Math Operations
For beginners learning arithmetic, it's important to understand the 4 important mathematical operations. So, what exactly does "math operation" mean?
Arithmetic involves both numbers and operations. The operations tell you how to manipulate these numbers. For example, addition tells us to add the values of two numbers together. For example, 6+4=10. 6 plus 4 equals 10, this is addition. Subtraction tells us to subtract one number from another. For example, 10-4=6. Subtracting 4 from 10 leaves us with 6.
Multiplication is repeating a number a certain number of times. It's essentially repeated addition. For example, 5x2=10 means combining two groups of 5 (5+5) to get a total of 10. In other words, 5x4=5+5+5+5=20, understand? Finally, division is dividing a number into several equal parts. For example, 20÷4=5, which means we divide 20 into 4 equal parts, each part being 5. For convenience, each operation has its own symbol, and some operations even have multiple symbols.
| Operation | Symbol(s) | Common Name |
| Addition | + | Plus sign |
| Subtraction | − | Minus sign |
| Multiplication | ×, ·, * | Times sign |
| Division | ÷, / | Division sign |
Results of Operations
The result of addition is called the "sum," the result of subtraction is called the "difference," the result of multiplication is called the "product," and the result of division is called the "quotient." Knowing the meaning of these terms will help you understand what others are asking. For example, "What is the product of 5 and 5?" 5x5=25, understand?
| Operation | Answer |
| Addition | Sum |
| Subtraction | Difference |
| Multiplication | Product |
| Division | Quotient |
Equality (=) and Inequality (≠)
As the name suggests, the equals sign indicates that two quantities are equal. 7+3=6+6, which is an equation. The inequality sign indicates that the left and right sides are not equal. For example, 5+5≠5+6, which is an inequality.
Properties of Arithmetic
1. Commutative Property
In addition and multiplication, you can swap the order of the numbers, and the result remains the same. For example, the result of 3+2 and 2+3 is both 5, and the result of 4x5 and 5x4 is both 20. When the order of the numbers in an operation can be interchanged and the result remains the same, the mathematical term for this is that the operation is "commutative," which is the commutative property.
2. Non-Commutative Operations
Subtraction and division do not satisfy the commutative property. If you swap the order of the numbers, the problem changes, and you will get different answers. For example, the answer to 6-2 is 4, while the answer to 2-6 is -4, which are completely different answers. Another example is 4÷2=2, while 2÷4=1/2, the latter being a fraction.
3. Inverse Operations
In mathematics, addition and subtraction are inverse operations. For example, 3+4=7, and you can get 3 by using 7-4.
Similarly, multiplication and division are also inverse operations. For example, 2x3=6, and conversely, 6÷3=2.
Multiplication Table
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |
Summary
The more you practice, the more you learn. During practice, you can use our free math solver tool to verify your answers. Thank you for reading our content. There are many more mathematical concepts, please read our other content.
