To find the remainder of a sum when divided by a number, you can find the remainder of each term in the sum individually, add those remainders together, and then find the remainder of that sum when divided by the original number.
Here's a breakdown:
-
Understand Remainders: A remainder is what's left over after division. According to the provided reference, if you divide a number N by a number D, you get a quotient Q and a remainder R, represented as N = Q x D + R.
-
Individual Remainders: Find the remainder of each number in the sum when divided by the divisor.
-
Sum the Remainders: Add up all the individual remainders you found in the previous step.
-
Final Remainder: Divide the sum of the remainders by the original divisor. The remainder you get from this division is the remainder of the original sum.
Example
Let's say we want to find the remainder when (17 + 25 + 31) is divided by 5.
-
Individual Remainders:
- 17 divided by 5 has a remainder of 2.
- 25 divided by 5 has a remainder of 0.
- 31 divided by 5 has a remainder of 1.
-
Sum the Remainders: 2 + 0 + 1 = 3
-
Final Remainder: 3 divided by 5 has a remainder of 3.
Therefore, the remainder when (17 + 25 + 31) is divided by 5 is 3.
In Summary
This method works because the remainder represents the "excess" beyond multiples of the divisor. Adding the excesses (remainders) and then finding the remainder again essentially accounts for any further multiples of the divisor that might appear when the remainders are combined.
