Represent the rational number - 4 3 on the number line.

Given to represent - 4 3 on a number line. We know that, - 4 3 can be written as - 1 1 3 . Thus, - 4 3 lies between - 1 and - 2 . Draw a line and choose any point on it to represent zero. Divide the portion between - 1 and - 2 into 3 equal parts as the denominator of - 4 3 is 3 and mark them as - 1 1 3 , - 1 2 3 and - 2 . The point B represents - 4 3 or - 1 1 3 on the number line.

Represent the rational number - 4 - 3 on the number line.

Given to represent - 4 - 3 on a number line. We know that, - 4 - 3 = 4 3 can be written as 1 1 3 . Thus, 4 3 lies between 1 and 2 . Draw a line and choose any point on it to represent zero. Divide the portion between 1 and 2 into 3 equal parts as the denominator of 4 3 is 3 and mark them as 1 1 3 , 1 2 3 and 2 . The point B represents 4 3 or 1 1 3 on the number line.

Arrange - 5 6 , 11 12 , 2 3 in ascending order.

Given rational numbers are - 5 6 , 11 12 and 2 3 . In order to arrange the given rational numbers in ascending order, we need to equate the denominators by taking their LCM and then compare the numerators of the numbers. We know that the LCM of 3 , 6 , 12 is 12 . ∴ - 5 6 = - 5 × 2 6 × 2 = - 10 12 11 12 = 11 × 1 11 × 1 = 11 12 2 3 = 2 × 4 3 × 4 = 8 12 Since, the denominators of - 10 12 , 11 12 and 8 12 are equal, comparing the numerators we get, - 10 12 < 8 12 < 11 12 Hence, the ascending order of the given rational numbers is - 5 6 < 2 3 < 11 12 .

Arrange 1 2 , - 3 - 4 , - 2 3 in descending order.

Given rational numbers are 1 2 , - 3 - 4 and - 2 3 . In order to arrange the given rational numbers in descending order, we need to equate the denominators by taking their LCM and then compare the numerators of the numbers. We know that, The LCM of 2 , 3 , 4 is 12 . ∴ 1 2 = 1 × 6 2 × 6 = 6 12 - 3 - 4 = - 3 × - 3 - 4 × - 3 = 9 12 - 2 3 = - 2 × 4 3 × 4 = - 8 12 Since, the denominators of 6 12 , 9 12 and - 8 12 are equal, comparing the numerators we get, 9 12 > 6 12 > - 8 12 Hence, the descending the order of the rational numbers is - 3 - 4 > 1 2 > - 2 3 .

If a = 1 5 , b = 1 3 and c = 2 5 , then verify that a × b × c = a × b × c .

Given, a = 1 5 , b = 1 3 and c = 2 5 . We know that, Product of two rational numbers = Product of numerators Product of denominators Therefore, LHS = a × b × c = 1 5 × 1 3 × 2 5 = 1 15 × 2 5 = 1 × 2 15 × 5 = 2 75 RHS = a × ( b × c ) = 1 5 × 1 3 × 2 5 = 1 5 × 2 15 = 1 × 2 5 × 15 = 2 75 ∴ a × b × c = a × b × c = 2 75 The above expression shows the associative property of multiplication of rational numbers. Hence, verified.

If a = 1 5 , b = 1 3 and c = 2 5 , then verify that : a b + c = a × b + a × c

Given, a = 1 5 , b = 1 3 and c = 2 5 . We know that, Product of two rational numbers = Product of numerators Product of denominators Therefore, LHS = a b + c = 1 5 × 1 3 + 2 5 = 1 5 × 1 3 + 2 5 = 1 5 × 5 + 6 15 = 1 5 × 11 15 = 1 × 11 5 × 15 = 11 75 RHS = a × b + b × c = 1 5 × 1 3 + 1 5 × 2 5 = 1 × 1 5 × 3 + 1 × 2 5 × 5 = 1 15 + 2 25 = 1 15 + 2 25 = 5 + 6 75 = 11 75 Therefore, a b + c = a × b + a × c = 11 75 Hence, verified.

If a = 1 5 , b = 1 3 and c = 2 5 , then verify that : a b - c = a × b - a × c

Given, a = 1 5 , b = 1 3 and c = 2 5 . We know that, Product of two rational numbers = Product of numerators Product of denominators Therefore, LHS = a b - c = 1 5 × 1 3 - 2 5 = 1 5 × 1 3 - 2 5 = 1 5 × 5 - 6 15 = 1 5 × - 1 15 = 1 × - 1 5 × 15 = - 1 75 RHS = a × b - a × c = 1 5 × 1 3 - 1 5 × 2 5 = 1 × 1 5 × 3 - 1 × 2 5 × 5 = 1 15 - 2 25 = 5 - 6 75 = - 1 75 Therefore, a b - c = a × b - a × c Hence, verified.

If a = 1 5 , b = 1 3 and c = 2 5 , then verify that a + b + c = a + b + c

Given, a = 1 5 , b = 1 3 and c = 2 5 . To verify that, a + b + c = a + b + c Taking the LHS and RHS, we get, LHS = a + b + c = 1 5 + 1 3 + 2 5 = 3 + 5 15 + 2 5 = 8 15 + 2 5 = 8 + 6 15 = 14 15 RHS = a + b + c = 1 5 + 1 3 + 2 5 = 1 5 + 5 + 6 15 = 1 5 + 11 15 = 3 + 11 15 = 14 15 Thus, a + b + c = a + b + c The above expression, shows the associative property of addition of rational numbers. Hence, verified.

E M B I B E

Joy Of Mathematics 8>Chapter 2 - Rational Numbers>Revision Time

S.N. Chhibber Solutions for Chapter: Rational Numbers, Exercise 6: Revision Time

Author:S.N. Chhibber

S.N. Chhibber Mathematics Solutions for Exercise - S.N. Chhibber Solutions for Chapter: Rational Numbers, Exercise 6: Revision Time

Attempt the practice questions on Chapter 2: Rational Numbers, Exercise 6: Revision Time with hints and solutions to strengthen your understanding. Joy Of Mathematics 8 solutions are prepared by Experienced Embibe Experts.