When you add a number that has a remainder of 1 when it is divided by 3 to a number that has a remainder of 2 when it is divided by 3 then what is the remainder of the sum when you divide it by 3?

When you add a number that has a remainder of 1 when it is divided by 3 to a number that has a remainder of 2 when it is divided by 3 then what is the remainder of the sum when you divide it by 3?
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The remainder is 0.If A has a remainder of 1 when divided by 3, then A = 3m + 1 for some integer mIf B has a remainder of 2 when divided by 3, then B = 3n + 1 for some integer n→ A + B = (3m + 1) + (3n + 2)= 3m + 3n + 1 + 2= 3m + 3n + 3= 3(m + n + 1)= 3k where k = m + n + 1 and is an integer→ A + B = 3k + 0→ remainder when A + B divided by 3 is 0-------------------------------------------------------------------------From this, you may be able to see that:if A when divided by C has remainder Ra; andif B when divided by C has remainder Rb; then(A + B) divided by C will have remainder equal to the remainder of (Ra + Rb) divided by C
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