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# Division strategies for decimal quotients

## Thuyết minh video

in this video we're going to come up with some strategies for division when the quotient isn't a whole number when it's going to be a decimal so let's try to compute 3/2 pause the video and see if you can figure out what that is going to be and I'll give you a hint it's not going to be a whole number all right now let's try to work this together and like all things in mathematics there's multiple strategies that you can use to try to figure out what 3/2 is one strategy is well let's just rewrite this as a fraction so 3/2 you could write that as you could write that as 3 over 3 over 2 now or you could say this is the same thing as 3 halves but how can we express this as a decimal well you might recognize that 3 halves is the same thing as 2 halves plus 1/2 let me write that down so this is the same thing as 2 plus 1 over 2 and I'm really doing every step here to hopefully make things clear which is the same thing as 2 over 2 so that's 2 over 2 plus 1 over 2 plus 1/2 I could break this up into 2 over 2 plus 1/2 now 2 over 2 is just 1 and so this is going to be equal to 1 and 1/2 now this might you might meet let's say hey 1/2 I could write that as 5/10 and that would be exactly right you could just if you want to spell out every step we could say this is equal to 1 and since it when we write it in decimal form we express things as tenths or hundredths or thousandths so 1/2 is the same thing as 5/10 and if we wanted to express that as a decimal this would be equal to 1 and 5 tenths 1 and 5/10 now I did every step here as you get more practice you say ok this is the same thing as 3 halves 3 halves 2 goes into 3 one time and there's a half left over so written writing this as a mixed number it's one and a half and a half written as a decimal is five tenths so this is one and five tenths now another way that we could have thought about this this is okay I'm not getting a whole number when I divide 3/2 maybe I'll get something in terms of tenths so let me express each of these in terms of tenths so three is how many tenths well three is thirty ten thirty tenths and we'd be dividing by two we're going to be dividing so we're going to be dividing it by two so thirty tenths divided by two well that's going to be equal to fifteen tenths this is equal to fifteen tenths which is equal to 10 10 10 5 tenths or 1 & 5 tenths so both of these are equally legitimate strategies for figuring out what 3/2 is I like the first one a little bit it let leverage is what we know about fractions but let's do another example let's do a few more examples this is fun okay let's figure out what 34 divided by 4 is divided by 4 and like before pause this video and try to figure it out and try to see if you can use some of the strategies that we used in the last video all right so as we just said we could re express this as a fraction but this is the same thing as 34 divided by 4 34 divided by 4 or 34 fourths now what is this going to be equal to well 4 goes into 34 8 times so it's going to go 8 times and you're going to have two left over so this is 8 and 2 fourths 8 so let me write it well now our eight and two fourths you've got two in that blue District fun 8 & 8 & 2 / 4 8 & 2 voice so how do I do this again I said 4 goes into 34 eight times and I have two left over so I'm gonna have two forts left over another way if you want to see all the steps you could say hey I could rewrite this as 32 over 4 plus 2 over 4 - 32 over 4 is our 8 so 8 and 2/4 well 2/4 that's the same thing as 1/2 that's the same thing as 1/2 and if we want to express that in terms of tenths this is equal to 8 and 1/2 is the same thing as 5 tenths 8 & 5 tenths which if we want to express it as a decimal is of course 8 and 5 tenths or 8.5 and we are done let's do another one of these and actually let's do one of them where we are dividing into a decimal where a decimal itself is being divided so let's say we wanted to calculate eight point four divided by seven pause this video and see if you can figure it out so when you look at this you might have means this too long okay I know 84 is divisible by seven we know if you know you're seven times tables we know that 7 times 12 is equal to 84 or that 84 divided by 7 is equal to 12 but this isn't 84 this is 8.4 so how do we think about it well one ways we can think about it in terms of tenths eight point four is the same thing as 84 tenths and so 84 tenths divided by seven well 84 of anything divided by seven is going to be 12 of that thing so it's going to be 12 10 and 12 tenths we can rewrite as 1 & 2 tenths or 1.2 1.2 and we are done so this is equal to one point to another way that we could have thought about this is we could have said you know what 84 tenths is the same thing as 84 over 10 in fact you would read this as 84 tenths and now you want to divide this by step so you want to divide this by seven this is the same thing when you divide by something is the same as multiplying by the reciprocal so it's 84 over 10 times 1/7 times 1/7 which is equal to we can change let me write it this way this is equal to 84 over 10 times 7 over 10 times 7 and now we could simplify this if we divide the numerator in the denominator by 7 84 divided by 7 is 12 7 divided by 7 is 1 12 divided by 10 this is going to be equal to 12 tenths which is 1.2 we could write this as 1 & 2 tenths or 1.2 let's do one more example that's kind of related let's say we want to figure out what 7 divided by 70 is pause this video and try to figure it out well we can rewrite this as we've been doing as 7 over 70 instead of writing it as 70 let me write that as 7 times 10 and what's valuable about this is we can divide the numerator and the denominator by 7 we go if we divide the numerator by 7 we get a 1 we divide the denominator by 7 we get a 1 remember we can do the same thing to the numerator number if we multiply or divide by the same value we're not changing the value of the actual fraction and so you're left with 1/10 which if you express it as a decimal you go to the tenths place you say I have one of those tenths that's 1/10 so this is 1/10 another way to think about it is this is the same thing as and really this is what we wrote over here but you could write this as 7 divided by 7 divided by the blue 7 and then you divide by 10 if you're dividing by 7 times 10 we're dividing actually let me write that out if you're dividing by 7 times 10 and this essentially another way of writing what we have over here this is going to be equal to 7 divided by 7 divided by 10 / 10 well 7 divided by 7 is 1 so you get 1 divided by 10 which is 1/10 1/10