Rational Numbers Test

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Rational Numbers Test - 1

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Question 1
1 / -0

Which of the following statements is correct?

A
The additive inverse of number 0 does not exist.

B
The additive inverse of number 1 does not exist.

C
The multiplicative inverse of number 0 does not exist.

D
The multiplicative inverse of number 1 does not exist.

Solution

It is known that rational number c/d is called the multiplicative inverse of rational number α/b if their product equals 1 i.e., if α/b × c/d = 1.

There is no rational number which when multiplied by 0 gives 1.

Therefore, the multiplicative inverse of number 0 does not exist.
Question 2
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Which of the following statements is incorrect?

A
Rational numbers are closed under addition.

B
Rational numbers are closed under subtraction.

C
Rational numbers are closed under multiplication.

D
Rational numbers are closed under division.

Solution

For any rational number a, a ÷ 0 is not defined.

So, rational numbers are not closed under division.
Question 3
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Which of the following statements is incorrect?

A
0 is a rational number.

B
Mixed fractions are rational numbers.

C
Rational numbers are infinite in number.

D
Rational numbers include only positive numbers.

Solution

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

Rational numbers may be positive or negative.

For example, the rational number 3/4 is positive and the rational number-3/4 is negative.
Question 4
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Which expression shows the multiplicative identity of rational numbers?

A
a × 0 = 0 × a = 0, where a is a rational number.

B
a × 1 = 1 × a = a, where a is a rational number.

C
a × (b × c) =(a × b) × c, where a, b and c are rational numbers.

D
None of the above

Solution

When any rational number is multiplied with 1, it gives the same rational number, i.e. a × 1 = 1 × a = a, where a is a rational number.

For this reason, 1 is said to be the multiplicative identity of rational numbers.

Therefore, the expression given in alternative B shows the multiplicative identity of rational numbers.