5.6 Using the average method, find five rational numbers between the numbers given below and
represent them on the number line.
3
(a)
}
and
4
Answers
answer
Rational number is any number that can express in the form of
q
p
of two integers, where 'q' cannot be zero.
i) First rational number between 3 and 4 can be calculated by finding average between them, which is
2
3+4
=
2
7
Now, we have three numbers i.e. 3,
2
7
and 4, so other remaining rational numbers can be calculated by taking average between 3 and
2
7
, and between
2
7
and 4.
ii) Second rational number between 3 and
2
7
can be calculated by finding average between them.
2
2
7
+3
=
2
2
7+6
=
4
13
iii) The third rational number between 4 and
2
7
can be calculated by finding the average between them.
2
2
7
+4
=
2
2
7+8
=
4
15
iv) Similarly fourth rational number between 3 and
4
13
can be calculated by finding the average between them.
2
4
13
+3
=
2
4
13+12
=
8
25
v) Similarly, fifth rational number between 4 and
4
13
can be calculated by finding average between them.
2
4
13
+4
=
2
4
13+16
=
8
29
Then the rational numbers between 3 and 4 are
2
7
,
4
13
,
4
15
,
8
25
,
8
29
Given : "Five rational numbers" between 2 and 3 are: 2.5, 2.25, 2.125, 2.75, 2.875.
To find:
"5 rational numbers" between 2 and 3 using the mean method
Solution:
A "rational number" is a number which of the form a/b where a and b are integers.
Number 1: Take the "average of 2 and 3"
2+3 = 5 = 2.5
Number 2: Take the "average of 2 and 2.5"
2+2.5
=
4.5 = 2.25numbers 3 and 4
To Find : five rational numbers between 3 and 4
Solution :
A "rational number" is a number which of the form a/b where a and b are integers.
Number 1: Take the "average of 3 and 4"
3+4 = 7 = 3.5
2 2
Number 2: Take the "average of 3 and 3.5"
3+3.5 = 3.25
2
Number 3: Take the "average of 4 and 3.5"
4+3.5 = 3.75
2
Number 4: Take the "average of 4 and 3.25"
4+3.25 = 3.625
2
Number 5: Take the "average of 3 and 3.25"
3+3.25 = 3.125
2
Thus, "5 rational numbers" between 3 and 4 are:
3.5, 3.25, 3.75, 3.625, 3.125