REMAINDERS

[RobertoB400]

When reading the following problem I assumed that n = AB (A=tens digit, B=unit digit) and when n / 5 = ... ,A (A being the remainder). So from n/5 and n=3 (6 was going to be the remainder and tens digit of n). I don't get it:
What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.

[tim]

Your post contains two sentence fragments, so I can't tell what you're trying to ask. Can you rewrite, paying particular attention to the wording you're using?

[RonPurewal]

yeah, i don't really understand what you're asking, either.

in general, though, for remainder problems it's almost always easiest to just make a list of possibilities.
it's usually easy to come up with numbers that satisfy a given statement involving remainders. doing algebra with remainders, on the other hand, is often very difficult, and sometimes even impossible.

e.g., for statement 1, i can just make a list of all the numbers that do this:
11, 16, 22, 27, 33, 38, 44, 49
that's the whole list.

can you do the same thing for the other statement?

[RobertoB400]

Thanks Ron, your process engages with a similar process for statement 2. Statm 1 and 2 share then the factor 49 which makes C the correct answer.

Sorry for being previously unclear with my question. I do not understand why do we consider 13 divided by 5 = 2 with a remainder of 3. I thought that 5 fits twice in 13 and 3 being 6/10 of 5 would have given 2.6 as the result for that division.

Am I looking at things too theoretically or do I have a completely wrong idea of what remainder actually means? Is it perhaps just the left-over part of a number that can't be wholly divisible by another number such as 100 divided by 70 gives a remainder of 30?

I think I always considered remainder as the decimal part of a division and somehow always got away with it in high school...

[RonPurewal]

Thanks Ron, your process engages with a similar process for statement 2. Statm 1 and 2 share then the factor 49 which makes C the correct answer.

Sorry for being previously unclear with my question. I do not understand why do we consider 13 divided by 5 = 2 with a remainder of 3. I thought that 5 fits twice in 13 and 3 being 6/10 of 5 would have given 2.6 as the result for that division.

you have 13 apples. you want to put them into bags of 5.
• you can make 2 full bags
• you'll have 3 apples left over
... so the remainder is 3.

Is it perhaps just the left-over part of a number that can't be wholly divisible by another number such as 100 divided by 70 gives a remainder of 30?

yes.

[RonPurewal]

remember, "remainder" is something kids learn before they learn what fractions/decimals mean. so, it's a concept in terms of whole numbers. (when i personally think about remainders, i quite literally think about putting apples into bags.)

so, when you say 13/5 is ...
... 2.6
... 2 and 3/5
... 2 with a remainder of 3
... then, clearly, all the blue things are close cousins of one another.

I think I always considered remainder as the decimal part of a division and somehow always got away with it in high school...

that's probably because you don't use remainders in high school (well, not in the USA at least). you use fractions and decimals instead. (: