This lesson provides basic rules and concepts of arithmetic, the area of math that involves addition, subtraction, multiplication, and division. This lesson shares details about each operation and how they relate to one another in arithmetic.
What Is Arithmetic?
As fancy as the word sounds, arithmetic actually describes one of the most basic areas of mathematics. When you think about doing math, what usually pops into your head first? It's probably some form of adding or subtracting, maybe even division and multiplication. Well, guess what? All four of those mathematical functions make up arithmetic!
When performing addition, you take at least two numbers and add them together. You started with 1 apple and then you added 1 more? Oh, now you have 2 apples. You're standing alone and 3 friends join you? Oh, now there are 4 of you. By simply putting two numbers together, you are performing arithmetic.
There are certain rules, or properties, that go along with addition. The first is the commutative property. Basically, this tells us that 2 + 1 is the same as 1 + 2. The order you follow when adding numbers doesn't matter. Either way, the answer is 3.
If you add a third number, the grouping of the numbers to be added does not matter. In other words, (6 + 1) + 2 = (2 + 6) + 1 = (1 + 2) + 6 and so on. That is the associative property. You can think of it this way: it doesn't matter which pair(s) of numbers are associated with each other, the sum remains the same.
Another important property is the identity property. If you add 0 to any number, the number will remain the same. If someone gives you nothing, you're still you, right? It works the same with numbers:
6 + 0 = 6
3 + 0 = 3
As you can imagine, addition is a pretty big part of arithmetic.
Let's say you want to try subtraction instead, taking items away from a group. This is the inverse, or opposite, of addition, and it's a part of arithmetic, too. You see 2 people walk away from your group of 4? There are now 2 people left. Lost 1 of those 2 apples? Now, you're left with 1, and you've just completed more arithmetic.
It doesn't stop there, though. As previously mentioned, arithmetic also includes multiplication and division, two operations that many people find at least a little more difficult than addition and subtraction.
In multiplication, you're basically counting groups instead of individual numbers. What exactly does that mean? Let's say you need to figure out 3 multiplied by 5, or 3 times 5. This is like having 3 groups with 5 people in each group. If you counted these people one by one, you would find that you have 15 total. Multiplication allows us to count differently, adding the number 5 to itself 3 times, as follows:
5 + 5 + 5 = 15
Looking at it this way, you see that 3 fives gives you 15. Interestingly, 5 times 3 is the same as 3 times 5, like this:
3 + 3 + 3 + 3 + 3 = 15
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Based on these calculations, you may have noticed that the commutative and associative properties also apply to multiplication. Arithmetic at its best!
So, how about division? Well, it's kind of like multiplication in reverse, so it is often considered to be the inverse of multiplication. Instead of adding multiple groups, you're basically seeing what happens when you break a number into smaller groups.
Let's say you need to divide 13 bags of candy among 4 children. Who gets what? Well, if you start to pass the candy out 1 piece at a time, you will find that after every child has 3 pieces of candy, there is one piece of candy left over. There is not enough to give every child a fourth piece. So, that means that 13 divided by 4 is 3, with a remainder of 1 left over. In other words, the number 4 goes into the number 13 evenly 3 times, with a remainder of 1.
Dividing numbers can also leave you with fractions, or pieces of a whole. Suppose you have one cake and want to divide it between 4 people. If you cut it evenly, you'll have 4 pieces of cake, each equaling 1/4, or one quarter, of the cake. That's division.
These operations form the basics of arithmetic. Once you have mastered working with numbers using these operations, you'll find it easier to apply the concepts in many different ways, including working with negative numbers, decimals, and even more fractions. You'll also find it easier to understand additional properties and how they apply to addition, subtraction, multiplication, and division.
While the basics of arithmetic can seem difficult, practice makes perfect. By knowing how to add, subtract, multiply, and divide numbers, you're preparing for many other levels of mathematics and more advanced problem-solving. The commutative, associative and identity properties apply to functions in arithmetic and dictate how numbers relate to one another consistently.
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