Strategies for dividing by tenths

- [Instructor] Let's do a few more examples of thinking of strategies for dividing decimals. In the future, we're gonna come up with a more systematic way of doing it, but it's really important to come up with some of these strategies because it gives you an intuition for dividing decimals. And frankly, it's an easier thing to do, especially when you're trying to eventually divide decimals in your head. So let's say we want to figure out what six divided by 0.2, or 2/10, is. Pause the video, and see if you can figure it out. So we've already explored multiple strategies. One strategy is, well, let's express this as a fraction. This is the same thing as 6 over 0.2, And maybe we can multiply the numerator and the denominator by some value so we're not dealing with decimals anymore. And, if you wanna get rid of the decimal in the bottom, we have 2/10, well we can multiply the bottom by 10. But if we multiply the bottom by 10 we need to multiply the numerator by 10. So essentially we're multiplying this fraction by 10/10, which is just multiplying it by 1, so it doesn't change its value. So this is going to be equal to 60, so 6, 0, over 2/10 times 10, let's go and move the decimal one to the right, and that's just going to be equal to 2. Now what is 60 divided by 2? Well, 60 divided by 2 is fairly straightforward, 6 divided by 2 is 3 so 60 divided by 2 is going to be equal to 30. So that's 30. And so we're done. Now another strategy is you could've thought of all of these numbers in terms of tenths. You could've said this is 6, do that orange color, You could've said this is 6 tenths divided by, oh, let me be careful, this is 60 tenths, 6, is 60 tenths, 60 tenths divided by 2 tenths is equal to, well if 60 is something and I were to divide it into groups of two of that something I would have 30 groups. That's going to be equal to 30. Let's do another example. This will be our most involved one, before we really try to show you the standard way of dividing decimals. Let's say we wanted to compute 4.2, or 4 and two tenths, divided by 3 tenths. Pause the video and see if you can figure that out. Well you've already seen multiple techniques for tackling this. It never hurts to try to write this as a fraction. So this, you could write it as 4.2 divided by 3 tenths. And now we could try to get rid of the decimals. Now the best way to do that I could imagine, I have tenths here, I have tenths here, If I multiply the numerator and the denominator by 10, that might help out a lot, because the numerator, this would move the decimal one to the right, so the numerator I would get 42, 4.2 times 10 is 42, over 3 tenths times 10, well that is going to be equal to 3. And so what is 42 divided by 3? Well, there's multiple ways to do that, you can try to do it in your head, or you just try to actually do a little bit of medium long division, this shouldn't be too long. So let's see, 3 goes into 4 one time, 1 times 3 is 3, subtract, 4 minus 3 is, oh why did I write 43, I knew something was fishy, 42. 3 goes into 42, my brain is malfunctioning. Alright, 3 goes into 4 one time, 1 times 3 is 3, you subtract 4 minus 3 is 1, bring down the 2, 3 goes into 12 four times. So this is equal to 14. And so this one right over here is going to be equal to 14. And just like we saw in the last example, you could also think of this as 42 tenths, divided by 3 tenths, in which case 42 tenths, 42 of something divided into groups of 3 of that something, you're gonna end up with 14 groups, you're gonna end up with 14. So hopefully you appreciate these ideas, express it as a fraction, see if you can multiply the numerator and denominator by the same value so maybe the decimals get eliminated, maybe you can think of these numbers in terms of tenths, or hundredths, and then think of it that way. And any of these combinations are gonna be effective strategies, or hopefully effective strategies, for dividing decimals or dividing numbers where the quotient might be a decimal. And in future videos we're gonna learn a more standard systematic way of doing it but this is always valuable. I still, if someone walked up to me on the street and said what's 4.2 divided by 0.3, this is how I would actually do it. I would say okay that's the same thing as 42 divided by 3, and then I would say okay, 3 goes into 42, let's see, 3 times 10 is 30, and then 3 times 4 is 12, yeah that would be 14 times. That's how my brain would do it if I was trying to do it in my head.