Question

Compare the following rational numbers 8/-4□6/-8​

Answer 1

Answer:

We will learn the comparison of rational numbers. We know how to compare two integers and also two fractions. We know that every positive integer is greater than zero and every negative integer is less than zero. Also every positive integer is greater than every negative integer.

Similar to the comparison of integers, we have the following facts about how to compare the rational numbers.

(i) Every positive rational number is greater than 0.

(ii) Every negative rational number is less than 0.

(iii) Every positive rational number is greater than every negative rational number.

(iv) Every rational number represented by a point on the number line is greater than every rational number represented by points on its left.

(v) Every rational number represented by a point on the number line is less than every rational number represented by paints on its right.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.1. Which of the two rational numbers 3535 and −23−23 is greater?

Solution:

Clearly 3535 is a positive rational number and −23−23 is a negative rational number. We know that every positive rational number is greater than every negative rational number.

Therefore, 3535 > −23−23.

2. Which of the numbers 3−43−4 and −56−56 is greater?

Solution:

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

One number = 3−43−4 = 3×(−1)(−4)×(−1)3×(−1)(−4)×(−1) = −34−34.

The other number = −56−56.

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

Therefore, −34−34 = (−3)×34×3(−3)×34×3 = −912−912 and −56−56 = (−5)×26×2(−5)×26×2 = −1012−1012

Clearly, −912−912 > −1012−1012

Hence, 3−43−4 > −56−56.