Page 34 - Math Skill - 5

32 Maths

Let’s Attempt

Example 1: Multiply 2357 by 394.

Solution: 394 = 300 + 90 + 4
L TTh Th H T O
2 3 5 7
× 3 9 4
9 4 2 8 (2357 × 4)
2 1 2 1 3 0 (2357 × 90)
+ 7 0 7 1 0 0 (2357 × 300)

9 2 8 6 5 8
Thus, 2357 × 394 = 928658

Example 2: Multiply 8283 by 1642.

Solution: 1642 = 1000 + 600 + 40 + 2

C TL L TTh Th H T O
8 2 8 3
× 1 6 4 2
1 6 5 6 6 (8283 × 2)
3 3 1 3 2 0 (8283 × 40)
4 9 6 9 8 0 0 (8283 × 600)
+ 8 2 8 3 0 0 0 (8283 × 1000)
1 3 6 0 0 6 8 6

Thus, 8283 × 1642 = 13600686

Properties of Multiplication

1. Commutative Property: Two or more numbers can be multiplied in any order, their
product remains the same.
For example, 75000 × 40 = 40 × 75000

75000 × 4 × 10 = 4 × 75000 × 10 = 4 × 10 × 75000
2. Associative Property: Three numbers can be grouped and multiplied in any sequence,
their product remains the same.

For example, (32000 × 50) × 6 = 1600000 × 6 = 9600000
32000 × (50 × 6) = 32000 × 300 = 9600000

(32000 × 6) × 50 = 192000 × 50 = 9600000
Thus, (32000 × 50) × 6 = 32000 × (50 × 6) = (32000 × 6) × 50

3. Distributive Property of Multiplication (Over Addition): Product of a number and the
sum of other numbers is same as the sum of the product of the first number with the other
numbers individually.

For example, 7152 × (120 + 360) = 7152 × 120 + 7152 × 360.