Adding Signed Numbers

Mental Math · Axiom Academy

Adding a negative is a move to the left. After that, two moves either pile up or fight — and that is the whole topic. 1. Adding a Negative Is a Move to the Left Two symbols are doing two different jobs here, and confusing them is what makes this look hard. In 8 + (-5) the plus sign is the instruction : make this move, starting from where you are. The minus attached to the 5 is the direction : leftward. Put together they say "from 8, go five steps to the left" — which drops you on 3, exactly where 8 - 5 drops you. One journey, two ways of writing it down. Each of these is a rightward start followed by a leftward move. Rewrite it as a plain subtraction and you already know how to finish: 2. Same Signs: The Moves Pile Up Now combine two moves that point the same way . Three steps left and then four more steps left is seven steps left — the second move does not interfere with the first, it extends it. So -3 + (-4) = -7 . The direction never changed; only the distance grew. The mirror image on the other side is the addition you have done since you were small: 3 + 4 = 7 . When both signs match, add the two sizes and keep the sign . Same direction, so the sizes add Read each one as a size and a side. In the first, 6 and 9 are both on the minus side, so the sizes add to 15 and the answer stays there. An account already 3 dollars overdrawn that takes another 4-dollar charge is the same sum: -3 + (-4) = -7 , now seven dollars overdrawn. 3. Different Signs: The Moves Fight

This is the written version of the interactive lesson above. See the full Mental Math course.