Rational Numbers

Short Answer Questions(SAQs)

What are rational numbers?

A number that can be represented as the quotient pq of two integers such that q ≠ 0 is called a rational number.

What are properties of rational numbers?

• Closure property
• Commutative property
• Associative property
• Distributive property
• Identity property
• Inverse property

What is remainder theorem?

The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial x − a, the remainder of that division will be equivalent to f(a).

MCQs

1. Which of the following is a rational number?

(a) 34

(b) 50

(c) π

(d) √2

► (a) 34 is a rational number because both 3 and 4 are integers and the denominator is not zero.

2. Which of these is not a property of rational numbers?

(a) Closure

(b) Commutative

(c) Transitive

(d) Associative

► (c) Transitive is not a standard property of rational numbers like closure, commutative, associative, etc.

3. What is the additive identity of rational numbers?

(a) 1

(b) 0

(c) -1

(d) None of the above

► (b) 0 is the additive identity for rational numbers because any number plus 0 equals the same number.

4. The multiplicative inverse of -35 is:

(a) 5-3

(b) -53

(c) 35

(d) None of these

► (b) -53 is the multiplicative inverse because it satisfies the rule a × (1/a) = 1.

5. Which property is used: a × (b + c) = a×b + a×c?

(a) Commutative

(b) Distributive

(c) Associative

(d) Closure

► (b) Distributive property explains that a number multiplied by a sum equals the sum of the products of that number with each addend.

6. What is the additive inverse of 79?

(a) -79

(b) 97

(c) 7-9

(d) None of these

► (a) The additive inverse of 79 is -79 because adding both gives 0.

7. Rational numbers are closed under:

(a) Addition

(b) Subtraction

(c) Multiplication

(d) All of these

► (d) Rational numbers are closed under addition, subtraction, and multiplication.

8. Which of the following is a rational number?

(a) √5

(b) 01

(c) π

(d) √3

► (b) 01 is a rational number as 0 and 1 are integers and denominator is non-zero.

9. What is the multiplicative identity of rational numbers?

(a) 0

(b) 1

(c) -1

(d) None of the above

► (b) 1 is the multiplicative identity as any number multiplied by 1 remains unchanged.

10. Which rational number lies between 23 and 34?

(a) 1115

(b) 910

(c) 56

(d) 78

► (c) 56 lies between 23 and 34.

11. Which of the following is equal to 69?

(a) 23

(b) 32

(c) 45

(d) 12

► (a) 69 simplifies to 23.

12. What do we get when we divide a rational number by itself (except 0)?

(a) 0

(b) 1

(c) The same number

(d) Undefined

► (b) Any rational number divided by itself gives 1 (except 0).

13. Which rational number is equal to its own reciprocal?

(a) 0

(b) 1

(c) -1

(d) Both (b) and (c)

► (d) Both 1 and -1 are equal to their own reciprocals.

14. Which of these is not a rational number?

(a) 57

(b) -29

(c) √7

(d) 05

► (c) √7 is irrational; the rest are rational numbers.

15. Rational numbers are dense in:

(a) Whole numbers

(b) Integers

(c) Natural numbers

(d) Real numbers

► (d) Rational numbers are dense in real numbers, meaning between any two real numbers, a rational number exists.

16. The reciprocal of 05 is:

(a) 50

(b) 0

(c) 1

(d) Not defined

► (d) The reciprocal of 0 is not defined because division by 0 is undefined.

17. If ab = cd, then:

(a) ad = bc

(b) ab = cd

(c) a = c, b = d

(d) None of these

► (a) If two fractions are equal, their cross products are also equal: ad = bc.

18. Rational numbers include:

(a) Integers

(b) Fractions

(c) Terminating decimals

(d) All of the above

► (d) Rational numbers include all integers, fractions, and terminating or repeating decimals.