Properties of Whole Numbers
5 Minutes
Properties of whole numbers for students, covering commutative, associative, distributive, and identity rules. A short maths lesson in English.
- Commutative and associative rules using egg boxes and cake
- Commutative and associative addition shown with ice creams
- Distributive and identity properties using mental math and bills
What this lesson teaches
Properties of whole numbers are mathematical rules that describe how numbers behave during operations like addition and multiplication. These rules show when numbers can be rearranged or regrouped to make calculations easier, and when strict order must be maintained.
Commutative and associative properties
- The commutative property states that changing the order of two numbers does not change the result in addition (4 + 2 = 2 + 4) or multiplication (3 × 4 = 4 × 3).
- The associative property states that grouping numbers differently when calculating three values does not change the final sum or product, such as finding cake volume by multiplying length, breadth, and height in any order.
- Neither rule applies to subtraction or division, because operations like 4 minus 2 and 24 divided by 12 cannot be reversed without altering the result.
Distributive property
- The distributive property allows difficult multiplication problems to be broken down into easier addition or subtraction steps.
- To calculate 25 × 98, the number 98 can be rewritten as 100 minus 2, making the problem (25 × 100) minus (25 × 2), which equals 2,450.
- To calculate 25 × 102, the number 102 can be split into 100 plus 2, making the sum (25 × 100) plus (25 × 2), which equals 2,550.
Identity properties
- The additive identity is zero, because adding zero to any whole number leaves the value unchanged, just like adding zero tax to a bill.
- The multiplicative identity is one, because multiplying any whole number by one gives the exact same number, seen when buying a quantity of one in a supermarket.
- These identity elements preserve the original value of any number they operate on.
Why order matters
- Addition and multiplication are flexible operations where numbers can be added or multiplied in any order without changing the outcome.
- Subtraction and division must always follow a strict order, because changing the position of the numbers changes the entire answer.
- Understanding these properties allows people to solve everyday arithmetic and test problems quickly through mental maths.