Olympiad Test: Rational Numbers - 2 - Class 8 MCQ

According to the rules of exponents, any non-zero number raised to the power of zero is equal to 1. This rule applies regardless of whether the number is rational or irrational, as long as it is not zero.

• x is a non-zero rational number.
• x° = 1.

Therefore, the value of x° is 1.

To determine which fraction is the largest, we convert each to a decimal

: - A: 7/-18 ≈ -0.388

- B: 4/-9 ≈ -0.444

- C: -5/12 ≈ -0.4167

- D: -2/3 ≈ -0.6667

Among these, A (-0.388) is the closest to zero, making it the largest number.

LCM of 12, 6, 18, 24 = 72

Closure property of rational numbers is satisfied for addition, subtraction and multiplication.
Closure property : The sum of two rational numbers will be a rational of addition for rational number. 

p – q = 22, pq = 240.

Explanation: 5/4 – 8/3

Making the denominator equal:

[(5/4) x (3/3)] – [(8/3) x (4/4)]

= (15/12) – (32/12)

= (15 – 32)/12

= -17/12

                  = 9/2

= 

= 3.954 × 10^-3

x + y = 24

The difference between x and y is 10. In other words, x minus y equals 10 and can be written as equation B:

x - y = 10

Now solve equation B for x to get the revised equation B:

x - y = 10

x = 10 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 24

10 + y + y = 24

10 + 2y = 24

2y = 14

y = 7

Now we know y is 7. Which means that we can substitute y for 7 in equation A and solve for x:

x + y = 24

x + 7 = 24

x = 17

So x/y = 17/7