NCERT Exercise 9.1 Question 10
Rational Numbers 7th Math
NCERT Exercise 9.1 Question 10
In this section, we will learn to compare more than two rational numbers. And after comparison, we need to arrange them into ascending order. In question number 10 of the NCERT Exercise 9.1, class seven, math, three questions have been given. In each of the questions, three rational numbers have been given. We need to arrange them in their ascending orders.
Solution of the NCERT Exercise Question Number 10
Question (10) Write the following rational numbers in ascending order:
(i) – 3/5, – 2/5, – 1/5
Solution :
Given rational numbers are – 3/5, – 2/5, – 1/5
Then their ascending order =?
After observation, we can see that denominators of all the given rational numbers are equal. And among the numerators – 3 is the smallest while – 1 is the greatest.
If the denominators of the rational numbers are equal, the the rational number having a greater numerator is greater and the rational number having smaller numerator is smaller.
Thus the ascending order of the numerators is – 3 < – 2 < – 1.
Therefore, the ascending order of the given rational numbers is
– 3/5 [<] – 2/5 [<] – 1/5 Answer
Comparison of rational numbers after converting them into decimal forms.
Here the given rational numbers are – 3/5, – 2/5, – 1/5
Now, – 3/5 = – 0.6
And, – 2/5 = – 0.4
And, – 1/5 = – 0.2
Thus, here – 0.2 is the greatest and – 0.6 is the smallest.
Thus, their ascending order is – 0.6 < – 0.4 < – 0.2
Thus, the ascending order of the given rational number is
– 3/5 [<] – 2/5 [<] – 1/5 Answer
Question (10) (ii) – 1/3, – 2/9, – 4/3
Solution :
Given rational numbers are – 1/3, – 2/9, – 4/3
Thus their ascending order = ?
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 ascending order = 9
Thus, in order to compare the given rational numbers, let first make their denominator equal, their numerators and denominators are multiplied by suitable numbers
Thus, given rational numbers
= – 1 × 3/3 × 3, – 2/9, – 4 × 3/3 × 3
= – 3/9, – 2/9, – 12/9
Here, – 12 is the smallest, – 3 is the smaller and – 2 is the greatest.
This means the ascending order of the numerators of the rational numbers is – 12 < – 3 < – 2
Thus, the ascending order of the rational numbers will be – 12/9 < – 3/9 < – 2/9
Thus, ascending order of given rational numbers is
– 4/3 < – 1/3 < – 2/9 Answer
Comparison of rational numbers after converting them into decimal forms.
Here the given rational numbers are – 1/3, – 2/9, – 4/3
Now, – 1/3 = – 0.333
And, – 2/9 = – 0.222
And, – 4/3 = – 1.333
Thus, the ascending order is – 1.333 < – 0.333 < – 0.222
Thus, asceding order of the given rational number is
– 4/3 < – 1/3 < – 2/9 Answer
Question (10) (iii) – 3/7, – 3/2, – 3/4
Solution :
Given rational numbers are – 3/7, – 3/2, – 3/4
Thus ascending order = ?
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 = 28
Thus, in order to compare the given rational numbers, let first make their denominator equal, their numerators and denominators are multiplied by suitable numbers
Thus, given rational numbers
– 3 × 4/7 × 4, – 3 × 14/2 × 14, – 3 × 7/4 × 7
= – 12/28, – 42/28, – 21/28
Here, the ascending order of the numerators is – 42 < – 21 < – 12
Thus, asceding order of the rational numbers is
= – 42/28 < – 21/28 < – 12/28
Thus, ascending order of given rational numbers is
– 3/2 < – 3/4 < – 3/7 Answer
Comparison of rational numbers after converting them into decimal forms.
The rational numbers can be compared easily after converting them into decimal forms.
Here, the given rational numbers are – 3/7, – 3/2, – 3/4
Now, – 3/7 = – 0.428
And, – 3/2 = – 1.5
And, – 3/4 = – 0.75
Thus, their ascending order is – 1.5 < – 0.75 < – 1.5
Thus, ascending order of the given rational numbers is
– 3/2 < – 3/4 < – 3/7 Answer
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