Express 5 8 as a rational number with numerator - 25 ?

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is 5 8 . So, p = 5 , q = 8 Therefore, numerator = 5 and denominator = 8 . As we know 5 × - 5 = - 25 so, we need to multiply both the numerator and denominator by - 5 . Hence, we get: 5 × - 5 8 × - 5 = - 25 - 40 It is the required solution.

Express 4 7 as a rational number with denominator 21 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is 4 7 . So, p = 4 , q = 7 Therefore, numerator = 4 and denominator = 7 . To make the denominator 21 we need to multiply the numerator and denominator by 3 as 7 × 3 = 21 . Hence, 4 7 = 4 × ( 3 ) 7 × ( 3 ) = 12 21 It is the required solution.

Express 4 7 as a rational number with denominator - 35 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is 4 7 . So, p = 4 , q = 7 Therefore,numerator = 4 and denominator = 7 . To make the denominator - 35 we need to multiply the numerator and denominator by - 5 as 7 × - 5 = - 35 . Hence, 4 7 = 4 × ( - 5 ) 7 × ( - 5 ) = - 20 - 35 It is the required solution.

Express - 4 5 as a rational number with numerator - 12 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is - 4 5 . So, p = - 4 , q = 5 Therefore,numerator = - 4 and denominator = 5 . As we know - 4 × 3 = - 12 . So, we need to multiply both the numerator and denominator by 3 . Hence we get - 4 × 3 5 × 3 = - 12 15 It is the required solution.

Express - 4 5 as a rational number with numerator 60 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is - 4 5 . So, p = - 4 , q = 5 Therefore, numerator = - 4 and denominator = 5 . To make the numerator 60 we need to multiply the numerator and denominator by - 15 as - 4 × - 15 = 60 . Hence, - 4 5 = - 4 × ( - 15 ) 5 × ( - 15 ) = 60 - 75 It is the required solution.

Express - 36 24 as a rational number with denominator - 40 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is - 36 24 . So, p = - 36 , q = 24 Therefore, numerator = - 36 and denominator = 24 . First, we have to find the simplest from of the rational number. For doing that we need to divide the numerator and denominator with a same number i.e., 12 . Now, dividing numerator and denominator by 12 we have, - 36 ÷ 12 24 ÷ 12 = - 3 2 To make the denominator - 40 we need to multiply the numerator and denominator by - 20 as 2 × - 20 = - 40 . Hence, - 3 2 = - 3 × - 20 2 × - 20 = 60 - 40 It is the required solution.

Express - 36 24 as a rational number with denominator 32 .

A rational number can be represented in the form of p q ( p , q are integers and q ≠ 0 ) where numerator be p and the denominator is q or it can be expressed as the fraction of two integers when the denominator can not be zero. Given the rational number is - 36 24 . So, p = - 36 , q = 24 Therefore,numerator = - 36 and denominator = 24 . Firstly,we have to find the simplest from of the rational number.For doing that we need to divide the numerator and denominator with a same number i.e., 12 . Now,dividing numerator and denominator by 4 we have, - 36 ÷ 12 24 ÷ 12 = - 3 2 To make the denominator 32 we need to multiply the numerator and denominator by 16 as 2 × 16 = 32 . Hence, - 3 2 = - 3 × 16 2 × 16 = - 48 32 It is the required solution.

E M B I B E

Tryout Maths A book on Mental Maths 7>Chapter 4 - Rational Numbers>Exercise 13

S K Khanuja Solutions for Chapter: Rational Numbers, Exercise 1: Exercise 13

Author:S K Khanuja

S K Khanuja Mathematics Solutions for Exercise - S K Khanuja Solutions for Chapter: Rational Numbers, Exercise 1: Exercise 13

Attempt the free practice questions on Chapter 4: Rational Numbers, Exercise 1: Exercise 13 with hints and solutions to strengthen your understanding. Tryout Maths A book on Mental Maths 7 solutions are prepared by Experienced Embibe Experts.