Identity Property of Multiplication

If I ask you to name four things that every one interested in mathematics should learn, what would they be? Undoubtedly it would be the ability to add, subtract, multiply and divide numbers. Without these basic math skills, you would be totally lost, when it comes to accounting for your day-to-day expenses. While addition and subtraction are perhaps the easiest to grasp, division and multiplication take some time to be understood.

One of the toughest tasks for a math teacher is to teach multiplication. The symbolism of mathematics takes some time to be completely understood and children need to be clearly explained what they actually do when they multiply numbers. Firstly, you need to make the connection between numbers as actual qualities of things.

Children find it difficult to manipulate numbers as symbols, but if you can make the connection between numbers and objects, they find it easier to comprehend. It is essential to maintain the connection between mathematics and reality and abstraction makes it less interesting for children.

Definition

Of all the natural numbers, the only number which is quite different from the rest is '1'; also called numero uno, it is the first number children learn to count. The identity property of multiplication is concerned with the multiplication of a number by 1. Here is the property, stated in the simplest form:

"The product of any number and 1 is the same number."

In terms of equations, for a variable or number 'a', this property can be expressed as follows:

a x 1 = a

This property seems quite obvious if you try to interpret it in simpler terms. When you multiply two numbers, you count how much the first number times the second number would be. That is, in the above example, 'a' times 1, would be 1 counted 'a' times, which would give you 'a' again. Let me provide some examples of this property in the next section.

Examples

Understanding an actual worked out example is the best way to learn math. Here are some examples of identity property of addition, which will clarify the concept:

• m x 1 = m
• 1 x 2/5 = 2/5
• 56 x 6 x 1 = 56 x 6
• 43.99 X 1 = 43.99
• (2 + 5) x 1 = (2 + 5)
• 1000000 x 1 = 1000000

Thus, in a way, when any number is multiplied by 1, the product is reflected as the value of the same number. In this sense, in case of multiplication, the number 1 is the 'Identity Element'.

To put the property in simplest of words, the number 'one' multiplying any other number gives the same number as the product. Though this property seems and actually is quite trivial, it is necessary that it should be defined. As an exercise, compare the identity property of addition with the identity property related to multiplication and note the differences between the two. To summarize, the property can be expressed as '1 multiplied by any number, gives back the same number'.