Basic division confusion.

[finite echo]

Hey guys i have a question. Why are these two different ? I watched a video about division and when i typed it on the calculator another number popped up. Im not the best at division but Im trying to improve and actually understand it.

[strange cairn]

It's not different. The video shows a remainder, the calculator shows a decimal.

But 3/6 = 0.5.

[gray wasp]

Yeah schools tend to teach remainders first then they will eventually convert them into decimals/fractions in the decimal places.

[strange cairn]

And in my opinion they're not great at the remainders either.

[gilded forge]

okay so a kinda cool way to think about this would be to use fractions. now i love fractions because theyre super useful in learning how to divide without a calculator.

when you divide 57 by 6, its the same as the fraction 57/6. you would then think: "what is the biggest number you can divide by 6 (aka being a multiple of 6) that goes into (goes into meaning the biggest number you can subtract from the number youre dividing by that wont turn you into a negative) 57?? obviously its 54 because 57-54 is 3 and 57-60 (the next biggest multiple) would be a negative. so now you can rewrite your fractions as 54/6+3/6, and then you can simplify 54/6 to be 9 by taking out 6 (dividing both numbers by 6 and simplifying). now youre probably seeing how this is the exact same process as doing long division, but now we can actually use and conceptualize our remainder. so when you simplify 3/6ths by taking out your factor of 3, youre left with 9 and a half. so 9.5!!! this is exactly why i love using fractions to help with long division because its so intuitive and a great way to conceptualize remainders in your actual answer when learning about long division.

now, as you move along and get better with long division, you can skip straight to dividing your remainder by your divisor. so if you skipped straight to dividing it, you would get 9 and 3/6ths, which would be 9 and a half, so 9.5!!!

i guess its easier to always skip straight to diving your remainder by the divisor, but i just thought id share a cool little thought excersize to show why it works!! ^_^

sorry for the long message.... and sorry if its confusing....

[rose spindle]

you have done it wrong when we divide it we get 9.5 as 9 times 6 = 54 leaving remainder 3 then after putting decimal we can add 0 that is 30 and 5 times 6 = 30 so 9.5

not 9.3

[wintry trench]

Think of it like this:

How many 6s can I fit in 57?

With 1 six you have 51 left, 5 sixes you have 27 left, 9 sixes you have 3 left (since 6×9 = 54 and 57−54 = 3)

Can you fit a 6 inside a 3?

You cannot, so we say that 3 is the remainder and that 9 is the quotient.

Think of it as a subtraction of the number 6 from the original number n times until what is left ("remainder") is less than the divisor.

57 can be written as:

57 = 6×9 + 3
Where 6 is the divisor, 9 is the quotient, and 3 is THE remainder (Euclidean division only has ONE remainder that we call THE remainder; modulo has an infinite set of remainders).

holy

i just realized this is pretty old