Page 15 - SM inner class 8.cdr

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Representation of Rational Numbers on written in mixed fraction as -1 . So the
the Number Line 3
number lies between -1 and -2.
Rational numbers can also be represented on -1 -2
the number line.To express rational numbers 3. So left side of zero, mark, ,
3 3
appropriately on the number line, divide each
æ -3 ö -4 -5 æ -6 ö
unit-length into as many numbers of equal ç = - ÷ 1 , , , ç = - ÷ 2
è 3 ø 3 3 è 3 ø
parts as the denominator of the rational
number and then mark the given number on –2 –1
5 4 3 2 1 0
the number line. – 6 – – – – –
3 3 3 3 3 3
Basic rules on representing rational
How to find Rational Numbers between
numbers on number line
Two Rational Numbers?
1. If the rational number (fraction) is proper
then, it lies between 0 and 1. Finding Rational Number Between Two

2. If the rational number(fraction) is Rational Number
improper then, first convert it to mixed We have learnt haw many natural number lie
fraction and then the given rational
between two natural numbers and how many
number, lie between the whole number integers lie between two integers, before
and next whole number.
extending our studies for rational numbers let
Example 16. Use the following steps to us consider some examples.
represent 4 / 7 on the number line.
Between 1 and 9 there are seven natural
Solution: numbers namely 2, 3, 4, 5, 6, 7, 8. Similarly

1. Draw a number line. between -6 and 2, there are seven integers
namely -5, -4, -3, -2, -1, 0, 1.
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
Now Consider two rational numbers as a and
4
2. As the number is a positive number so b. How many rational numbers are there
7 between them?
it will be on right side of zero.
1 2 3 4 5 6 Remember that
3. So after zero mark, , , , , , ,
7 7 7 7 7 7 Between two natural number or integers, a fixed
æ 7 ö number of natural number or integers can be found.
ç = 1÷.
è 7 ø
First Method :
1
Let ‘a’ and ‘b’ be any two given rational
0 1 2 3 4 5 6 7 numbers. We can find many rational
7 7 7 7 7 7 7
numbers q q q, , ,... in between a and b as
-5 1 2 3
Example 17. Represent on the number line. follows:
3 a q q 1 b
2
Solution: a q q q 1 b
3
2
a b
1. Draw a number line.
1
b
q = (a + )
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 2
1
-5 q = (a + q )
2. As the number is a negative number 2 2 1
3
-5 1
so it will be on left of zero. can be q = (a + q 2 ) and so on.
3
3 2
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Mathematics In Focus - 8