Real-World Applications പ്രയോഗങ്ങൾ
Negative numbers are everywhere something can go two ways from a starting point: warmer or colder, credit or debt, up or down, ahead or behind. On every lab below, a slider sets the numbers and the page shows the sum, difference or product with its sign – exactly the rules of this chapter.
1. Temperatures: Leh, Munnar and the freezer
In winter Leh in Ladakh can drop to −15 °C at night, and a home freezer runs at about −18 °C. A temperature that rises is a positive change; one that falls is a negative change.
In the exam this looks like: "The temperature at night was −8 °C; by noon it rose by 15 °C. Find the noon temperature." → −8 + 15 = 7 °C.
2. Bank balance and overdraft
Money in the account is positive; money owed to the bank (an overdraft) is negative. A payment is a negative change.
In the exam this looks like: "A balance of ₹1200 pays bills of ₹1500 and then gets ₹600. Final balance?" → 1200 + (−1500) + 600 = 300.
3. Lifts and basements
Ground floor is 0, basements are −1, −2, −3. Going down is a negative move.
In the exam this looks like: "A lift goes from floor −2 to floor 6. How many floors did it rise?" → 6 − (−2) = 8.
4. Above and below sea level
Heights are measured from sea level (0 m). Kuttanad in Kerala is one of the few places in the world where farming happens below sea level, around −2 m. The shore of the Dead Sea is about −430 m and the top of Everest +8849 m.
In the exam this looks like: "A diver at −25 m rises to a boat 3 m above sea level. How far did she rise?" → 3 − (−25) = 28 m.
5. Goal difference
League tables rank teams with equal points by goal difference, which is often negative.
In the exam this looks like: "A team's goal difference is −4 and it has scored 9. How many goals did it concede?" → 9 − x = −4, x = 13.
6. Profit and loss
In the exam this looks like: "Profits of ₹5000 and ₹3000 and a loss of ₹9000. Net result?" → 5000 + 3000 + (−9000) = −1000, a loss of ₹1000.
7. Time zones
Clocks around the world are set as offsets from London time (UTC): India is UTC +5:30, Tokyo +9, New York −5 (in winter).
Difference of clocks = offset of one city − offset of the other: India − New York = 5.5 − (−5) = 10.5 hours.
In the exam this looks like: "City A is UTC +3, city B is UTC −4. How many hours ahead is A?" → 3 − (−4) = 7.
8. Golf scores
Each hole's score is strokes − par: below par is negative (good!), above par positive. The round's score is their sum.
In the exam this looks like: "A golfer scores −2, +1, 0 and −1 on four holes. Total?" → −2 + 1 + 0 + (−1) = −2.
9. A ball thrown up: one equation for the whole flight
The textbook's side box (page 139): a ball thrown up at 49 m/s loses 9.8 m/s each second, stops at 5 s and then falls faster and faster. With upward speed positive and downward negative, one equation works: v = 49 − 9.8t.
In the exam this looks like: "Using v = 49 − 9.8t, find v at t = 8 and say what the sign means." → v = −29.4: falling at 29.4 m/s.
10. Fortunes and debts: a little history
In 628 CE the Indian mathematician Brahmagupta wrote down rules for "fortunes" (positive numbers) and "debts" (negative numbers): a debt minus zero is a debt; a fortune minus a debt is a fortune added; the product of two debts is a fortune. These are exactly the rules of this chapter – written 1400 years ago, centuries before negative numbers were accepted in Europe.
11. Try these word problems
- Pick a zero and a positive direction; then every quantity is a signed number.
- Final = start + change; change = final − start, even when they are negative.
- Signs in a product follow the sign table; one equation then covers every case.
Next: Summary and quick quiz ▶