Page 62 - Math Genius C4

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\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

4. Grouping Property: The product of three numbers does not change when we
change the grouping of the numbers.

Example: 20 × (6 × 5) = 20 × 30 = 600
(20 × 6) × 5 = 120 × 5 = 600 Same

So, 20 × (6 × 5) = (20 × 6) × 5.
The grouping property of multiplication is also known as the Associative Property of

multiplication.
Distributive property of Multiplication

Rohan went to the stationery shop with his friend Kartik. Both of them bought a pencil
each worth `5 and an eraser each worth `3. How much money did they spend altogether?
Rohan calculated the amount as:

Total amount for two pencils and two erasers = 2 × `5 + 2 × `3
= `(10 + 6) = `16

Kartik used another way to calculate the total amount as:
Cost of one pair of a pencil and an eraser = `5 + `3
So, total amount for two pencils and two erasers = 2 × (`5 + `3) = 2 × `8 = `16
Is the same amount of money obtained in each case? (Yes)

Hence, we can say 2 × (5 + 3) = (2 × 5) + (2 × 3)
This is called the distributive property of

multiplication over addition. We say that Think Tank Critical Thinking
multiplication distributes over addition. Fill in the blanks.
1. 5 × 8 tens = _________.
Thus, the product of a number multiplied 2. 250 × 4 × 4 =_________.
by the sum of two numbers is the same as 3. The number of zeros in the product
of 1001 × 10 is _______.
the sum of the products of that number 4. The cost of one book is `180. The
with the two numbers separately. cost of 100 such books is _________.

practice time 3e

1. Fill in the blanks.

(a) 457 × 0 = _____ (b) 761 × _____ = 761 (c) _____ × 1 = 278

(d) 321 × 1 = _____ (e) 3241 × _____ = 0 (f) 48 × 165 = 165 × _____
(g) 432 × 522 = _____ × 432 (h) 169 × _____ = 215 × 169

(i) 12 × (16 × 19) = (12 × _____) × 19
(j) 62 × ( _____ × 49) = (62 × 93) × 49

(k) 27 × (9 + 15) = (27 × 9) + (27 × _____)

(l) 102 × (100 + 58) = (102 × _____ ) + (102 × 58)

60 Mathematics-4