We have learned to perform basic math operations like addition, subtraction, multiplication, and division. We can simpli fy these operations by keeping in mind some special properties of numbers. Learn the properties of numbers that will help you evaluate expressions quickly with the help of some examples. . Read More Read Less
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Number properties lay down some rules that we can follow while performing mathematical operations.
There are four number properties: commutative property, associative property, distributive property and identity property. Number properties are only associated with algebraic operations that are addition, subtraction, multiplication and division. However, some of these properties are not applicable to subtraction and division operations.
The word commute means “to travel back and forth”. If a number is commutative, that means it is movable. The commutative property states that changing the order of addends or factors does not change the sum or the product.
Let’s see how this is applicable to the numbers in an expression.
Consider the expression 3 + 5 .
We know that 3 + 5 = 8 . But 5 + 3 is also equal to 8 .
When two numbers are added together, the sum remains the same even if we change the order in which the addition operation is performed. That means the expression gives us the same result even if the position of the numbers change. This is known as the commutative property of addition.
Just like we saw in addition, the commutative property is also applicable to multiplication.
For example, \(3 \times 5 = 15\)
And \(5 \times 3 = 15\) .
So, when two numbers are multiplied together, the product of the two numbers remain the same irrespective of the order in which they are multiplied. This is known as the commutative property of multiplication.
Some math expressions with more than two terms can be solved easily by grouping the terms in the expression. To “associate” numbers means to group numbers. The associative property states that changing the grouping of addends or factors does not change the sum or the product.
Let’s see how associative property can be used in addition. Consider the following equation:
Whenever we perform this addition in our mind, we usually add two numbers first and then add the third number to the sum of the first two numbers. We can perform this addition in two ways.
5 + (7 + 6) = 5 + 13 = 18
And (5 + 7) + 6 = 12 + 6 = 18
In both cases, the answer remains the same.
So, when three numbers are added, the sum remains the same irrespective of the way in which they were grouped. This is known as the associative property of addition.
Let’s try out associative property in the case of multiplication.
\(1 \times 2 \times 3 = 6\)
We can perform this multiplication in two ways.
\(1 \times (2 \times 3) = 6\)
And \((1 \times 2) \times 3 = 6\)
When three or more numbers are multiplied, the product remains the same irrespective of the way in which the numbers were grouped. This is known as the associative property of multiplication.
