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Multi-digit division strategies for decimals

Thuyết minh video

in a previous video we started thinking about strategies for dividing numbers where either the numbers or decimals or their quotients are going to be decimals so now let's continue that we're going to do slightly more involved examples so let's say we want to figure out what 500 divided by 200 is divided by 200 pause this video and see if you can figure that out well one strategy for doing this is to just really Express this as a fraction and see if you can simplify this fraction in a way that it's straightforward to express it as a decimal so for example this is going to be the same thing this is equal to five hundred five hundred over two hundred and now we can simplify this we could say this is the same thing as five times 105 times 100 over two times 100 the reason why that is useful if you say hey look I have a hundred in the numerator I have 100 in the denominator 100 divided by 100 is just going to be one so you could just view this this is equal to five has five halves x times 100 over 100 times 100 over 100 which is just going to be equal to which is just going to be equal to one another way to think about it you could divide the numerator by 100 and you would have five and as long as you divide the denominator by the same thing you're not changing the value of the fraction so if you divide the denominator by 100 you're going to get two so anyway you think about it this could be simplified as five halves but we're not done yet that is that is what 500 divided by 200 is but can we express this as a decimal well we can rewrite five halves as a mixed number so five halves is going to be equal to well how many times was 2 going to five well it goes two times and then you have one half left over so this is going to be two and 1/2 and 1/2 and now how do we express this right over here as a decimal well you might recognize that 1/2 is the same thing as 5/10 so this is going to be equal to 2 and 5 over 10 which of course we can write as 2 point 5 or 2 and 5 tenths so 500 divided by 200 is 2 point 5 let's do another example let's say we wanted to figure out what 0.6 3 divided by divided by zero point zero 7 is pause this video and see if you can come up with a strategy for doing this well there's multiple ways to tackle it one way is real is to think about both of them in terms of hundreds so for example this is 63 hundredths under its and this right over here is seven hundred hundreds and so if you have 63 of something and you're dividing that by 700 what are you going to get well you're going to this if you took your seven hundredths and you multiply it by nine you're going to get 63 hundreds and so 63 of something divided by seven of that same something is going to be equal to nine this is going to be equal this is going to be equal to 9 7 times 9 is 63 so seven hundredths times nine is going to be 63 hundredths another way to think about it is we can express this as a fraction so in the numerator you have zero point six three and the denominator you have zero point zero seven and if the decimals are bothering us we can multiply both the numerator and the denominator by the same value to get rid of the decimals so let's multiply the numerator by 100 and also multiply the denominator by a hundred this doesn't change value of the expression because multiplying by 100 over 100 is just the same thing as multiplying by 1 so this would be equal to 63 hundredths times 100 well we would move the decimal two to the right this is going to be equal to 63 over seven hundredths times 100 once again we move the decimal two to the right this is going to be seven so 63 divided by seven once again that is going to be equal to that is going to be equal to nine