Question 6 - Figure it out - Page 154-156 - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

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Question 6 A number leaves a remainder of 3 when divided by 7, and another number leaves a remainder of 5 when divided by 7. What is the remainder when their sum, difference, and product are divided by 7?Let number A have remainder 3 when divided by 7 A = 7x + 3 Let number B have remainder 5 when divided by 7 B = 7y + 5 Sum: A + B = (7x + 3) + (7y + 5) = 7x + 7y + 8 Since 8 > 7 Dividing 8/7, we get remainder 1 Thus, remainder is 1 Difference: A – B = (7x + 3) – (7y + 5) = 7x + 3 – 7y – 5 = (7x – 7y) + (3 – 5) = 7(x – y) – 2 Thus, remainder is –2 Since usually we subtracted higher number from lower This remainder will be positive ∴ Remainder is 2 Example: For 10 & 12 Difference = 2 Thus, remainder is 2 Product: Product will be A × B = (7x + 3) × (7y + 5) = 7x (7y + 5) + 3 (7y + 5) = 7x × 7y + 7x × 5 + 3 × 7y + 3 × 5 = 49xy + 35x + 21y + 15 Since 15 > 7 Dividing 15/7, we get remainder 1 Thus, remainder is 1 Note: We can find remainder using addition, subtraction and product of remainders 3 & 5 only as well. We do not need to multiple A & B