Question

Solve using suitable arrangement & property ( Class6)
17 x 10817 x 108
2) 102 x103102x103
3) 25x7534x4x50x225x7534x4x50x2

Answer 1

To find :

1) 7 x 10817 x 108

2) 102 x103102x103

3) 25x7534x4x50x225x7534x4x50x2

Solution :

1) 7 × 10817 × 108

= (10 - 3) × 10817 × (100 + 8)

= (108170 - 10817×3) × (100 + 8)

= 108170×100 + 108170×8 - 3×1081700 - 3×10817×8

= 10817000 + 108170×(10 - 2) - 3×1081700 - 3×10817×(10 - 2)

= 10817000 + 1081700 - 2×108170 - 3×1081700 - 3×108170 - 6× 10817

= 10817000 - 2×1081700 - 5×108170 - 6×10817

= 10817000 - 2163400 - 540850 - 64902

= 8047848

2) 102 x 103102 x 103

= (100 + 2) × 103102 × (100 + 3)

= (10310200 + 2×103102) × (100 + 3)

= 1031020000 + 3×10310200 + 2×10310200 + 6×103102

= 1031020000 + 5×10310200 + 6×103102

= 1031020000 + 51551000+ 618612

= 1083189612

3) 25 x 7534 x 4 x 50 x 225 x 7534 x 4 x 50 x 2

= 25 × 7534 × 200 × 225 × 7534 × 200 × 2

= (25 × 2) × 40000 × 7534 × 7534 × 225

= 50 × 10000 × 7534 × 7534 × (4 × 225)

= 5 × 100000 × 7534 × 7534 × 900

= 10000000 × (5 × 7534) × 7534 × 9

= 10000000 × 37670 × 67806

= 10000000 × 2554252020

= 25542520200000000