Question 7 - Figure it out - Page 28, 29, 30 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 7 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?Let’s find 5% of 40 and 40% of 5 5% of 40 5% of 40 = 5/100 × 40 = 200/100 = 2 40% of 5 40% of 5 = 40/100 × 5 = 200/100 = 2 Similarly, lets find 25% of 12 and 12% of 25 25% of 12 25% of 12 = 25/100 × 12 = 300/100 = 3 12% of 25 12% of 25 = 12/100 × 25 = 300/100 = 2 12% of 25 12% of 25 = 12/100 × 25 = 300/100 = 2 Finally finding 15% of 60 and 60% of 15 15% of 60 15% of 60 = 15/100 × 60 = 900/100 = 9 60% of 15 60% of 15 = 60/100 × 15 = 900/100 = 9 Thus, we can say that x% of y = y% of x x% of y x% of y = 𝑥/100 × y = 𝒙𝒚/𝟏𝟎𝟎 y% of x y% of x = 𝑦/100 × x = 𝒚𝒙/𝟏𝟎𝟎 Since xy = yx, the two values are identical