Question 2 - Page 8 - Finding Percentage Quickly - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 2 - Page 8 Suppose you have to mentally calculate the following percentages of some value: 75%, 90%, 70%, 55%. How would you do it? Discuss.How to find 𝟕𝟓% Think of 75% as "three-quarters." There are two great ways to do this: Method A (The Addition Way): Break it into 50%+25%. First, find half the number (50%). Then, find half of that number (25%). Add them together. Example - Finding 75% of 80: Half is 40 Half of that is 20. Thus, answer is 40+20=𝟔𝟎 Method B (The Subtraction Way): Think of it as 100%−25%. Take the whole number. Subtract a quarter ( 25% ) from it. Example - Finding 75% of 80: A quarter of 80 is 80/4=20. Thus, answer is 80−20=𝟔𝟎 How to find 90% Don't try to calculate 90 directly! It's too big. Instead, look at what is missing. The Shortcut: 90% is just 𝟏𝟎𝟎%−𝟏𝟎%. Find 10% (just move the decimal one spot to the left). Subtract that from the original number. Example - Finding 90% of 400: 10% is 40 . So, answer is 400−40=𝟑𝟔𝟎 How to find 70% We can build this up using our 10% block. Method A (Multiplication): 70% is just 𝟕 × 𝟏𝟎%. Find 10%. Multiply it by 7 . Example - Finding 70% of 50: 10% is 5 And, answer is 5 × 7=𝟑𝟓 Method B (Addition): We use 70%=𝟓𝟎%+𝟐𝟎%. Find half ( 50% ) Find 10% and double it to get 20%. Add them. Example - Finding 70% of 50: Half, i.e. 50% is 50/2 = 25 10% is 5 20% is 5 × 2 = 10 And, answer is 25 + 10 = 35 How to find 55% This is a classic "Half plus a little bit" problem. The Breakdown: 𝟓𝟓%=𝟓𝟎%+𝟓%. Step 1: Find 50% (Half the number). Step 2: Find 5% (Just 10% cut in half!). Step 3: Add them together Example - Finding 55% of 200: 50% is 100 . 10% is 20 , so 5% is 10 . And, answer is 100+10=𝟏𝟏𝟎