Question

5. Find each of the following products, using distributive laws:
a. 740 x 105
b. 245 x 1008
c. 996 x 367
d. 472 x1097
e. 439 x 997
f. 1553 x 198
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Answer 1

Answer:

Distributive Property of multiplication over addition and subtraction is given as follows:

a × ( b + c ) = a × b + a × c

a × ( b - c ) = a × b - a × c

1).

740 × 105 = 740 × ( 100 + 5 )

= 740 × 100 + 740 × 5

= 74000 + 3700 = 77700

Thus, 740 × 105 = 77700

2).

245 × 1008 = 245 × ( 1000 + 8 )

= 245 × 1000 + 245 × 8

= 245000 + 1960 = 246960

Thus, 245 × 1008 = 246960

3).

947 × 96 = 245 × ( 100 - 4 )

= 947 × 100 - 947 × 4

= 94700 - 3788 = 90912

Thus, 947 × 96 = 90912

4).

996 × 367

= 367 × 996 = 367 × ( 1000 - 4 )

= 367 × 1000 - 367 × 4

= 367000 - 1468 = 365532

Thus, 996 × 367 = 365532

5).

472 × 1092 = 472 × ( 1100 - 8 )

= 472 × 1100 - 472 × 8

= 519200 - 3776 = 515424

Thus, 472 × 1092 = 515424

6).

580 × 64

= 64 × 580 = 64 × ( 500 + 80 )

= 64 × 500 + 64 × 80

= 32000 + 5120 = 37120

Thus, 580 × 64 = 37120

7).

439 × 997 = 439 × ( 1000 - 3 )

= 439 × 1000 - 439 × 3

= 439000 - 1317 = 437683

Thus, 439 × 997 = 437683

8).

1553 × 198 = 1553 × ( 200 - 2 )

= 1553 × 200 - 1553 × 2

= 310600 - 3106 = 307494

Thus, 1553 × 198 = 307494

Answer 2

Answer:

740× 105= 777,00

245× 1008= 246,960

996× 367= 365,532

472× 1097= 92,984