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Properties of Multiplication

1. Numbers can be multiplied in any order; the product will remain the same.
For example: 254 × 6 = 6 × 254 = 1524

2. When a number is multiplied by 1, the product is the number itself.
For example: 524 × 1 = 524 and 368 × 1 = 368

3. When a number is multiplied by 0, the product is always 0.
For example: 293 × 0 = 0 and 643 × 0 = 0

4. The product of three numbers does not change when the grouping of the
numbers is changed.
For example: (16 × 12) × 15 = (16 × 15) × 12 = (12 × 15) × 16 = 2880 (Associative
property)

5. If the sum or difference of two numbers is multiplied by another number, then
the two numbers can be multiplied separately and then added or subtracted.
For example: (12 + 5) × 10 = 17 × 10 = 170

or (12 + 5) × 10 = (12 × 10) + (5 × 10) (Distributive property)
= 120 + 50 = 170

and (12 – 5) × 10 = 7 × 10 = 70
or (12 – 5) × 10 = (12 × 10) – (5 × 10) = 120 – 50 = 70

Multiplication of Large Numbers

Large numbers are multiplied in the same way as smaller numbers. Just follow these
steps.
Step 1. Start multiplication from the ones place.

Step 2. Move to the tens place, hundreds place and so on.

Step 3. Do not forget to add the number carried over, if any.
Example 1. Multiply 3647 by 6.
Solution.

Method 1. Column method Method 2. Expanded form method

TTh Th H T O 3647 × 6

3 2 4 = (3000 + 600 + 40 + 7) × 6

3 6 4 7 = 3000 × 6 + 600 × 6 + 40 × 6 + 7 × 6
= 18000 + 3600 + 240 + 42
× 6
= 21882
2 1 8 8 2

Thus, 3647 × 6 = 21882.

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Mathematical Operations