Remainders: Part-1
When a particular number is divided by any another number(divisor) we get quotient and remainder.
For example: On dividing 9 with 4 we get 2 as the quotient and 1 as the remainder. Here 9 is dividend and 4 is divisor.

Tool tip:The value of the remainder is always less than the divisor.
Find the remainder when 39 is divided by6 ?
We can write 39 = 6(6) + 3. Here quotient is 6 and 3 is remainder. Note that remainder 3 is less than divisor 6.

Find the remainder when 79 is divided by11 ?
We can write 79 = 11(7) + 2. Here quotient is 7 and 2 is remainder. Note that remainder 2 is less than divisor 7.

If divisor is same then it hardly creates any difference whether we add numbers and then divide by divisor to calculate remainder or we separately calculate remainders and then add.

Let’s understand first of all whether we deal numbers separately while calculating remainders or we deal together it doesn’t create any difference. Lets understand meaning of above with help of example

Suppose we have 53 sticks in a bundle and we are told to divide it in groups of 5. So we all know that while dividing 53 in groups of 5, three sticks will be left.

Let’s consider another bundle of 21 sticks and we are told to divide it in groups of 5. So we all know that while dividing 21 in groups of 5, one stick will be left.
Now if we add the above two bundles we have total of 53 + 21=74 and again divide it in groups of 5
Then we will be left with 4 sticks.

Hence instead of mixing we can treat them by two groups as well and we can make groups of 5 separately and total numbers of remaining sticks are simply 4(3+1)i.e. addition of remaining sticks in the two groups separately.
Since 4 is lesser than 5 we cannot make another group of 5 from remaining sticks

But if instead of 21 sticks we had 22 sticks then the remainder would be 2 and the total remaining sticks would have been 5, and then we can make a new group of 5 with the remaining sticks with no remnant left.

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