Find a number that has a remainder of 3 when divided by 5. Write more such numbers.
Formula: Numbers with remainder 3 when divided by 5 can be expressed as 5k + 3, where k is any non-negative integer.
Calculation: For k = 0: 5(0) + 3 = 3 For k = 1: 5(1) + 3 = 8 For k = 2: 5(2) + 3 = 13 The sequence continues as 18, 23, 28, 33, 38, 43, 48, ...
Answer: Numbers that leave a remainder of 3 when divided by 5 are: 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, ...
These numbers are all 3 more than a multiple of 5.
Explanation
The chapter explains that numbers leaving remainder 3 when divided by 5 can be expressed as 5k + 3, where k is any non-negative integer. Starting with k = 0: 5(0) + 3 = 3. For k = 1: 5(1) + 3 = 8. For k = 2: 5(2) + 3 = 13. The sequence continues as 18, 23, 28, 33, 38, 43, 48, ... Each number is exactly 3 more than a multiple of 5.
Solution Steps
Express numbers with remainder 3 when divided by 5 as 5k + 3, where k is any non-negative integer.
Calculate for k = 0: 5(0) + 3 = 3
Calculate for k = 1: 5(1) + 3 = 8
Calculate for k = 2: 5(2) + 3 = 13
Continue the sequence: 18, 23, 28, 33, 38, 43, 48, ...
Each number is exactly 3 more than a multiple of 5.