Question

Find each of the following products, using distributive laws:
(i) 740 × 105
(ii) 245 × 1008
(iii) 947 × 96
(iv) 996 × 367
(v) 472 × 1097
(vi) 580 × 64
(vii) 439 × 997
(viii) 1553 × 198

Answer 1

(i) 740 × 105
= 740 × (100 + 5)
= 740 × 100 + 740 × 5 (Using distributive law of multiplication over addition)
= 74000 + 3700
= 77700

(ii) 245 × 1008
= 245 × (1000 + 8)
= 245 × 1000 + 245 × 8 (Using distributive law of multiplication over addition)
= 245000 + 1960
= 246960

(iii) 947 × 96
= 947 × ( 100 − 4)
= 947 × 100 − 947 × 4 (Using distributive law of multiplication over subtraction)
= 94700 − 3788
= 90912

(iv) 996 × 367
= 367 × (1000 − 4)
= 367 × 1000 − 367 × 4 (Using distributive law of multiplication over subtraction)
= 367000 × 1468
= 365532

(v) 472 × 1097
= 472 × ( 1000 + 97)
= 472 × 1000 + 472 × 97 (Using distributive law of multiplication over addition)
= 472000 + 45784
= 517784

(vi) 580 × 64
= 580 × (60 + 4)
= 580 × 60 + 580 × 4 (Using distributive law of multiplication over addition)
= 34800 + 2320
= 37120

(vii) 439 × 997
= 439 × (1000 − 3)
= 439 × 1000 − 439 × 3 (Using distributive law of multiplication over subtraction)
= 439000 − 1317
= 437683

(viii) 1553 × 198
= 1553 × (200 − 2)
= 1553 × 200 − 1553 × 2 (Using distributive law of multiplication over subtraction)
= 310600 − 3106
= 307494