Question

Compare the 21/35and42/65​

Answer 1

Answer:

Which of the two rational numbers 35 and −23 is greater?

Solution:

Clearly 35 is a positive rational number and −23 is a negative rational number. We know that every positive rational number is greater than every negative rational number.

Therefore, 35 > −23.

Answer 2

Answer:

Which of the two rational numbers 35 and −23 is greater?

Solution:

Clearly 35 is a positive rational number and −23 is a negative rational number. We know that every positive rational number is greater than every negative rational number.

Therefore, 35 > −23.

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

Solution:

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

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

The other number = −56.

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

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

Clearly, −912 > −1012

Hence, 3−4 > −56.

3. Which of the two rational numbers 57 and 35 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, 57 = 5×77×7 = 2549 and 35 = 3×75×7 = 2135