Page 65 - Maths Skills - 7

Rational Numbers 63

1
Let us represent and –1 on a number line by following these steps:
3 3
Step 1: Draw a line and mark 0 at a point O.
O

0
Step 2: Mark unit lengths OA and OA′ to the right and left of O respectively. Point A represents +1 and A′
represents –1.
A' O A
–1 0 +1

Step 3: Now divide both OA and OA′ into three equal parts as shown below :
A' O A
–1 0 +1

Step 4: Mark the equal parts as shown:
A' P' O P A
–1 –1 0 1 +1
3 3
1 −1 −1
Points P and P′ represent rational numbers and respectively. Note that is to the left of zero and is at the
3 3 3
1 −2 2 −2
same distance from zero as is to its right. Can you find where and will lie? Of course lies mid way
3 3 3 3
−1 2 1
between and –1 and lies mid way between and 1.
3 3 3

COMPARISON OF RATIONAL NUMBERS
We can compare two rational numbers by two different methods:

(i) Comparing the Numerators
First convert the given numbers into rational numbers with denominator equal to LCM of their denominator and
then compare their numerator.

1 1
Let us compare − and .
2 − 5
−1 and  −  1 (on changing to positive denominator)
2   
 5
LCM of 2 and 5 is 10.

1 −×15 − 5 1 −×12 − 2
− = = , − = =
2 25 10 5 52 10
×
×
Now let us compare their numerator –5 and –2. We know that –5 < –2
− 5 − 2
So, <
10 10
1 1
or − < −
2 5