Math Resources Hub

Adding & Subtracting Signed Numbers

Before a single coordinate, slope, or length calculation in geometry will go smoothly, one thing has to be automatic: adding and subtracting signed numbers. Not "I can work it out if I slow down" — automatic, the way you know 7+37 + 3. This card builds that fluency from the idea up, then drills it until it sticks.

Skill

Adding & Subtracting Signed Numbers

  1. What & why

    A signed number carries a direction as well as a size. Positive means one way, negative the other — and they're everywhere you'll look in this course:

    • A point at x=−3x = -3 sits three units left of the origin.
    • A line going downhill has a negative slope.
    • Cooling from 4°4° to −2°-2° is a drop you find by subtracting.

    Think of a number line. Every number is a spot on it; adding and subtracting just means moving along it — right for positive, left for negative. Get that picture solid and the rules stop being rules you memorize and start being things you can see.

  2. Watch how it works

    Adding a negative moves you left. Take 5+(−8)5 + (-8). Start at 55, then move 88 to the left. You pass 00 and keep going three more, landing on −3-3:

    5+(−8)=−35 + (-8) = -3

    −4−3−2−10123456−8start 5land −35 + (−8) = −3

    Subtracting a negative moves you right — it's the same as adding its opposite. Take −2−(−6)-2 - (-6). Subtracting −6-6 is adding 66, so start at −2-2 and move 66 to the right, landing on 44:

    −2−(−6)=−2+6=4-2 - (-6) = -2 + 6 = 4

    −3−2−1012345+6start −2land 4−2 − (−6) = 4

    Two moves, two directions. That's the whole game: a positive step goes right, a negative step goes left, and "subtract" flips the step's direction.

  3. Reason through one together

    Here's the case that trips everyone up at first — subtracting a negative. Picture the number line before you peek.

    Make a prediction: Start at 3. What is 3 − (−5)?

  4. Practice until it’s automatic

    Fresh problems, one at a time. Build a streak — the goal is getting them right without stopping to think.

    Streak0/ 5Accuracy0%(0/0)

    −3 − 2 = ?

  5. Prove it

    Harder, applied problems at the level you’ll meet on the Regents. Get them all right to earn this skill.

    Question 1 of 8

    Evaluate x − y when x = −4 and y = 7.

For teachers

Standard, common misconceptions, and suggested use will live here.