Question 24 of 37intermediate🔍 AnalyzeShort Answer2 marks

Observe the differences you get in each step above. Do you notice anything in common?

Correct Answer

Observation: All the differences obtained in each step are multiples of 9.

Example: 36, 27, 45, and 9 are all divisible by 9.

Step 1: Observe differences: 36, 27, 45, 9

Step 2: Check divisibility: 36 ÷ 9 = 4 27 ÷ 9 = 3 45 ÷ 9 = 5 9 ÷ 9 = 1

Step 3: All are multiples of 9.

Mathematical Reason: For any two digits a and b:

  • Number = 10a + b
  • Reverse = 10b + a
  • Difference = (10a + b) − (10b + a) = 9(a − b)

∴ The result is always a multiple of 9.

Exercise: Pastime Mathematics | Q: 3(1) | (Page Page 12)
For More Understanding

Explanation

The mathematical reason is that for any two digits a and b, the difference between the number (10a + b) and its reverse (10b + a) equals 9(a - b), which is always a multiple of 9.

Solution Steps

  1. Step 1: Observe differences: 36, 27, 45, 9

  2. Step 2: Check divisibility: 36 ÷ 9 = 4, 27 ÷ 9 = 3, 45 ÷ 9 = 5, 9 ÷ 9 = 1

  3. Step 3: All are multiples of 9

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