Question 39 of 45intermediate🔍 AnalyzeShort Answer4 marks

What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? What do you notice? Can you make a general statement and justify it using algebra, comparing x% of y and y% of x?

Correct Answer

Calculations: 5% of 40 = 0.05×400.05 \times 40 = 2 40% of 5 = 0.40×50.40 \times 5 = 2

25% of 12 = 0.25×120.25 \times 12 = 3 12% of 25 = 0.12×250.12 \times 25 = 3

15% of 60 = 0.15×600.15 \times 60 = 9 60% of 15 = 0.60×150.60 \times 15 = 9

Observation: Each pair gives the same result.

General Statement: x% of y = y% of x

Algebraic Proof: x% of y = (x/100) × y = xy/100 y% of x = (y/100) × x = xy/100 ∴ x% of y = y% of x

Exercise: Figure it Out (Section 5) | Q: 7 | (Page Page 29)
For More Understanding

Explanation

The chapter encourages pattern recognition. This property shows that percentage calculation is commutative - the order doesn't matter because multiplication is commutative.

Solution Steps

  1. 5% of 40 = 0.05×400.05 \times 40 = 2

  2. 40% of 5 = 0.40×50.40 \times 5 = 2

  3. 25% of 12 = 0.25×120.25 \times 12 = 3

  4. 12% of 25 = 0.12×250.12 \times 25 = 3

  5. 15% of 60 = 0.15×600.15 \times 60 = 9

  6. 60% of 15 = 0.60×150.60 \times 15 = 9

  7. General statement: x% of y = y% of x

  8. x% of y = (x/100) × y = xy/100

  9. y% of x = (y/100) × x = xy/100

  10. Therefore, x% of y = y% of x

PreviousNext