Page 35 - SM inner class 7.cdr

Now we divide each segment of the above number line into two equal parts, as given in the
following diagram.
11 10 9 7 6 5 3 2 1 1 2 3 5 6 7 9 10 11
– – – – – – – – – + + + + + + + + +
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
12
– 8 4 4 8 12
4 – 4 – 4 + 4 + 4 + 4

–3 –2 –1 0 +1 +2 +3
Fig. : 3

In the figure 3, the number line represents the following rational numbers.
12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5
K, - , - , - , - , - , - , - , - , - - , - - , 0 , + , + , + , + , + ,
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
6 7 8 9 11 12
+ + + , + , + , + ......,
4 4 4 4 4 4
Since we have to consider 3 complete units and
Similarly, we can divide each segment of a part of the fourth unit. Divide the third unit
number line into three, five and even more into 3 equal parts. Take 1 part out of these 3
equal parts and we can also represent any parts. Thus this point represents the rational
rational number on a number line by using the number
above given method. 1 10
Ex am ple 1. Draw a num ber line and rep re sent -3 = -
-10 3 3
the ra tio nal num ber .
3 – 2 – 1
3 3
So lu tion : Draw a num ber line and mark
0, - 1, - 2, ... to the left on it. –4 –3 1 –3 –2 –1 0
-10 æ 1 ö 3
We know that = - ç3 + ÷
3 è 3 ø

E xercise 4.1

1. Write “T” for a true and “F” for a false state ment.
(a) Positive numbers are rational numbers. (b) “0” is not a rational number.
p
(c) An integer is expressed in , form. (d) Negative numbers are not rational numbers.
q
p
(e) In any rational number q can be zero.
q

2. Rep re sent each ra tio nal num ber on the num ber line.
5 2
(a) - (b)
2 3
4 3
(c) 1 (d) 1
5 5
3
(e) -2
4

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Mathematics In Focus - 7