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 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 6 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 strategies 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 want to get rid of the decimal on the bottom we have 2/10 well we can multiply the bottom by 10 if we multiply the bottom by 10 we need to multiply the numerator by 10 so it's essentially we're multiplying this fraction times 10 tens 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 going to 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 strategies you could have thought of all of these numbers in terms of tenths you could have said this is 6 doing that orange color you could have said this is 6 tenths divided by / or let me be careful this is 60 tens 6 is 60 tenths 60 tenths divided by 2 tenths two tenths is equal to well I have 60 is something and if I were to divide it into groups of two of that something I would have 30 group 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 the standard way of dividing decimals let's say we wanted to compute 4 point 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 four point two divided by three tenths and now we could try to get rid of the decimals now the best way to do that I could imagine I have 10 see I have 10 see if I multiply the numerator in the 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 three tenths times 10 well that is going to be equal to three and so what is 42 divided by three 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 so it shouldn't be too long so let's see 3 goes into 4 one time one times three is three subtract 4 minus 3 is a why do 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 4 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 42 tenths divided by 3 tenths divided by 3 tenths in which case 42 10 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 hopefully appreciate these ideas express it as a fraction see if you can multiply the numerator and denominator by the same values 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 going to be effective strategies you're hopefully expected strategies for dividing decimals or dividing numbers where the quotient might be a decimal and in the 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 four point two 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 three and then I would say okay 3 goes into 42 let's see 3 times 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