What are even and odd numbers? (We explain in candy)
Imagine that you have a bag of chocolates and you want to divide them equally between two friends. If you have 6 candies, everyone will get 3 and there will be nothing left in the bag. But if there are 7 candies, then everyone will receive 3, and one candy will remain “extra”.
In mathematics everything works exactly the same. All integers are divided into two large camps:
- ✅ Even numbers: These are obedient numbers that are divisible by 2 without remainder. They can be broken down into ideal pairs.
Examples: 2, 4, 6, 8, 10, 12... - ❌ Odd numbers: These are numbers that are not exactly divisible by 2. When dividing, there is always a “tail” in the form of a unit (residue 1).
Examples: 1, 3, 5, 7, 9, 11...
The main secret: how to check a huge number?
Imagine that in front of you is the number 5,834,971. How do you know if it is even or not? Do you really have to divide it by 2 in a column? Of course not!
There is a golden rule in mathematics: to determine the parity of any number, it is enough to look only at its very last digit.
| If the number ends with... | This means the whole number: | Examples of huge numbers |
|---|---|---|
| 0, 2, 4, 6 or 8 | Even | 132, 5000, 999998 |
| 1, 3, 5, 7 or 9 | Odd | 457, 1001, 888883 |
🔥 The most common question on the test: A zero (0) - what number is this?
Many people get confused and think that zero is a special number without parity. But the correct mathematical answer is: Zero is an even number!
Why? Let us remember the main rule: an even number must be divisible by 2 without a remainder. If we divide 0 by 2, we get 0 (no remainder). This means that zero fits perfectly into the team of even numbers.
What happens if you add and multiply them? (Rules)
If you are solving a long example, you can know in advance whether the answer will be odd or even, even without counting the exact numbers. There are simple rules for this:
- ➕ Even + Even = Even. (For example: 4 + 6 = 10)
- ➕ Odd + Odd = Even. Two “singles” always find each other and form a pair! (For example: 3 + 5 = 8)
- ➖ Even + Odd = Odd. If you add one “single” to even pairs, he will no longer get a pair. (For example: 4 + 3 = 7)
Where do we see this every day?
These properties of numbers are used everywhere in real life and modern technology:
- 🏠 Addresses on the streets: Pay attention to the numbering of houses. On one side of the street there are always even-numbered houses (2, 4, 6), and on the other side there are odd-numbered houses (1, 3, 5). This helps postmen find the right address faster.
- 🚂 Trains and tickets: If you buy a ticket for a reserved seat or a compartment, remember: odd seats (1, 3, 5) are always the bottom bunks, and even seats (2, 4, 6) - upper shelves.
- 🚗 Parking: In large cities, road signs often prohibit parking on “even” or “odd” days of the month so that snow removal equipment can clear different sides of the road.
- 💻 Sites and programs: When programmers create calculators or smart tables, they often color the rows one at a time: even rows are gray, odd rows are white. To do this, the computer constantly checks whether the line number is divisible by 2 without a remainder.