Page 66 - Maths Skills - 7

64 Maths

(ii) By Cross Multiplying
By cross multiplying the numerator of first with denominator of second and numerator of second with
denominator of first:
a c
To compare and , we calculate a × d and c × b.
b d
Then if Fact-o-meter
a c � Every positive rational number is greater than 0.
(a) a × d > c × b, then >
b d � Every negative rational number is less than 0.
a c � Every negative rational number is less than every
(b) a × d < b × c, then < positive rational number.
b d
� We can compare two negative rational numbers by
a c ignoring their signs and then reversing their order.
(c) a × d = b × c, then =
b d

RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS

We can find infinite rational numbers between two given rational numbers. Let us see how.
2 3
Let us consider and.
5 4
Now, reduce both of them to equivalent rational number having denominator equal to the LCM of 4 and 5,
i.e., 20.
2 = 2 × 4 = 8 and 3 = 35× = 15
5 54× 20 4 45× 20
8 15
Since 815< ⇒ <
20 20
Now, we can say that
9 10 11 12 13 14 8 and 15 .
,
,
,
,
,
20 20 20 20 20 20 all these rational numbers lie between 20 20
Now, we write
8 = 80 and 15 = 150
20 200 20 200

80 81 82 140 149 150
∴ < < < ... < < < . This way we can find approximately 69 rational numbers.
200 200 200 200 200 200
8 800 15 1500
And similarly, = and = and hence we can find many more rational numbers.
20 2000 20 2000

Let’s Attempt

3 3
Example 1: Represent and − on the number line.
5 5
Solution: Draw a number line as shown in Fig. Let A represents 1, O represents 0 and A′ represents – 1.
Divide the segments OA and OA′ into 5 equal parts. And name these as OP, PQ, QR, RS and SA
on OA; and OP′, P′Q′, Q′R′, R′S′ and S′A′ on OA′ as shown. Segment OR shows 3 parts out of 5.