.40, or what is 96 divided by 0.40, or I guess we could say 0.4.

0:52So this could all boil down to, we could say 96 divided by, we could write it this way, 0.4. Ah, it's a different shade of blue. Here we go. 0.4, which is the same thing as 0.40, or we could write it this way. 96 divided by 0.4, like this. How do we figure out this?

1:18There's many ways, and you will learn more in future videos of how you might be able to divide by a decimal. But one way to think about it is, what if we were to multiply the top and bottom of this fraction by a number that would remove this decimal? So for example, if I were to multiply both the numerator and the denominator by 10, what is going to happen?

1:41And, really, what I'm doing is I'm just multiplying by 10 over 10, which is just multiplying by one, so I'm not changing the value of it. Well, in the numerator, I am going to end up with 960 when I multiply those together. And then in the denominator, I'm going to end up, if at 0.4 times 10, that's gonna be the same thing as just straight up, straight up 4.

2:07And so, now we know how to divide whole numbers like this. This was useful to us. It essentially allowed us to get rid of that decimal. 96 divided by 0.4 is the same thing as 960 divided by 4. So what is that? We're gonna take 4 and we're going to go into 960.

2:29And so 4 goes into 9, 2 times 4 is 8. Subtract, 9 minus 8 is 1. Bring down this 6. 4 goes into 16 exactly four times. 4 times 4 is 16. Subtract. 0. Bring down that 0. 4 goes into 0. 0 times 0 times four is 0. And we have no remainder. So there we have it. 960 divided by 4 is 240, which is the same thing as 96 divided by 0.4.

3:03So this is also 240, which is also the number of cookies sold. Let's do another example of this. Here, we are told, "A parking meter charges $0.80 per hour for parking. A car was parked and was charged a total of $4. How many hours was the car parked?" Pause this again and try to work it out.

3:28So you might recognize that this is going to be $4 divided by $0.80. Or actually, let me write it this way first. Divided by $0.80. Divided by $0.80, which is equivalent to, so I won't write the dollar signs here just to simplify it. This is the same thing as 4 divided by 80 cents is 0.80.

3:55That's the same thing as 0.8. So that's the same thing as 0.8. Now what if we were to write both of these in terms of tenths? We know that this one right over here, this is 8. Actually, let me write it this way. This is 8 tenths. How would we write 4 in terms of tenths?

4:20Well, a whole is 10/10, so four wholes is 40 tenths. So we could write this as 40 tenths. So I could rewrite this expression as 40 tenths divided by 8 tenths. And so if you have 40 of something divided by 8 of that something, what are you going to get? Well, you are going to get the same thing as 40 divided by 8, which is going to be equal to 5.

4:53How many times does 8 tenths go into 40 tenths? It goes exactly five times. So how many hours was the car parked? It was parked for five hours, and you could double-check that. If you take five hours times 0.80 per hour, you're going to see that that is exactly $4.