What are negative numbers?
Imagine that you decide to buy a new game or phone. It costs 10 thousand rubles, but you only have 7 thousand in your piggy bank. You ask a friend to lend you the missing 3 thousand. You buy a phone, but now you don’t just have “zero” money. You are in debt!
Your financial balance is now −3 thousand. This debt, this lack of something, in mathematics is called a negative number.
Where do these numbers live? (Coordinate line)
To avoid confusion, mathematicians have come up with an excellent cheat sheet - the coordinate line. Imagine a long ruler.
- 🛑 Zero (0) is the center. This is the border between plus and minus.
- ➡️ To the right of zero there are ordinary (positive) numbers: 1, 2, 3, 100. These are our real apples, money and warmth.
- ⬅️ To the left of zero there are negative numbers: −1, −2, −3, −100. These are our debts and frost.
The main trap: how to compare them?
Almost all newbies make mistakes here! We are used to the idea that 100 is greater than 5. But in the world of negative numbers, everything works the other way around.
The number −5 is GREATER than the number −100!
How is this easy to understand? Remember winter. Temperature -5 degrees is a slight chill, you can build a snowman. But -100 degrees is a terrible cosmic frost, it’s much colder there. This means there is more heat at −5. Or remember money: a debt of 5 rubles is much better (and closer to wealth) than a huge debt of 100 rubles.
Rules of mathematics: how to calculate them?
When you type a complex example into an online calculator, it spits out the answer in a split second. But in order to solve such problems in a notebook, you need to remember a few simple rules. Let's look at them with examples.
| Action | Rule (how to remember) | Example |
|---|---|---|
| Addition of two minuses | Debt plus debt = big debt. We add up the numbers themselves, and put a minus in the answer. | (−3) + (−4) = −7 |
| Plus and minus together | Whoever is stronger wins! We subtract the smaller from the larger and put the sign of the number that was larger. | (−10) + 15 = 5 (There were more pluses) |
| Multiplication: Minus by Minus | The magic of mathematics: two minuses when multiplying or dividing always turn into a PLUS! | (−5) × (−2) = 10 |
| Multiplication: Plus by Minus | If the signs are different (one is a minus, the other is a plus), then the MINUS always wins in the answer. | 4 × (−3) = −12 |
🔥 Interesting fact: When did people come up with numbers with minus?
For a very long time people did not want to believe in negative numbers! The ancient Greeks and Egyptians did not understand them at all. They first began to be actively used in Ancient China about 2000 years ago. Chinese mathematicians wrote positive numbers in red ink (these were profits) and negative numbers in black (these were debts).
Where do we meet them every day?
You might think this is just a boring school topic, but in fact we see these numbers all the time:
- ❄️ Weather forecast: In winter, we always look at how much the temperature has dropped below zero (for example, −20°C).
- 🏢 Underground parking: When you take the elevator down in a shopping center, the buttons say −1 or −2 floor.
- 📉 Discounts in the store: Price tags often say −50%. This means that the price has become lower.
- 📊 Server load and finance: Programmers use negative values to show a loss on charts or a drop in system performance.