Question

Find each of the following products, using distributive laws:
(i) 3576 × 9
(ii) 847 × 99
(iii) 2437 × 999

Answer 1

Distributive property of multiplication over addition states that a (b + c) = ab + ac
Distributive property of multiplication over subtraction states that a (b − c) = ab - ac
(i) 3576 ​× 9
= 3576 × (10 − 1)
= 3576 ​× 10 − 3576 × 1
= 35760 − 3576
= 32184

(ii) 847 × 99
= 847 × (100 − 1)
= 847 × 100 − 847 × 1
= 84700 − 847
= 83853

(iii) 2437 × 999
= 2437 × (1000 − 1)
= 2437 × 1000 − 2437 × 1
= 2437000 − 2437
= 2434563