Adding Integers

Pre-Algebra · Axiom Academy

Adding two integers is a walk on the number line — each number is a jump, and where you land is the sum. 1. Same Signs — the Jumps Pile Up When the two integers share a sign, both jumps point the same way . They don't fight each other — they stack, end to end. Watch (-3)+(-4) : start at -3 , then take a second jump of 4 more to the left. Two leftward jumps, lengths 3 and 4, stack into one jump of 7 Add the two absolute values and keep the shared sign. The lengths add because the jumps go the same direction. 2. Different Signs — the Jumps Fight When the signs differ, the two jumps point in opposite directions , so part of one undoes part of the other. Watch (-6)+9 : jump 6 left, then 9 right. The first 6 of that rightward jump just walks back to where you started — only the leftover 3 counts. Six steps left, landing on -6 . Nine steps right — it crosses back over zero. The shared 6 steps undo each other; that's the subtraction. 9-6=3 steps of rightward jump remain, so the sum is +3 . 7+(-3) jumps 7 right then 3 back left, landing on 4 . And (-8)+5 jumps 8 left then only 5 back right — the leftward jump is longer, so you stop at -3 , on the negative side. 3. The Rule: Bigger Magnitude Wins For different signs, picture the two jumps as a tug-of-war from zero : one pulls right by its absolute value, the other pulls left by its absolute value. The longer pull drags the result onto its own side, by exactly the difference of the two lengths. Watch (-8)+5 settle it.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.