How to solve rational numbers problems
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This document provides solutions to two problems about finding rational numbers between given values. For the first problem, it finds the three rational numbers between 1 and 2 using an average method and a number line method. For the second problem, it finds the three rational numbers between 1/3 and 7/2 again using an average method and a method of converting the fractions to a common denominator. The document explains each step of the solutions in detail.
How to solve rational numbers problems
- 1. Number System Problems Tutorial on Rational Number’s Class 9
- 2. Problems on Rational Numbers Problem 1 Find the 3 rational number between 1 and 2 Solution Method 1 Average method We know the average of two rational number lies between them and it is a rational number Step 1: First average = 1+2 2 = 3 2 So 3/2 lies between 1 and 2 Step 2: Average of 1 and 3/2 will also lie between 1 and 3/2 and hence 1 and 2, So = 1 2 1 + 3 2 = 5 4 Step 3.: Again Average of 3/2 and 2 will also lie between 1 and 2. So 1 2 3 2 + 2 = 7 4
- 3. Continued • Method 2: Another simple way would be from Number line So we knows 2.1,2.2,2.3 lies between 2 and 3 Since they are terminating decimal, they are rational numbers
- 4. Problems on Rational Numbers Problem 2 Find the 3 rational number between 1/3 and 7/2 Solution Method 1 Average method We know the average of two rational number lies between them and it is a rational number So step 1: First average =(1/3+7/2)/2=23/24 So 23/24 lies between 1/3 and 7/2 Step 2: Average of 1/3 and 23/24 will also lie between 1/3 and 23/24 and hence 1/3 and 7/2 So = 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
- 5. Continued • Method 2: Another simple way would be to convert the denominator into same value 1/3 =2/6 7/2=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
- 6. For more notes and study material please visit our website http://physicscatalyst.com