Question 1 of 19beginner🔧 ApplyShort Answer1 mark

Find a number that has a remainder of 3 when divided by 5. Write more such numbers.

Correct Answer

Formula: A number that leaves remainder 3 when divided by 5 can be expressed as 5k+35k + 3 for some integer k≥0k \geq 0.

Calculation: For k=0k = 0: 5(0)+3=35(0) + 3 = 3 For k=1k = 1: 5(1)+3=85(1) + 3 = 8 For k=2k = 2: 5(2)+3=135(2) + 3 = 13 And so on.

Answer: Numbers that leave a remainder of 3 when divided by 5 are: 3, 8, 13, 18, 23, 28, 33, 38, ...

These numbers are 3 more than multiples of 5.

Exercise: What Remains? | Q: 1 | (Chapter: Page 10)
For More Understanding

Explanation

A number that leaves remainder 3 when divided by 5 can be expressed as 5k + 3 for some integer k ≥\geq 0. For k = 0: 5(0) + 3 = 3. For k = 1: 5(1) + 3 = 8. For k = 2: 5(2) + 3 = 13. And so on. These numbers are 3 more than multiples of 5.

Solution Steps

  1. Express the number as 5k+35k + 3 where kk is an integer ≥0\geq 0

  2. Substitute k=0k = 0: 5(0)+3=35(0) + 3 = 3

  3. Substitute k=1k = 1: 5(1)+3=85(1) + 3 = 8

  4. Substitute k=2k = 2: 5(2)+3=135(2) + 3 = 13

  5. Continue the pattern to find more numbers: 18, 23, 28, 33, 38, ...

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