Comparison of Rational Numbers

We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.

Let's use the same method for rational numbers also. We can mark rational numbers on the number line. We can mark the points: −12 and −15 by divided the numberline into 1025 parts.

She marked −12 and −15 as follows: and found −12 >< −15

For example, to compare −75 and −53, we first compare 75 and 53.

We get 75 <> 53 and conclude that −75 >< −53.

Take five more such pairs and compare them.

Which is greater −38 or −27−27−38 ? And for: −43 or −32 −43−32?

Comparison of a negative and a positive rational number is obvious. A negative rational number is to the leftright of zero whereas a positive rational number is to the rightleft of zero on a number line. So, a negative rational number will always be lessgreater than a positive rational number.

Thus −27 <=> 12

To compare rational numbers −3−5 and −27 reduce them to their standard forms and then compare them.

Do 4−9 and −1636 represent the same rational number?

Solution:

YesNo

Because 4−9 = 4x−49x−4 = −16363616−1016

−1636 = −16+−435÷−4 = −4−994410

Reshma wanted to count the whole numbers between 3 and 10. From her earlier classes, she knew there would be exactly 6 whole numbers between 3 and 10. Similarly, she wanted to know the total number of integers between –3 and 3. The integers between –3 and 3 are –2, –1, 0, 1, 2. Thus, there are exactly integers between –3 and 3.

Thus, we find that number of integers between two integers are limited (finite). Will the same happen in the case of rational numbers also? Reshma took two rational numbers −35 and −13

So, we could find one more rational number between −35 and −13.

By using this method, you can insert as many rational numbers as you want between two different rational numbers.

Instruction

List three rational numbers between – 2 and – 1.

Solution:

Instruction

Write four more numbers in the following pattern: −13 , −26 , −39 , −412....

Solution:

Instruction