Multiply (i) 54 × 56(ii) 108 × 112(iii) 137 × 9999

1.	Multiply (i) 54 × 56(ii) 108 × 112(iii) 137 × 9999
Answer» (i) 54 × 56 54 × 56 = 54 + 4 + 56 + 6 = 5(54 + 6)/4 × 6 = 5 × 60/24 = 300/24 = 3024 (ii) 108 × 112 108 × 112 = 108 + 08 × 112 + 12 = 1(108 + 12)/08 × 12 = 1 × 120/90 = 12096 (iii) 137 × 9999 L.H.S = 0137 – 1 = 0136 R.H.S. = 9999 – 0136 = 9863 137 × 9999 = 0137 – 1/9999 – 0136 = 1369863

Answer»

(i) 54 × 56

54 × 56 = 54 + 4 + 56 + 6

= 5(54 + 6)/4 × 6 = 5 × 60/24

= 300/24 = 3024

(ii) 108 × 112

108 × 112 = 108 + 08 × 112 + 12

= 1(108 + 12)/08 × 12

= 1 × 120/90 = 12096

(iii) 137 × 9999

L.H.S = 0137 – 1 = 0136

R.H.S. = 9999 – 0136

= 9863 137 × 9999

= 0137 – 1/9999 – 0136

= 1369863

Discussion