NCERT Exercise 9.2 Question 2
Rational Numbers 7th Math
NCERT Exercise 9.2 Question 2
In this chapter, we are learning mathematical operations on rational numbers. In Question Number 2 of the chapter of NCERT Exercise 9.2, math, class seven, five questions based on the subtraction of rational numbers have been given. In these questions, one rational number is to be subtracted from another.
Solution of NCERT Exercise 9.2 Question Number 2, class seven, math
Question (2) Find
Question (2) (i) 7/24 – 17/36
Solution :
Given, 7/24 – 17/36
To subtract, first of all, the LCM of the denominators of the given rational numbers is to be found.
The LCM of the denominators 24 and 36 of the given rational number is = 72
= (7 × 3) – (17 × 2)/72
= 21 – 34/72
= – 13/72
= – 13/72
Now, since there is no common factor other than 1 in the numerator and denominator
Thus, – 13/72 Answer
Alternate Method to find the difference between given two rational numbers 7/24 – 17/36
Given, 7/24 – 17/36
The LCM of the denominators 24 and 36 of the given rational numbers, is = 72
Thus, to make the denominators of both of the rational numbers equal to 72, we need to multiply the denominator and numerator of the first rational number by 3, and the numerator and denominator of the second rational number are multiplied by 2
∴ the given rational numbers will become 7 × 3/24 × 3 – 17 × 2/36 × 2
= 21/72 – 34/72
Now, since the denominators of both of the rational numbers became equal, thus we can subtract their numerators.
= 21 – 34/72
= – 13/72
= – 13/72
Now, since there is no common factor other than 1 in the numerator and denominator, so it is the standard or simplest form of a rational number.
Thus, – 13/72 Answer
Question (2)(ii) 5/63 – (– 6/21)
Solution :
Given, 5/63 – (– 6/21)
5/63 + 6/21
To solve this question, first of all, we need to calculate the LCM of the denominators of the given rational numbers.
The LCM of denominators of given rational number = 63
= (5 × 1) + (6 × 3)/63
= 5 + 18/63
= 23/63
Now, as there are no common factors other than 1 in the numerator and denominator, so it is the simplest form of a rational number.
Thus, 23/63 Answer
Alternate Method to find the difference between given two rational numbers 5/63 – (– 6/21)
After the removal brackets, we get
5/63 + 6/21
The LCM of the denominators 63 and 21 of the given rational numbers, is = 63
Thus, to make the denominators of both of the rational numbers equal to 63, we need to multiply the denominator and numerator of the second rational number by 3
∴ The given rational numbers will become = 5/63 + 6 × 3/21 × 3
= 5/63 + 18/63
= 5 + 18/63
= 23/63
Now, as there is no common factor other than 1 in the numerator and denominator, so it is the simplest form of a rational number.
Thus, 23/63 Answer
Question (2) (iii) – 6/13 – (– 7)/15
Solution :
Given, – 6/13 – (– 7/15)
= – 6/13 + 7/15
In order to solve this problem, first of all, we need to find the LCM of the denominators of the given rational numbers.
The LCM of denominators of given rational number = 13 × 15 = 195
= – 6 × 15 + (7 × 13)/195
= – 90 + 91/195
= 91 – 90/195
= 1/195 Answer
Question (2) (iv) – 3/8 – 7/11
Solution :
Given, – 3/8 – 7/11
In order to solve this problem, first of all, we need to find the LCM of the denominators of the given rational numbers.
The LCM of denominators of given rational number = 8 × 11 = 88
= (– 3 × 11) – (7 × 8)/88
= ( – 33 – 56)/88
= – 89/88
Since there are no common factors other than 1 in the numerator and denominator
Thus, – 89/88 Answer
(v) – 21/9 – 6
Solution :
Given, – 2 1/9 – 6
One of the given rational numbers is in the form of a mixed fraction, thus, after simplifying it into the form of a simple fraction, we get
– 19/9 – 6
The LCM of denominators of obtained rational number = 9 × 1 = 9
= – 19 – (6 × 9)/9
= – 19 – 54/9
= – 73/9
Since there are no common factors other than 1 in the numerator and denominator, thus it is the simplest form of a rational number.
Thus, – 73/9 Answer
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