Properties of Multiplication

Multiplication is used when we have to multiply two or more numbers to find the product. Let us learn more about multiplication in this article. If there are 4 packets of ice cream and each box has 6 ice creams, find the total number of ice creams.
Solution: We can solve this question by adding 6 + 6 + 6 + 6 = 24. But it takes a lot of time and effort, so we solve it as 6 × 4 = 24. In other words, multiplication is the repeated addition of numbers.
 

Commutative Property: This property states that when we multiply two numbers, changing their order doesn't affect the product. Multiplying 3 rows by 4 columns or 4 columns by 3 rows gives the same result:
3 × 4 = 4 × 3 = 12.

Associative Property: This property tells us that if we multiply three or more numbers one after the other, the grouping of the numbers doesn't have an impact on the outcome of the product. For example, let us take 2, 4, and 3.
If we multiply them in the same order, we get: (2 × 4) × 3 = 24(2 × 4) × 3 = 24.
If we rearrange the order and multiply: 3 × (2 × 4) = 24 
(2 × 4) = 8, then 8 × 3 = 24

Distributive Property: According to this property, if we multiply a number by a sum, the result will be equal to another expression where we multiply the same number by each addend separately and then add the products. Let's see this with an example:

First multiply 2 × 4 = 8, then 2 × 2 = 4, finally add 8 + 4 = 12.
2 × (4 + 2) = (2 × 4) + (2 × 2) = 8 + 4 = 12

Properties of multiplication are often applied to practical calculations in everyday life. Some of them are listed below:

• When you're shopping, the order in which you multiply the number of items and the price doesn’t matter. For example, if you buy 3 notebooks for ₹50 each = ₹150. Its reverse, i.e., 50 notebooks for ₹3 each = ₹150. The total cost will be the same!

• When organizing a group of people into smaller teams, how you group them doesn’t change the total number of people. For example, if you have 2 groups of 3 people, and each group is made of 4 smaller teams, you can multiply in any order (2 × 3 × 4 = 24) to find the total number of people.

• When calculating a total cost, you can break it down into parts to make it easier. For example, if a shirt costs ₹200 and pants cost ₹300, you can use the distributive property to find the total cost for 2 sets of clothes:
  2 × (200 + 300) = (2 × 200) + (2 × 300) = ₹400 + ₹600 = ₹1000.

• Multiplying any number by 1 leaves it unchanged. For example, if you’re copying 1 document 5 times, the total number of copies is still just 5 (1 × 5 = 5). It helps in counting or keeping the original quantity unchanged.

• Multiplying any number by 0 gives 0. For example, if there are 0 apples, and you want to multiply them by 5 (0 × 5), you’ll still have 0 apples — nothing changes.