Strategies for dividing by tenths

Let's do a few more examples of thinking of strategies for dividing decimals. In the future, we're going to 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. 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 6 divided by 0.2 or 2 tenths is. Pause the video and see if you can figure it out.

We've already explored multiple strategies. One strategy is to 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. If you want to get rid of the decimal on the bottom, we have two tenths. 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 over 10, which is just multiplying it by one, so it doesn't change its value. This is going to be equal to 60 over 2 tenths times 10. That's going to move the decimal 1 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 have thought of all of these numbers in terms of tenths. You could have said this is 6, I'm doing that in orange color. You could have said this is 60 tenths divided by 2 tenths. Two tenths is equal to... Well, I have 60 of something, and if 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 2 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 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 10c. If I multiply the numerator and denominator by 10, that might help out a lot because in 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.

So, what is 42 divided by 3? Well, there's multiple ways to do that. You could try to do it in your head, or you just try to actually do a little bit of medium long division. It shouldn't be too long.

So, let's see, three goes into four one time. One times three is three. Subtract 4 minus 3 is... Oh, why did I write 43? I knew something was fishy! 42! My brain is malfunctioning!

Alright, 3 goes into 42. My brain is functioning now. Okay, 3 goes into 4 one time. One 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. 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 three of that something. You're going to end up with 14 groups, that you're going to 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.

Any of these combinations are going to be effective strategies, or hopefully expected strategies for dividing decimals or dividing numbers where the quotient might be a decimal. In future videos, we're going to learn a more standard systematic way of doing it, but this is always valuable.

You'll see, 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." 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.