Class 7 Maths Rational Numbers Comparison of Rational Numbers

Comparison of Rational Numbers

In order to compare any two rational numbers, we can use the following steps:

Step I: Obtain the given rational numbers.

Step II: Write the given rational numbers so that their denominators are positive.

Step III: Find the LCM of the positive denominators of the rational numbers obtained in step II.

Step IV: Express each rational number (obtained in step II) with the LCM (obtained in step III) as

common denominator.

Step V: Compare the numerators of rational numbers obtained in step having greater numerator is the

greater rational number.

Step VI: To compare two negative rational numbers, we compare them ignoring their negative signs and

then reverse the order.

Problem: Which of the two rational numbers 5/7 and 3/5 is greater?

Solution:

Clearly, denominators o f the given rational numbers are positive. The denominators are 7 and 5. The

LCM of 7 and 5 is 35. So, we first express each rational number with 35 as common denominator.

Therefore, 5/7 = (5 * 5)/(7 * 5) = 25/35 and 35 = (3 * 7)/(5 * 7) = 21/35

Now, we compare the numerators of these rational numbers.

Therefore, 25 > 21

⇒ 25/35 > 21/35

⇒ 5/7 > 3/5

Problem: Which of the two rational numbers 3/(−4) and −5/6 is greater?

Solution:

First we write each of the given numbers with positive denominator.

One number = 3/(−4) = {3 * (−1)}/((−4) * (−1)}  = −3/4

The other number = −5/6

Now, we ignore the sign of the numbers and take the rational numbers as 3/4 and 5/6

Now, L.C.M. of 4 and 6 = 12

Therefore, 3/4 = (3 * 3)/(4 * 3) = 9/12

and 5/6 = (5 * 2)/(6 * 2) = 10/12

Now, 9 < 10

=> -9 > -10

=> −9/12 > −10/12

Hence, 3/(−4) > −5/6

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