Why the Number Line Left of 0 Makes Negative Numbers | Think Math · G7 · Integers & Rationals ①

What's 3 minus 5? With counting numbers there's no answer. When you need a number below zero — freezing temperatures, debt, below sea level — you extend the number line to the left of 0 to make negatives.

Right is the direction of getting bigger, holding 1, 2, 3. The opposite, the left, is where numbers under 0 live. Fold +2 across 0 and it lands on -2 — a negative is a positive flipped across zero, its mirror image.

So -3 is three steps the opposite way from 0. Like 3 below zero, 3 floors down, 3,000 in debt — same size, opposite direction. The minus sign simply means 'the other way'.

Count down from 3: 3, 2, 1, 0, -1, -2 — five less than 3 now has a home on the line: -2. (Exactly why 'going left' means 'subtracting' comes in the operations episode.)

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