Ratio & Proportions - Quick Summary

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Ratio & Proportions - Quick SummaryFirst, we learn about Ratios Suppose I have 10 Euros & Ravi has 30 Euros I can say, Ravi has 20 Euros more than me And I can also say, Ravi has 3 times as much money than me While writing 3 times, I divided Ravis’s money to my money (𝑹𝒂𝒗𝒊^′ 𝒔 𝑴𝒐𝒏𝒆𝒚)/(𝑴𝒚 𝑴𝒐𝒏𝒆𝒚) = 𝟑𝟎/𝟏𝟎 = 3/1 Here 3/1 is ratio We also write is as 3 : 1 Let’s take some more examples Simplest Form of RatiosLet’s consider two ratios 60 : 40 and 90 : 60 How do we compare them? To compare them, first we convert them into simplest form To convert Ratio into Simplest form, we follow these steps Find the HCF of both numbers in the ratio Divide both numbers by HCF Let’s look at some examples Find simplest form of Ratio 60 : 40 Finding HCF first Now, 60 = 2 × 2 × 3 × 5 40 = 2 × 2 × 2 × 5 Thus, HCF (60, 40) = 2 × 2 × 5 = 20 So, we divide both 60 & 40 by 20 Ratio = 60/40 = 3/2 ∴ Simplest form of ratio is 3 : 2 We can also find simplest form by Converting ratio into a fraction Dividing both numerator and denominator until we cannot divide anymore Let’s do some examples ProportionIf two ratios are equal, we say they are in proportion Example: To check how they are equal, We simplify the ratios 2 : 4 = 2/4 4 : 8 = 4/8 So, we write 2 : 4 ∷ 4 : 8 And we say that, 2, 4, 4, 8 are in proportion When we write 4 numbers in proportion - 2, 4, 4, 8 It means 2 : 4 ∷ 4 : 8 And, 2, 8 are called extreme terms 4, 4 are called middle terms Let’s do a question Are 10, 20, 40, 80 in proportion? Ratio of 10 & 20 = 10/20 = 1/2 = 1 : 2