Start from zero — the basic math you need before everything else
Numbers can go below zero. You meet them every day: a temperature of −3 degrees, or owing someone £5 (a balance of −5). On the number line, negative numbers sit to the left of zero, mirror images of the positives.
Moving along the line is what matters here. Adding moves you to the right. Subtracting moves you to the left. The surprising one is subtracting a negative: it turns around and moves you right, so two minuses make a plus. And when you multiply, two negatives give a positive, while one negative gives a negative.
Picture a lift in a building with basement floors. Ground is zero, floors above are positive, basement levels are negative. Going up adds, going down subtracts. Cancelling a £5 debt is like removing a −5: taking away a negative leaves you better off, which is why subtracting a negative moves you up.
▶ Negative Numbers