Write two rational numbers between - 6 10 and 4 5

Given numbers are - 6 10 and 4 5 . Now, - 6 10 = - 6 ÷ 2 10 ÷ 2 = - 3 5 The rational numbers lie between - 3 5 and 4 5 are - 2 5 , - 1 5 Therefore, the two rational numbers between - 6 10 and 4 5 are - 2 5 , - 1 5

By taking x = 2 5 and y = - 3 10 verify | x + y | ≤ | x | + | y |

Given x = 2 5 and y = - 3 10 L.H.S = x + y = 2 5 + - 3 10 (substitute values of x and y ) = 2 5 × 2 2 - 3 10 (Make the denominators same by using their LCM) = 4 10 - 3 10 = 1 10 = 1 10 R.H.S = x + y = 2 5 + - 3 10 = 2 5 + 3 10 = 2 5 × 2 2 + 3 10 = 4 10 + 3 10 = 7 10 By comparing we get : 1 10 < 7 10 Therefore, | x + y | ≤ | x | + | y | Hence proved

By taking x = 2 5 and y = - 3 10 verify | x y | = x . y

Given x = 2 5 and y = - 3 10 L.H.S = x y = 2 5 × - 3 10 (substitute values of x and y ) = - 6 50 = 6 50 R.H.S = x . y = 2 5 × - 3 10 = 2 5 × 3 10 = 6 50 L.H.S=R.H.S Hence proved

Represent 3 4 on a number line.

Given: 3 4 Step 1 : First draw a straight line with arrows at each end. Step 2 : Mark 0 in the middle of the line and then mark 1 , 2 , 3 and so on, on the right of 0 with equal spacing between them. Step 3 : Now divide the each space between numbers into equal portions based on the denominator of the rational number. Here it is 4 . Step 4 : Now mark the required rational number based on numerator on the number line. Representation on number line

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START UP MATHEMATICS>Chapter 4 - Rational Numbers>REVIEW EXERCISES

Rahul Sofat Solutions for Chapter: Rational Numbers, Exercise 5: REVIEW EXERCISES

Author:Rahul Sofat

Rahul Sofat Mathematics Solutions for Exercise - Rahul Sofat Solutions for Chapter: Rational Numbers, Exercise 5: REVIEW EXERCISES

Attempt the free practice questions on Chapter 4: Rational Numbers, Exercise 5: REVIEW EXERCISES with hints and solutions to strengthen your understanding. START UP MATHEMATICS solutions are prepared by Experienced Embibe Experts.