Multiplication is a basic math process that is used to show repeated addition or to figure out how many things are in a group or an array as a whole. But did you know What are the Five Properties of Multiplication and that there are five important things about multiplication that make it a unique and powerful tool?
If you know about these things, you can solve problems more quickly and with more confidence. This post will look at the five properties of multiplication and show how they can be used to make hard numbers easier. This overview of the basics of multiplication will give you a good place to start learning more, whether you are a student, a teacher, or just interested in math.
What are the Properties of Multiplication?
In math, there are five main things to know about multiplying. Here are the things:
- Commutative Property: This property says that the order of the factors has no effect on the product. In other words, the effect of multiplying two integers is the same no matter what order they are multiplied in. For instance, 2 x 3 means 3 x 2.
- Associative Property: This trait says that the way the parts are put together has no effect on the result. In other words, if you multiply three or more numbers, the answer is always the same no matter how you group them. For example, (2 x 3) x 4 means 2 x (3 x 4).
- Distributive Property: This property says that when a number is multiplied by the sum (or difference) of numbers, the multiplication can be spread out over each term in the sum (or difference). 2 x (3 plus 4) is equal to (2 x 3) + (2 x 4).
- Identity Property: This means that if you multiply any number by 1, you get the same number back. In other words, the identity factor for multiplication is the number 1. For instance, 2 x 1 equals 2.
- Zero Property: This trait says that if you multiply any number by 0, the result is 0. In other words, 0 is the way to stop multiplying. For instance, 2 x 0 equals 0.
|Property Name||Property Statement||Example|
|Commutative Property||The order of factors does not affect the product||2 x 3 = 3 x 2|
|Associative Property||The grouping of factors does not affect the product||(2 x 3) x 4 = 2 x (3 x 4)|
|Distributive Property||Multiplication can be distributed over addition or subtraction||2 x (3 + 4) = (2 x 3) + (2 x 4)|
|Identity Property||Multiplying any number by 1 gives the same number||2 x 1 = 2|
|Zero Property||Multiplying any number by 0 gives 0||2 x 0 = 0|
These five rules about multiplication are important because they let us change and improve multiplication formulas, which makes it easier to solve math problems.
The commutative feature of multiplication is often taught with the help of arrays or other visual models. Both arrays have 6 squares in total, so an array with 2 rows and 3 columns can be used to show that 2 x 3 is the same as 3 x 2. This feature is very helpful when dealing with larger multiplication problems because it lets you change the order of the parts to make the calculation easier or faster. It also helps with math because you can use this trait to make multiplication problems easier in your head.
Parentheses or other grouping marks are often used to show that multiplication is about putting things together. For example, (2 x 3) x 4 can be reduced by first multiplying 2 x 3 and then multiplying the result by 4, or by first multiplying 3 x 4 and then multiplying the result by 2. When working with bigger multiplication problems, this feature is very helpful because it lets you group factors to make the process easier or faster. It’s also good for mental math, since you can use this trait to order things in your head so they’re easy to multiply.
The distributive feature of multiplication is often shown with the distributive law, which says that (a x b) + (a x c) = (a x b) + (a x c). For example, 2 x (3 + 4) can be shortened to (2 x 3) + (2 x 4) by dividing the sum by two. This trait is especially helpful when solving math problems that involve adding or taking away. It helps you break the problem up into smaller, easier-to-handle pieces. It is also useful in math because it makes formulas that use multiplication, addition, or subtraction easier to understand.
The similarity principle of multiplication is often shown with the help of a multiplication table or another visual tool. For example, the multiplication table shows that every number times 1 gives the same number. When solving multiplication problems that require multiplying by one, this trait is very helpful because it lets you simplify the math by just writing down the original number. It is also useful in mathematics because it makes expressions that involve multiplying by one easier to understand.
When teaching the zero feature of multiplication, people often use the multiplication table or other models that can be seen. For example, the multiplication table shows that every number times 0 equals 0. This is especially helpful when you have to solve a multiplication problem that involves multiplying by zero, because you can simplify the equation by just writing down 0. It is also useful in math because it makes multiplication by 0 easier to understand. But remember that dividing by zero gives an undefined result, so this feature does not apply to division.