Examples with explanation of the properties of multiplication of integers
along with a small story to make it engaging. Lets dive into it.

1)Closure Property:

❖ Imagine a magical kingdom where every number has a home inside a big
fortress called “Integers”.
❖ If two residents (integers) join fortress (multiply) and their result (the
product) also become a resident of the same fortress!
Property: The product of two integers is always an integer.
Example: 3* (-4) = -12

2)Commutative Property:

❖ Two friends, Alex and Benny decide to paint a house. Alex paints first,
then Benny paints, and the house gets painted.
❖ If Benny starts and Alex follows, the result is still the same – a painted
house!
Property: The order of multiplying two integers doesn’t matter.
(ab = ba)
Example: (-3) * 5 = 5 * (-3) = -15

3)Associative Property:

❖ Three siblings, Ray, Mia and Sam build a tower using blocks.
❖ Ray and Mia first stack their blocks and then Sam adds his, or Sam and
Mia stack their first and Ray adds his.
❖ Either way, the tower height is the same!
Property: When multiplying three integers, the grouping doesn’t affect
the result. (a*b) *c = a * (bc) Example: (23) *4 = 2 * (3*4) = 24

4)Multiplicative Identity:

❖ Think of number 1 as a magic mirror. When any number looks into the
mirror, it stays exactly as it is.
❖ No changes, No surprises!
Property: Any integer multiplied by 1 remains the same. (a1 = 1a = a)
Example: 51 = 5 and 1 (-7) = -7

5)Distributive Property:

❖ A farmer has 3 baskets of fruits. Each baskets have apples and oranges.
❖ To count the fruits, the farmer could either count all the apples and
oranges together in each basket (combine, then multiply).
❖ Another way to count the apples first, then oranges and add them up.
❖ Both ways work perfectly
Property: Multiplication distributes over addition or subtraction.
a* (b + c) = (ab) + (ac)
Example: 3* (4 + 5) = (34) + (35) = 27

6)Multiplication by Zero:

❖ Imagine 0 is a magical number, if any integer multiply by 0, it always
remains 0.
Property: Any integer multiplied by 0, remains 0. (a0 = 0a = 0)
Example: 3*0 = 0 and 0 * (-5) = 0