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Question Find a few numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4. Write an algebraic expression to describe all such numbers.
Here, Remainder = 2, Dividend = 3 ∴ Number = (Quotient × Dividend) + Remainder = (K × 3) + 2 where, K = 1, 2, 3,….. Numbers = 1 × 3 + 2 = 3 + 2 = 5 Numbers = 2 × 3 + 2 = 6 + 2 = 8 Numbers = 3 × 3 + 2 = 9 + 2 = 11 Thus, 5, 8, and 11 are numbers that leave a remainder of 2 when divided by 3. Algebraic expression = 3K + 2 Here, Remainder = 2, dividend = 4 Number = 4K + 2, where K = 1, 2, 3, 4, … Numbers = 4 × 1 + 2 = 4 + 2 = 6 Numbers = 4 × 2 + 2 = 8 + 2 = 10 Numbers = 4 × 3 + 2 = 12 + 2 = 14 Algebraic expression = 4K + 2 Thus, 6, 10, and 14 are numbers that leave a remainder of 2 when divided by 4.