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## Rational Number Question and Answers

**1. The Rational Number that does not have a Reciprocal**

(a) 0

(b) 1

(c) 2

(d) 3

**Answer:** (a)

**2. The Rational Number that are equal to their reciprocal**

(a) 0 and 1

(b) 1 and -1

(c) 0 and -1

(d) 1 and 2

**Answer:** (b)

**3. Which of the following statements is true?**

(a) Natural numbers are commutative for subtraction

(b) Whole numbers are commutative for subtraction

(c) Integers are commutative for subtraction

(d) Rational numbers are not commutative for subtraction.

**Answer:** (d)

**4. Which of the following statements is false?**

(a) Natural numbers are commutative for multiplication

(b) Whole numbers are commutative for multiplication

(c) Integers are not commutative for multiplication

(d) Rational numbers are commutative for multiplication.

**Answer:** (c)

**5. Which of the following statements is true?**

(a) Natural numbers are commutative for division

(b) Whole numbers are not commutative for division

(c) Integers are commutative for division

(d) Rational numbers are commutative for division.

**Answer:** (b)

**6. Which of the following statements is true?**

(a) Natural numbers are associative for addition

(b) Whole numbers are not associative for addition

(c) Integers are not associative for addition

(d) Rational numbers are not associative for addition.

**Answer:** (a)

**7. Which of the following statements is true?**

(a) Natural numbers are associative for subtraction

(b) Whole numbers are not associative for subtraction

(c) Integers are associative for subtraction

(d) Rational numbers are associative for subtraction.

**Answer:** (b)

**8. Which of the following statements is true?**

(a) Natural numbers are not associative for multiplication

(b) Whole numbers are not associative for multiplication

(c) Integers are associative for multiplication

(d) Rational numbers are not associative for multiplication.

**Answer:** (c)

**9. Which of the following statements is true?**

(a) Natural numbers are associative for division

(b) Whole numbers are associative for division

(c) Integers are associative for division

(d) Rational numbers are not associative for division.

**Answer:** (d)

**10. 0 is not**

(a) a natural number

(b) a whole number

(c) an integer

(d) a rational number.

**Answer:** (a)

**11. Which of the following statements is false?**

(a) Natural numbers are closed under addition

(b) Whole numbers are closed under addition

(c) Integers are closed under addition

(d) Rational numbers are not closed under addition.

**Answer:** (d)

**12. Which of the following statements is false?**

(a) Natural numbers are closed under subtraction

(b) Whole numbers are not closed under subtraction

(c) Integers are closed under subtraction

(d) Rational numbers are closed under subtraction.

**Answer:** (a)

**13. Which of the following statements is true?**

(a) Natural numbers are closed under multiplication

(b) Whole numbers are not closed under multiplication

(c) Integers are not closed under multiplication

(d) Rational numbers are not closed under multiplication.

**Answer:** (a)

**14. Which of the following statements is true?**

(a) Natural numbers are closed under division

(b) Whole numbers are not closed under division

(c) Integers are closed under division

(d) Rational numbers are closed under division.

**Answer:** (b)

**15. Which of the following statements is false?**

(a) Natural numbers are commutative for addition

(b) Whole numbers are commutative for addition

(c) Integers are not commutative for addition

(d) Rational numbers are commutative for addition.

**Answer:** (c)

**16. 1/2 is 2**

(a) a natural number

(b) a whole number

(c) an integer

(d) a rational number.

**Answer:** (d)

**17. a + b = b + a is called**

(a) commutative law of addition

(b) associative law of addition

(c) distributive law of addition

(d) none of these.

**Answer:** (a)

**18. a × b = b × a is called**

(a) commutative law for addition

(b) commutative law for multiplication

(c) associative law for addition

id) associative law for multiplication.

**Answer:** (b)

**19. (a + b) + c = a + (b + c) is called**

(a) commutative law for multiplication

(b) commutative law for addition

(c) associative law for addition

id) associative law for multiplication.

**Answer:** (c)

**20. a × (b × c) = (a × b) × c is called**

(a) associative law for addition

(b) associative law for multiplication

(c) commutative law for addition

(d) commutative law for multiplication.

**Answer:** (b)

**21. a(b + c) = ab + ac is called**

(a) commutative law

(b) associative law

(c) distributive law

(d) none of these.

**Answer:** (c)

**22. The additive identity for rational numbers is**

(a) 1

(b) -1

(c) 0

(d) none of these.

**Answer:** (c)

**23. The multiplicative identity for rational numbers is**

(a) -1

(b) 1

(c) 0

(d) none of these.

**Answer:** (b)

**24. The multiplicative inverse of 1/2 is**

(a) 1

(b) -1

(c) 2

(d) 0

**Answer:** (c)

**25. The multiplicative inverse of 1 is**

(a) 0

(b) -1

(c) 1

(d) none of these

**Answer:** (c)

**26. The multiplicative inverse of -1 is**

(a) 0

(b) -1

(c) 1

(d) none of these

**Answer:** (b)

**27. How many rational numbers are there between any two given rational numbers?**

(a) Only one

(b) Only two

(c) Countless

(d) Nothing can be said.

**Answer:** (c)

**28. The rational number that does not have a reciprocal is**

(a) 0

(b) 1

(c) -1

(d) 1/2

**Answer:** (a)

**29. The rational number which is equal to its negative is**

(a) 0

(b) -1

(c) 1

(d) 1/2

**Answer:** (a)

**30. The reciprocal of a positive rational number is**

(a) a positive rational number

(b) a negative rational number

(c) 0

(d) 1

**Answer:** (a)

**31. The reciprocal of a negative rational number is**

(a) a positive rational number

(b) a negative rational number

(c) 0

(d) -1

**Answer:** (b)

**32. Which of the following type of numbers are closed under only multiplication?**

(a) Rational Numbers

(b) Integers

(c) Whole Numbers

(d) Natural Numbers

**Answer:** (c)

**33. By using the properties of rational numbers solve the following equation (8 + 0) + (6 * 3).**

(a) 26

(b) 24

(c) 28

(d) 0

**Answer:** (a)

**34. On a number line, the arrangement of numbers is as follows _________**

(a) Negative -> 0 -> positive

(b) Positive -> 0 -> negative

(c) Positive -> 0 -> positive

(d) Negative -> 0 -> negative

**Answer:** (a)

**35. The number line for natural numbers is ____________**

(a) the line that extends indefinitely on both sides

(b) the line that extends indefinitely to the right, but from 0

(c) the line that extends indefinitely only to the right side of 1

(d) the line that extends indefinitely on both sides, but you can see numbers only between –1, 0 and 0, 1 etc

**Answer:** (c)

**36. -8 is ____ than 8 and -12 is ____ than -9.**

(a) greater and smaller

(b) smaller and greater

(c) greater and greater

(d) smaller and smaller

**Answer:** (d)

**37. The maximum number of integers between two consecutive natural numbers is ________**

(a) zero

(b) 2

(c) 3

(d) infinite

**Answer:** (d)

**38. [….., -1, 0, 1, …….] the given set shows which type of numbers?**

(a) Rational numbers

(b) Integers

(c) Natural numbers

(d) Whole numbers

**Answer:** (b)

**39. In equation 3x + 4 = 10, by transposing the variable on RHS we get ________**

(a) -4 = 10 – 3x

(b) 4 = 3x + 10

(c) 4 = -3x + 10

(d) -4 = – 3x – 10

**Answer:** (c)

**40. Solve equation 7x + 14 = 21 to find value of x.**

(a) x = 1

(b) x =-1

(c) x = 2

(d) x = -2

**Answer:** (a)

**41. Pick the equation from the given one’s which have solution as z = 2.**

(a) 2z -2 = 3

(b) 3z -2 = -2

(c) 3z -3 = 3

(d) 4z + 3 = 3

**Answer:** (c)

**42. Pick the equation which has the solution in the form of prime number.**

(a) 2x = 3

(b) 3z = -6

(c) 4y – 3 = 2

(d) 2z – 2 = 2

**Answer:** (d)

**43. Solve: 16 = 3m – 2.**

(a) m = -5

(b) m = 5

(c) m = 6

(d) m = -6

**Answer:** (c)

## FAQs on Rational Numbers

### Are rational numbers closed under division?

Rational numbers are always closed under division.

### Are rational numbers integers?

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals.

### Are rational numbers terminating?

Any rational number can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal.

### Are rational numbers real numbers?

All rational numbers are real numbers, so this number is rational and real. Incorrect. Irrational numbers can’t be written as a ratio of two integers. The correct answer is rational and real numbers, because all rational numbers are also real.

### Are rational numbers closed under subtraction?

Rational numbers are closed under addition and multiplication but not under subtraction.

### Are rational numbers countable?

The set of rational numbers is countable. The most common proof is based on Cantor’s enumeration of a countable collection of countable sets.

### Are rational numbers closed under addition?

Rational numbers are closed under addition and multiplication but not under subtraction.

### Why rational numbers are denoted by q?

Rational numbers are denoted by Q because we basically know that every rational numbers are quotient. So we clearly understand that every rational numbers are given in a fraction method where denominator will never be zero and numerator will be given as a whole number.

### Why rational numbers are not closed under division?

The rationals are not closed under division because of the possibility of division by zero. Zero is a rational number and division by zero is undefined.

### Why rational numbers are not integers?

But rational numbers like -5/3, 8/11, 2/5, etc. are not integers as they don’t simplify to give us a whole number (including negatives of the whole numbers). ⇒ All integers are rational numbers but all rational numbers are not integers.

### Why rational numbers are countable?

The set of all rationals in [0, 1] is countable. Clearly, we can define a bijection from Q ∩ [0, 1] → N where each rational number is mapped to its index in the above set. Thus the set of all rational numbers in [0, 1] is countably infinite and thus countable.

### Why rational numbers are denoted by p/q?

We write it as p/q to show that it is a rational number, since by definition we have to be able to write it as p/q for it to be rational.

### Why rational numbers are important?

Rational numbers are needed because there are many quantities or measures that integers alone will not adequately describe. Measurement of quantities, whether length, mass, time, or other, is the most common use of rational numbers.