NCERT Exercise 9.1 Question 9
Rational Numbers 7th Math
NCERT Exercise 9.1 Question 9
In this section, we will learn to compare two rational numbers. In question number 9 of the NCERT Exercise 9.1, class seven, math, five questions have been given. In each of the questions, there are two rational numbers. We need to find the greater between the given of each of the two rational numbers.
Solution of NCERT Exercise 9.1 Question number 9
Question (9) Which is greater in each of the following:
(i) 2/3, 5/2
Solution :
Given rational numbers are 2/3, 5/2
As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.
Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.
Thus, to make the denominators of the given rational number equal, we need to find their LCM first.
Now, the LCM of denominators of given rational numbers = 3 × 2 = 6
Thus, in order to compare; to make denominators of given rational numbers equal, i.e. = 6; we have to multiply their numerators and denominators with suitable numbers.
Thus, given rational numbers become
= 2 × 2/3 × 2, 5 × 3/2 × 3
= 4/6, 15/6
Here, the numerator of the second rational number, which is equal to 15 is greater than the numberator of the first rational number which is equal to 4, thus the second rational number is greater.
Thus 15/6 is greater
Thus, between the given rational numbers, 5/2 is greater Answer
Comparing two rational numbers after conversion into decimal forms
We can compare two rational numbers after converting them to their decimal forms. After the conversion of rational numbers into their decimal forms, they can be compared easily.
Here, given rational numbers are 2/3, 5/2
Now 2/3 = 0.666
And, 5/2 = 2.5
Clearly, 2.5 is greater than the 0.666
Thus, the second rational number 5/2 = 2.5 is greater than the first rational number 2/3 = 0.666
Thus, between the given rational numbers, 5/2 is greater Answer
(ii) – 5/6, – 4/3
Solution :
Given rational numbers are – 5/6 and – 4/3
Thus greater = ?
As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.
Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.
Thus, to make the denominators of the given rational number equal, we need to find their LCM first.
The LCM of denominators of given rational numbers 6
Thus, in order to compare; to make denominators of given rational numbers equal, i.e. = 6; we have to multiply their numerators and denominators with suitable numbers.
Thus the given rational numbers
= – 5/6 and – 4 × 2/3 × 2
= – 5/6 and – 8/6
Thus, clearly, – 5/6 is greater than – 8/6
Thus, – 5/6 is greater than – 4/3
And, hence – 5/6 is greater Answer
Comparing two rational numbers after conversion into decimal forms
We can compare two rational numbers after converting them to their decimal forms. After the conversion of rational numbers into their decimal forms, they can be compared easily.
Here, given rational numbers are – 5/6 and – 4/3
Now, – 5/6 = – 0.8333
And, – 4/3 = – 1.333
Here, clearly, – 0.8333 is greater than – 1.333, because – 0.8333 lies right to the – 1.333 on a number line.
Thus, – 5/6 is greater than – 4/3
And, thus – 5/6 is greater Answer
Question (9) (iii) – 3/4, 2/– 3
Solution :
Given rational numbers are – 3/4 and 2/– 3
Thus, greater = ?
As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.
Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.
Thus, to make the denominators of the given rational number equal, we need to find their LCM first.
The LCM of denominators of given rational numbers 6
Thus, in order to compare; to make denominators of given rational numbers equal, i.e. = 4 × 3 = 12; we have to multiply their numerators and denominators with suitable numbers.
Thus the given rational numbers
= – 3 × 3/4 × 3 and 2 × 4/ – 3 × 4
= – 9/12 and 8/– 12
= – 9/12 and – 8/12
Here, since the numerator of the first rational number which is equal to – 9 is smaller the then numerator of the second rational number which is equal to – 8
Thus, second rational number is greater than the first rational number.
This means – 9/12 less than – 8/12
Thus, – 3/4 less than 2/– 3
And hence, 2/– 3 is greater Answer
Comparing two rational numbers after converting them into decimal forms
We can compare two rational numbers after converting them to their decimal forms. After the conversion of rational numbers into their decimal forms, they can be compared easily.
Here, given rational numbers are – 3/4 and 2/– 3
Now, – 3/4 = – 0.75
And, 2/– 3 = – 0.666
Here, clearly – 0.666 is greater than the – 0.75, because – 0.666 lies right to – 0.75 on a number line.
Therefore, 2/– 3 is greater Answer
Question (9) (iv) – 1/4, 1/4
Solution :
Given rational numbers are – 1/4 and 1/4
Thus, greater = ?
Negative numbers are smaller than positive ones.
Here, between two given one rational number is positive which is equal to 1/4. And another rational number is negative which is equal to – 1/4
Thus, clearly, – 1/4 is less than 1/4
And hence, 1/4 is greater Answer
Question (9) (v) – 3 2/3, – 3 4/5
Solution :
Given rational numbers are – 3 2/3, – 3 4/5
= – 11/3 and – 19/5
Thus, greater = ?
Here, both of the rational numbers are negative.
As we know, if the denominators of the two rational numbers are equal, then the rational number having a greater numerator is greater and the rational number having a smaller numerator is smaller.
Thus, in order to compare them, we need to make their denominators equal. After that we can compare them easily.
Thus, to make the denominators of the given rational number equal, we need to find their LCM first.
The LCM of denominators of given rational numbers = 3 × 5 = 15
Thus, in order to compare; to make denominators of given rational numbers equal, i.e. =15; we have to multiply their numerators and denominators with suitable numbers.
Thus, given rational numbers
= – 11 × 5/3 × 5 and – 19 × 3/5 × 3
= – 55/15 and – 57/15
We know that, if denominators of the two rational numbers are equal, then the rational number having greater numerator is greater and vice versa.
Here, – 55 is greater than the – 57,
Thus, clearly, – 55/15 is greater than the – 57/15
Thus, it is clear that – 3 2/3 is greater than – 3 4/5
Thus, – 3 2/3 is greater Answer
Comparing two rational numbers after converting them into decimal forms
We can compare two rational numbers after converting them to their decimal forms. After the conversion of rational numbers into their decimal forms, they can be compared easily.
Here, given rational numbers are – 3 2/3, – 3 4/5
= – 11/3 and – 19/5
Now, – 11/3 = – 3.666
And, – 19/5 = – 3.8
Clearly, – 3.666 is greater than the – 3.8
Thus, – 3 2/3 is greater Answer
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