Page 32 - Start Up Mathematics_5

2. Associative property

Three numbers can be grouped in any order and then multiplied. Their product will
remain the same.

For example, (24,169 × 1,203) × 58 = 24,169 × (1,203 × 58) = 1,68,63,67,806

3. Distributive property

The product of a number and a sum is equal to the sum of the individual products of
the addends and the number.

For example, 8,290 × (584 + 96) = (8,290 × 584) + (8,290 × 96)
This property can also be used for more than two addends.

For example, 684 × (729 + 156 + 320) = (684 × 729) + (684 × 156) + (684 × 320)

4. Property of zero

The product of a number and 0 is always 0. Mental Maths
For example, 78,243 × 0 = 0; 2,75,962 × 0 = 0 Fill in the blanks.
(a) 8,64,725 × 0 = ___________
5. Identity property
(b) 9,25,15,140 × 1 = ___________
The product of a number and 1 is the number (c) 543 × 684 × 0 = ___________
itself.
(d) 1 × 4,63,803 = ___________
For example, 3,20,145 × 1 = 3,20,145

1 is called the Multiplicative Identity.

Multiplication of two numbers

Example 14: Multiply 3,62,175 by 948.

Solution: Carry over of (3,62,175 × 900) → 5 1 1 6 4 Carry over of

2 3 2 → (3,62,175 × 40)

Carry over of (3,62,175 × 8) → 4 1 1 6 4

3 6 2 1 7 5
× 9 4 8

2 2 2
1 2 8 9 7 4 0 0 → (3,62,175 × 8)

1 4 4 8 7 0 0 0 → (3,62,175 × 40)

+ 3 2 5 9 5 7 5 0 0 → (3,62,175 × 900)
3 4 3 3 4 1 9 0 0

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