Dividing whole numbers by decimals examples

Let's say we want to figure out what eight divided by four tenths is. Pause this video and try to figure it out on your own before we do it together.

All right, now one way to approach this is to think about everything in terms of tenths. And why tenths, you ask? Well, I just described the second number as four tenths. So what would it be in terms of tenths? Well, we know that one whole is equal to ten tenths, so eight holes are going to be equal to 80 tenths. So I could write that down over here. Instead of eight, I can write that as 80 tenths, and I'm taking 80 tenths and I'm dividing that by four tenths. I'm just writing it out: four tenths.

So if I have 80 of something, and if I'm dividing it into groups of four of that something, how many equal groups am I going to have? Well, I'm gonna have 80 divided by four groups, or 80 divided by four. Eight divided by four, actually, let me just write it down: this is going to be equal to 80 over four, or 80 divided by 4. And 8 divided by 4 is 2, so 80 divided by 4 is going to be equal to 20. Thus, 8 divided by four tenths is equal to 20.

Another way that you could think about that is to rewrite 8 divided by four tenths as 8 over four tenths over four tenths. And then if you wanted to rewrite this, you could say, "Hey, can I multiply the numerator and the denominator by some quantity that'll get rid of the decimal in the denominator?" Well, I could multiply the denominator by 10, and if I don't want to change the value of the fraction, I have to multiply the numerator by that same amount. Well, what does that get us?

Well, this is going to be equal to, in the denominator right over here, I'm just going to have a 4, so we got rid of the decimal. And in the numerator, I am going to get 80. So once again, we get 80 over 4, which is equal to 20.

Let's do another example, but in this case, we'll deal with hundredths. So let's say we want to figure out what is 48 divided by 0.24, or 24 hundredths. Pause this video and try to figure that out.

All right, well, we can do something very similar. This time, we're dealing with hundreds. So we could try to express everything in terms of hundredths. So 48 is equal to how many hundredths? Well, we know that 1 is equal to 100 hundredths, so 48 is going to be equal to 48 times 100 hundredths. Maybe I'll just write it like that, or you might be able to say, "Hey, that's 48 hundred" or 4,800 hundredths. So let's just, actually, I'll write it that way: this is going to be 4,800 hundreds divided by this is 24 hundredths, 24 hundredths.

And so, what's that going to be? Well, same logic as we used up here. If I have 4,800 of something or 4,800 of something, and if I'm dividing it into equal groups of 24 of that something, well, I'm going to have four thousand eight hundred divided by 24 equal groups. So this is going to be equal to 4,800 over 24. We could express 4,800 as, of course, 48 times 100, so this is equal to 48 times 100 over 24.

And of course, you could view this as the same thing as this is equal to 48 over 24. Many of you might have already done it in your head: times 100. What's 48 divided by 24? Well, that is going to be equal to 2, so 2 times 100 is equal to 200. So this right over here is equal to 200.

You could also do it in this type, or do it in a similar way than we did this, where instead of expressing it out as words, you could express it as 48 over 24 hundredths. And instead of multiplying the numerator by 10, maybe you want to multiply it by something else to get whole numbers in both the numerator and denominator. Think about that after this video and try to work it out that way as well.