Number System

ProblemsTutorial on Rational Number’s

Class 9

Problems on Rational Numbers

Problem 1Find the 3 rational number between 1 and 2

Solution Method 1 Average methodWe know the average of two rational number lies between them and it is a rational numberStep 1: First average =So 3/2 lies between 1 and 2Step 2: Average of 1 and 3/2 will also lie between 1 and 3/2 and hence 1 and 2,So = Step 3.: Again Average of 3/2 and 2 will also lie between 1 and 2. So

Continued• Method 2: Another simple way would

be from Number line

So we knows 2.1,2.2,2.3 lies between 2 and 3Since they are terminating decimal, they are rational numbers

Problems on Rational Numbers

Problem 2Find the 3 rational number between 1/3 and 7/2 Solution Method 1 Average methodWe know the average of two rational number lies between them and it is a rational numberSo step 1: First average =(1/3+7/2)/2=23/24So 23/24 lies between 1/3 and 7/2Step 2: Average of 1/3 and 23/24 will also lie between 1/3 and 23/24 and hence 1/3 and 7/2So = ½(1/3+23/24)=31/48 Step 3.: Again Average of 23/24 and 7/2 will also lie between 1/3 and 7/2. So=1/2(23/24+7/2)=107/48

Continued• Method 2: Another simple way would

be to convert the denominator into same value

1/3 =2/67/2=21/6

Now 2/6 <3/6 < 4/6< 5/6 …..< 20/6 < 21/6

So This way we can easy find the rational numbers

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