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\\October 8, 2025 12:09 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

example 2: A factory produces 754 LED bulbs in a day. How many LED bulbs will the factory
produce in a year?
Solution: Number of LED bulbs produced in a day = 754 TL L tth th H T O

Number of LED bulbs produced in a year 7 5 4
3 6 5
= 754 × 365 × 3 7 7 0
Thus, the factory will produce 2,75,210 LED bulbs in 4 5 2 4 0
a year. + 2 2 6 2 0 0

2 7 5 2 1 0
Properties of Multiplication

1. Numbers can be multiplied in any order. The product will remain the same. It is called
the order property of multiplication.

example: 3354 × 6 = 6 × 3354 = 20124

2. When a number is multiplied by 1, the product is the number itself.
examples: 7824 × 1 = 7824 and 9878 × 1 = 9878

3. When a number is multiplied by 0, the product is always 0.
examples: 493 × 0 = 0 and 9643 × 0 = 0

4. The product of three numbers does not change when the grouping of the numbers is
changed. It is called the grouping property of multiplication.

example: (16 × 12) × 15 = (16 × 15) × 12 = (12 × 15) × 16 = 2880.

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

or (12 + 5) × 10 = (12 × 10) + (5 × 10) = 120 + 50 = 170
(b) (12 – 5) × 10 = 7 × 10 = 70

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

There is another method to multiply numbers called the double and Half method. It is
also known as the Peasant method, as it was practised by the farmers of Russia or Egypt.
Let us understand multiplication using this method.

(a) Let us multiply 25 × 14. 25 × 14 = 350
Double of 25 = 50 Half of 14 = 7 Double Half

50 × 7 = 350 50 × 7 = 350
(b) Let us multiply 48 × 50. 48 × 50 = 2400

Half of 48 = 24 Double of 50 = 100 Half Double
24 × 100 = 2400 24 × 100 = 2400

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