Question 4 - Figure it out - Page 122, 123 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 4 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.Since we need a number which when divided by 3 OR 4 leaves a remainder 2 We need a number which When divided by LCM of 3 & 4 leaves remainder 2 LCM of 3 & 4 LCM of 3 & 4 = 2 × 2 × 3 = 12 Now, So, Numbers which leave remainder 0 when divided by 12 = 12, 24, 36, 48, 60, …. We need to find numbers which leave remainder 2 So, let’s add 2 to all these numbers We get Numbers = 12 + 2, 24 + 2, 36 + 2, 48 + 2, 60 + 2, …. = 14, 26, 38, 50, 62…. And, we can write them as Numbers which leave remainder 2 on dividing by 12 = 12k + 2 Thus, Numbers that leave a remainder of 2 when divided by 3 and a remainder of 2 when divided by 4 are 12k + 2 Some examples are Putting k = 1, 12 × 1 + 2 = 12 + 2 = 14 Putting k = 2, 12 × 2 + 2 = 24 + 2 = 26 Putting k = 10, 12 × 10 + 2 = 120 + 2 = 122