Algebraic Proof

Represent general integers algebraically and transform expressions into forms that prove divisibility and parity claims.

Curriculum rangeYears 9–11

The sum of three consecutive integers is always a multiple of 3.

$n = 3, \; n+1 = 4, \; n+2 = 5$

$n + (n+1) + (n+2) = 3n + 3$

$3n + 3 = 3(n + 1)$

3(n + 1) is 3 times a whole number, so it's always a multiple of 3 -- whatever n is.

Check it for a chosen value of n

$3 + 4 + 5 = 12$

$3 \times 4 = 12$

This works for every whole number n -- that's what makes it a proof, not just an example.