Test: Rational Numbers- 2 - Class 8 MCQ

In multiplicative inverse we reciprocal the numbers by which we get the answer =1 that's why 1/4×4/1 which we consider as 4 so 4 is the multiplicative inverse of 1/4

additive inverse means adding what number will give you zero 
so let that no be x 
x + 4/5 = 0
x = -4/5
trick : just change the sign of number

The correct answer is: a) 1

Explanation:

The multiplicative identity for rational numbers means a number that, when you multiply it with any other number, the value does not change.

For example:

• 5 × 1 = 5

• -2 × 1 = -2

• 3/4 × 1 = 3/4

So, multiplying by 1 keeps the number the same.

Why not the others?

• b) -1: This changes the sign. For example, 4 × -1 = -4

• c) 0: This makes everything zero. 7 × 0 = 0

• d) None of these: This is wrong because we do have a correct answer, which is 1

This is how associative property works. It states that you can add or multiply numbers regardless of how they are grouped. Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.

(7/8) × (-4/21) = (7 × -4) / (8 × 21) = -28 / 168

Simplify -28 / 168 by dividing both the numerator and denominator by their greatest common divisor (28):

-28 / 168 = -1 / 6

To find a rational number x that equals its reciprocal, we solve the equation:

x = 1/x. This simplifies to:

x² = 1, giving solutions:

• x = 1
• x = -1

Both are rational numbers, so the correct answers are 1 and -1. Among the provided options, only:

• C) -1
• B) 1

Thus, both choices are correct.

A set is "closed under subtraction" if subtracting any two elements from the set always results in another element within the same set. Let's evaluate each option:

• a) Irrational numbers: Irrational numbers are not closed under subtraction. For example, √2 - √2 = 0, and 0 is a rational number, not irrational. Not closed.
• b) Negative numbers: Negative numbers are not closed under subtraction. For example, if we take two negative numbers, -3 and -5, then -3 - (-5) = -3 + 5 = 2, which is positive and not a negative number. Not closed.
• c) Rational numbers: Rational numbers are closed under subtraction. A rational number is of the form p/q, where p and q are integers and q ≠ 0. If we subtract two rational numbers, say a/b - c/d, the result is (ad - bc)/(bd), which is also a rational number (since ad, bc, and bd are integers, and bd ≠ 0). Closed.
• d) None of these: This would be correct only if none of the above sets were closed under subtraction, but rational numbers are closed.

Conclusion: c) Rational numbers are closed under subtraction.

Zero has no reciprocal. Because 1/0 is not defined and also remember any number multiplied by zero gives 0. Therefore, if reciprocal was supposed to be there then that reciprocal when multiplied by 0 should give 1 which is not possible.

Product of two rational numbers is always a rational number.
For example, 1/2 + 1/2 = 1

Given, A rational number is defined as a number that can be expressed in the form p/q , where p and q are integers

We have to find the condition that satisfies the definition.

A number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is called a rational number.

Therefore, the condition that satisfies the definition is q ≠ 0

3/7 + (-6/11) + (-8/21) + 5/22

= [3/7 + (-8/21)] + [(-6/11) + 5/22]
(by using commutativity and associativity)

= [9/21 + (-8/21)] + [-12/22 + 5/22]

LCM of 7 and 21 is 21; LCM of 11 and 22 is 22

= 1/21 + (-7/22)
= 22/462 + (-147/462)
= -125/462

Multiplicative inverse is nothing but a reciprocal of a number 2/9 which is 9/2.

A rational number between a and b is (a + b)/2
clearly it is there half so it will be between them
where a and b are numbers
a = 1/4, b = 1/2
Therefore, rational no. between 1/4 and 1/2 is
= (1/4 + 1/2)/2
=  [(1 + 2)/4]/2 
= 3/8

If you multiply any number with 1,the product will always be the same number which you multiply with 1. Therefore, 1 is the multiplicative identity.

Rational Numbers: This set is closed under addition, subtraction, multiplication, and division (with the exception of division by 0).