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1 2 7 3
And, < < <
3 5 15 5

3
Now, find the rational number between 7 and .
15 5
+
1  7 3 1  79 1 16 8
×  +  = ×   = × =
2  15 5 2  15  2 15 15
7 3 8
\ The rational number between and is .
15 5 15

7 8 3 1 2 7 8 3
Clearly, < < ⇒ < < < <
15 15 5 3 5 15 15 5
1 3 2 7 8
Thus, three rational numbers between and are: , and .
3 5 5 15 15

Continuing in this manner, we can find as many rational numbers as we want between the two
1 3
rational numbers and .
3 5
• By using the common denominator

−3 1
Let us find three rational numbers between and .
4 5
First, convert them into equivalent rational numbers. As the LCM of 4 and 5 is 20.

−×35 −15 14 4
×
Therefore, = and =
45 20 54 20
×
×
Clearly, −15 < −14 < −13 < −12 < ... < < 1 < 2 < 3 < 4 , we can take any three rational numbers
0
20 20 20 20 20 20 20 20
1
like: −14 , −13 1 between −3 and .
,
20 20 20 4 5
However, we can find unlimited (infinite) rational numbers between any two rational numbers.

Practice Time 1A

1. Convert the rational number 4 into equivalent rational number with
5
(a) denominator = 15 (b) denominator = –20

(c) numerator = 28 (d) numerator = –8
2 22
2. Is the standard form of − ? Give reason in support of your answer.
− 5 55
−3 1
3. Represent and on the same number line.
8 4

−12 12
4. Represent and on the same number line. Are these points equidistant from the origin?
5 5

13 Rational Numbers