Evaluate the following products without actual multiplication.

30.5 × 29.5

30.5 = and 29.5 =

⇒ 30.5 × 29.5 = ×

⇒ 30.5 × 29.5 = ×

⇒ 30.5 × 29.5 = …(i)

Consider 61 × 59

61 = (60 + 1)

59 = (60 – 1)

⇒ 61 × 59 = (60 + 1)(60 – 1)

using the identity (a + b) × (a – b) = a² – b²

here a = 60 and b = 1

⇒ 61 × 59 = 60² – 1²

⇒ 61 × 59 = 3600 – 1

⇒ 61 × 59 = 3599

From (i)

⇒ 30.5 × 29.5 =

Therefore 30.5 × 29.5 = 899.75