What is arithmetic? (We explain in simple words)
Remember your very first math lesson in first grade. You counted sticks, added cubes, and subtracted apples. This is arithmetic - the very first, ancient and basic step of the huge ladder called “Mathematics”.
To put it very simply, arithmetic is the science of numbers (natural numbers, integers, fractions) and what can be done with them. The name comes from the ancient Greek word arithmos, which is translated as “number”.
The four main pillars of arithmetic
This whole science rests on four basic actions. You do them every day when you go to the store or share pizza with friends.
| Action | What are we doing? | A simple example from life |
|---|---|---|
| ➕ Folding | Combine two piles of objects into one big one. | You have 100 rubles, your grandmother gave another 50. Total: 150 rubles. |
| ➖ Subtraction | We take away some of the items (look for the difference). | There were 10 candies, you ate 3. 7 candies left. |
| ✖️ Multiplication | This is a quick addition of identical numbers over and over again. | You bought 4 packs of juice for 50 rubles. 4 × 50 = 200 rubles. |
| ➗ Division | We distribute items equally to all participants. | We divide an 8-piece pizza among 4 friends. Everyone will receive 2 pieces. |
🔥 Strict prohibition: Why you can’t divide by zero?
Imagine you have 10 candies and you want to share them among zero people. You can't give candy to anyone, but it can't just disappear. In arithmetic, this action makes no sense, so mathematicians agreed: you cannot divide by zero!
Golden rules (laws) that simplify life
To count faster, there are three tricky rules in arithmetic. They sound a little scientific, but their essence is very simple:
- 🔄 Commutative law: “The sum does not change from changing the places of the terms.” It doesn’t matter whether you put 2 apples in the basket first, and then 3, or vice versa. There will always be 5 apples in the basket (2 + 3 = 3 + 2). This works for multiplication too!
- 🤝 Combination law: If you need to add three numbers, you can combine them into pairs whichever is more convenient. For example, (7 + 9) + 1 is more difficult to calculate in your head than 7 + (9 + 1).
- 🎁 Distributive law: Helps to multiply quickly. If 2 friends bought a burger (100 rubles) and a cola (50 rubles), we can calculate like this: 2 × (100 + 50). Or count burgers and cola separately: (2 × 100) + (2 × 50). The answer will be the same!
Where did arithmetic come from? (Brief History)
Arithmetic did not appear because someone wanted to torture children in schools. She appeared out of urgent need.
Ancient shepherds needed to know if all the sheep had returned to the fold. They took a bag of pebbles: they released one sheep and set aside one pebble. In the evening they drove the sheep back and took away the pebble. If the pebbles remain, it means the wolf ate the sheep.
Later, when people began to build cities and trade textiles and grain, counting on their fingers became inconvenient. The first computers appeared - the abacus. And then the ancient Indians and Arabs came up with those very convenient numbers from 0 to 9 that we still use today.
How is arithmetic different from algebra?
Many schoolchildren confuse these two concepts. It's very easy to remember the difference:
Arithmetic is the basis. It only works with specific numbers. You know for sure that you have 500 rubles, and a chocolate bar costs 100 rubles. Change will be 400 rubles. Everything is clear.
Algebra is the next level. Unknown letters (variables) appear in it. Imagine that the chocolate bar is in an opaque box. You don't know how much it costs. You write: 500 − X = change. Algebra teaches you to find these hidden numbers.