# Properties of Multiplication

Multiplication has some carefully defined rules called properties.  These properties dictate how numbers act within a multiplication equation.  Understanding these 5 properties of multiplication can help your child become more masterful at working with math equations.

## Commutative Property

The commutative property states that the two numbers in a multiplication problem can be written in any order without changing the product (answer).  Therefore, 6 x 9 = 54 and 9 x 6 = 54.  Even though you change the order of the two numbers being multiplied, your answer remains the same.

## Associative Property

The associate property simply tells us that you can change which numbers you group together in a multiplication problem. So the equation (7 x 2) x 5 is the same as 7 x (2 x 5).  Remember whatever is inside parentheses should be solved first.  The associative property lets us group numbers in a way that makes the multiplication easier to solve mentally.  It is tricky to solve the first equation in your head because you would be multiplying 14 x 5.  However, the second equation only asks you to solve 7 x 10.  This is much easier to figure out mentally.

## Identity Property

The identity property reminds us that multiplying any number times 1 results in the same number as an answer. Any number multiplied times 1 equals the same number.  While this seems simple and basic, it is an important concept for students to understand as they move into the older grades.

## Zero Property

The zero property tells us that any number times 0 will always equal 0.  It doesn’t matter what number you are working with, if you multiply it by 0, you will always get 0 as an answer.  A student who understands this can look at a problem like (4 x 5) x 0  and immediately know the answer is 0.

## Distributive Property

The distributive property allows us to break a large multiplication problem into two smaller problems which we then add together.  For example, 16 x 5 would be difficult for most children to solve mentally.  However, if we break 16 down into 8 + 8, we then get two separate multiplication problems – 8 x 5 and 8 x 5.  8 x 5 is a fact that many children have memorized.  Once your child has remembered that 8 x 5 is 40, it is easy for them to add 40 + 40 giving 80 as the answer.  We write that equation like this: 16 x 5 = (8 x 5) + (8 x 5).  While this property seems complicated, it actually makes large multiplication problems simpler for children to solve.

These 5 properties will help your children understand how multiplication works and how the numbers in a multiplication equation work together. You can help your child understand these properties by explaining them and practicing them with your child. Do you explain the properties of multiplication to your children when you teach multiplication?

Photo by:  Denis Mihailov 