Question

Find the product

(1) 4 ⊗₅ 3

(2) 5 ⊗₇ 8

(3) (4 ⊗₁₁ 3) ⊗₁₁ 7

(4) (5 ⊗₁₂ 2) ⊗₁₂ 6

Answer 1

means r is the remainder when (a × b) is divided by m.

(1)

Here, 4 × 3 = 12

Upon dividing 12 by 5, we get the remainder as 2.

Hence, .

(2)

Here, 5 × 8 = 40

Upon dividing 40 by 7, we get the remainder as 5.

Hence, .

(3)

To simplify the given expression, simplify the bracket first.

Consider .

Here, 4 × 3 = 12

On dividing 12 by 11, we get the remainder as 1.

∴

∴

Since 1×7 = 7 < 11,

Hence, .

(4)

To simplify the given expression, simplify the bracket first.

Consider.

Here, 5 × 2 = 10

Since 10 < 12,

∴

Now, 10 × 6 = 60

Upon dividing 60 by 12, we get the remainder as 0.

Hence,