Class 8 Rules: Subtracting a Bigger Number ചെറിയതിൽ നിന്നു വലുത് കുറയ്ക്കൽ
In Class 8 the question "3 °C falls by 7 °C – what is the temperature?" gave us the sum 3 − 7 = −4: taking a bigger number from a smaller one gives a negative number. From many such examples came three rules, which the textbook repeats at the start of this chapter. This page explains each one with the number line.
- Negative numbers sit left of 0 on the number line; right means bigger.
- 3 and −3 are opposites.
1. 3 − 7: going below zero
x, y എന്ന ഏതു രണ്ട് അധിസംഖ്യകളെടുത്താലും – for any two positive numbers x and y:
(i) if x < y, then x − y = −(y − x) (ii) −x + y = y − x (iii) −x − y = −(x + y)2. Rule (i): x − y = −(y − x) when x < y
Starting at x and going y steps left, we pass 0 after x steps and go y − x steps further: we land at −(y − x).
3. Rule (ii): −x + y = y − x
Start at −x (x steps left of 0) and move y steps right. If y is bigger than x we end at y − x, right of 0; if smaller, we stop before 0, at −(x − y), which is again y − x by rule (i).
4. Rule (iii): −x − y = −(x + y)
Start at −x and go y more steps left: altogether x + y steps left of 0.
5. They work for fractions too
The chapter keeps returning to these three rules: every new meaning – adding a negative, subtracting a negative – is reduced to one of them.
You have ₹300 and must pay ₹500: 300 − 500 = −(500 − 300) = −200, a debt of ₹200. A diver 6 m below the surface (−6 m) climbs 8 m: −6 + 8 = 8 − 6 = 2 by rule (ii), so she ends 2 m above the water, on the diving board.
6. Check yourself
- x − y = −(y − x) if x < y: 6 − 8 = −2.
- −x + y = y − x: −6 + 8 = 2.
- −x − y = −(x + y): −6 − 8 = −14.