RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS
There can be indefinite number of rational numbers between two given rational numbers.
Ques 1: Write four rational numbers between 0 and –2.
Ans: We can write 0 as 0/10
We can write (–2) as
Thus, the following rational numbers are between 0 and –2 are
We may take any four of these.
Ques 2: Find any seven rational numbers between
Ans: Let us convert the given rational numbers having the same denominators.
Now, the rational numbers between
We can have any seven of these.
Note: Between any two integers, we need not necessarily get an integer but there will always lie a rational number. So, we can use the idea of mean to find the rational numbers between any two given rational numbers.
Ques 3: Find three rational numbers between 1/2 and 1/5
Ans: Rational number between 1/2 and 1/5
Rational number between 1/5 and 7/20
Rational number between 7/20 and 1/2
Thus, the three rational numbers lie between .
Even between two consecutive integers, there are countless rational numbers.
Ques 4: Write the rational number for each point labelled with a letter.
Ans: (i) Here, the rational number for the point A is 1/5
The rational number for the point B is 4/5
The rational number for the point C is 5/5 or 1
The rational number for the point D is 8/5
The rational number for the point E is 9/5
(ii) The rational number for:
The point is F -2/6 or 1/3
The point G is -5/6
The point H is -7/6
The point I is -8/6 or -43
The point J is -11/6
Ques 1: Represent these numbers on the number line.
Ans: (i) To represent 7/4, we make 7 markings each of a distance equal to 1/4 on the right of 0. The 7th point represents the rational number 7/4 as shown in the figure.
The point A is 7/4
(ii) To represent on the number line, we make 5 markings each of a distance equal to 1/6 on the left of 0. We consider the 5th point as shown in the figure.
The point B represents
Ques 2: Represent on the number line.
Ans: To represent on a number line, we make 11 markings each being equal to distance on the left of 0.
The point A represents (-2/11)
The point B represents (-5/11)
The point C represents (-9/11)
Ques 3: Write five rational numbers which are smaller than 2.
Ans: There can be unlimited rational numbers below 2. Five of them are:
Ques 4: Find ten rational numbers between -2/5 and 1/2
Ans: To convert -2/5 and 1/2 having the same denominators:
∴ The rational numbers between
We can take any 10 of them.
∴ Ten rational numbers between
Ques 5: Find five rational numbers between:
(i) 2/3 and 4/5
(ii) -3/2 and 5/3
(iii) 1/4 and 1/3
Ans: (i) Converting 2/3 and 4/5 having same denominators such that difference between the numerators is more than 5.
Now, any five rational numbers between
(ii) Converting with same denominators, we have
∴ Five rational numbers between
(iii) Converting 1/4 and 1/2 to rational numbers with the same denominators, we have
Ques 6: Write five rational numbers greater than –2.
Ans: Five rational numbers greater than
Note: There can be many rational numbers greater than –2.
Ques 7: Find ten rational numbers between 3/5 and 3/4
Ans: Converting 3/5 and 3/4 such that they have common denominators and their numerators have, difference of more than 10, i.e.
∴ Ten rational numbers between 3/5 and 3/4 are