Page 42 - SM inner class 7.cdr

Now compare the numerator of rational So lu tion :
numbers with the same denominator. Step 1 : The L.C.M of de nom i na tors 4, 3 and
-99 < -41 12 is 12.
-99 -41 Step 2 : Re write the ra tio nal num bers with a
<
121 121 com mon de nom i na tor as,
´
1 1 3 3
9 - 41 = =
Thus, < 4 4 ´ 3 12
- 11 121
2 2 ´ 4 8
Arranging Rational Numbers in Orders = =
3 3 ´ 4 12
We can also arrange the given rational 1 1 1 1
´
numbers in ascending order (lowest to highest) = =
´
and in descending order(highest to lowest) in 12 12 1 12
the following steps. Step 3 : Compare the numerators 3, 8 and 1
and re ar range the ra tio nal num bers in
Step 1 : Find the L.C.M of the de nom i na tors of
given ra tio nal num bers. as cend ing order.
<
1 3 < 8
Step 2 : Re write the ra tio nal num bers with a
1 3 8 1 1 2
com mon de nom i na tor. < < or < <
12 12 12 12 4 3
Step 3 : Com pare the nu mer a tors and ar range
Thus, arranging in ascending order, we
the ra tio nal num bers in as cend ing or 1 1 2
de scend ing order. get , ,
12 4 3
Ex am ple 17. Arrange the rational numbers
1 2 7 Find a Rational Number Between two
, and in de scend ing order.
2 3 8 Given Rational Number
So lu tion : Let us find some rational numbers between
-5 5
Step 1 : The L.C.M of de nom i na tors 2, 3 and 8 two rational numbers, say, and .
is 24. 9 9
We know that there are nine integers between
Step 2 : Re write the ra tio nal num bers with a
-5 and 5. They are -4, -3, -2, -1 0 1 2 3, to 4.
,
,
,
,
com mon de nom i na tor as, Thus, we can say that the rational numbers
´
1 1 12 12 -4 -3 -2 -1 0 2 3 4 -5
= = , , , , , , and lie between
´
2 2 12 24 9 9 9 9 9 9 9 9 9
2 2 ´ 8 16 5
= = and . This is not the limit, we can write many
3 3 ´ 8 24 9
-5 5
7 7 ´ 3 21 more rational numbers between and . Since
= = 9 9
8 8 ´ 3 24 -5 -50 5 50 -49 -48 -47
= and = , therefore , ,
Step 3 : Com pare the nu mer a tors 12, 16 and 9 90 9 90 90 90 90
21 and rearrange the rational numbers in -46 , -45 , -44 ……… 1 , 2 , 3 ,……, upto 49
de scend ing order. 90 90 99 90 90 90 90
-50 50
>
>
21 16 12 all lie between and . That is they lie
21 16 12 7 2 1 90 90
> > or > > -5 5
24 24 24 8 3 2 between and . Similarly by writing
9 9
Thus, arranging in descending order, we get : -5 -500 5 500
7 2 1 = and = , we can insert other such
, , 9 900 9 900
8 3 2 rational numbers.
Ex am ple 18. Arrange the rational numbers Hence, we can say that there are count less rational
1 2 1
, and in as cend ing order. numbers between any two rational.
4 3 12
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Mathematics In Focus - 7