Proof: Sum of Multiples of 3 is Also a Multiple of 3

To prove that the sum of two multiples of 3 is also a multiple of 3, we'll use basic divisibility rules and integer properties.

Assumption: Let's assume 'm' and 'n' are both divisible by 3. This means we can express them as:

• m = 3p (where 'p' is an integer)* n = 3q (where 'q' is an integer)

Sum: Now, let's consider the sum 'm + n':

m + n = 3p + 3q

Factoring: We can factor out the common factor of 3:

m + n = 3(p + q)

Result: Since the sum of two integers (p + q) is also an integer, let's represent it as 'r':

m + n = 3r

This demonstrates that 'm + n' is a multiple of 3, as it can be expressed as 3 times an integer 'r'.

Conclusion: Therefore, we have proven that if 'm' and 'n' are both divisible by 3, their sum (m + n) is also divisible by 3.