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Dividing whole numbers by decimals examples

One approach to dividing whole numbers by decimals is to convert both numbers into the same base, such as tenths or hundredths. Another technique is to multiply the numerator and denominator to eliminate the decimal from the denominator.

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Video transcript

- [Instructor] Let's say we wanna figure out what eight divided by 4/10 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 4/10. So what would eight be in terms of tenths? Well, we know that one whole is equal to 10/10, so eight wholes is going to be equal to 80/10. So I could write that down over here. Instead of eight, I can write that as 80/10. And I'm taking 80/10 and I'm dividing that by, divided by 4/10. I'm just writing out, 4/10. So if I have 80 of something, and if I'm diving 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 that down. This is going to be equal to 80 over four or 80 divided by four. And eight divided by four is two, so 80 divided by four is going to be equal to 20. So eight divided by 4/10 is equal to 20. Another way that you could think about that is to rewrite eight divided by 4/10 as eight over 4/10. Over 4/10. 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 wanna 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 four. So we got rid of the decimal. In the numerator, I am going to get 80. So once again, we get 80 over four, 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 24/100? Pause this video and try to figure that out. All right, well, we can do something very similar. This time we're dealing with hundredths, so we could try to express everything in terms of hundredths. So 48 is equal to how many hundredths? Well, we know that one is equal to 100/100, so 48 is going to be equal to 48 times 100/100. Maybe I'll just write it like that. Or you might be able to say, "Hey, that's 4,800 "or 4,800/100." So let's just, actually, I'll write it that way. This is going to be 4,800/100 divided by, this is 24/100. 24/100. 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 4,800 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 a hundred. 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. 48 over 24, and 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 two. So two times a hundred is equal to 200. So this right over here is equal to 200. You can also do it in this type or do it similar to the way we did this where instead of expressing it out as words, you could express it as 48 over 24/100. And instead of multiplying the numerator and denominator by 10, maybe you wanna 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.