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

(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

The only rational number that is equal to its reciprocal is 1. This means that when you take the reciprocal of 1, you still get 1. Here’s why:

• The reciprocal of a number is found by flipping it. For example, the reciprocal of 2 is 1/2.
• For 1, when you flip it, you still have 1, since 1 is a whole number.
• This property makes 1 unique among rational numbers.

Other numbers do not have this property:

• For 2, the reciprocal is 1/2, which is not equal to 2.
• For 1/2, the reciprocal is 2, which is not equal to 1/2.
• For 0, the reciprocal does not exist as division by zero is undefined.

Therefore, the only rational number that is equal to its reciprocal is 1.

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.

The set of rational numbers is closed under addition; when you add any two rational numbers, the result is always a rational number.