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Identity Property of Multiplication

What You Ought to Know About the Identity Property of Multiplication

The most simple feature of multiplication as a mathematical operation is the identity property. It is explained with examples, in the following post.
Omkar Phatak
Last Updated: Jan 28, 2019
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 multiplying numbers. Firstly, you need to make their connection with 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, as abstraction makes it less interesting for children. Let us look at the identity property, demonstrated by multiplication.
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, which children learn to count. The identity property 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 this 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, 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'.
Though this property seems and actually is quite trivial, it is necessary that it should be defined. To summarize, the property can be expressed as '1 multiplied by any number, gives back the same number'.