CBSE Class 8 Maths Advanced Rational Numbers Very Short Answer Questions Set 01

Very Short Answer Questions

Question 1. Fill in the blank: All natural numbers that have one and itself as their only 2 distinct factors are ________.
Answer:
They are prime numbers.
In simple words: A number with exactly two factors, 1 and itself, is prime.

Teacher's Note:
1. Examples are 2, 3, 5, 7, 11.
2. 1 has only one factor, so it is not prime.

Question 2. Fill in the blank: \( \frac{5}{11} \) is __________ decimal.
Answer:
Since 11 is not of the form 2^m × 5ⁿ, the decimal never ends: 5/11 = 0.4545... = \( 0.\overline{45} \).
So it is a non-terminating repeating decimal.
In simple words: The digits 45 repeat for ever.

Teacher's Note:
1. Check the prime factors of the denominator.
2. Only 2s and 5s give a terminating decimal.

Question 3. Fill in the blank: Lowest form of 8/12 is ________ .
Answer:
HCF of 8 and 12 is 4; 8/12 = 2/3.
The lowest form is \( \frac{2}{3} \).
In simple words: Divide top and bottom by 4.

Teacher's Note:
1. Divide by the HCF to reach the lowest form.
2. Check that the new numerator and denominator have no common factor.

Question 4. Fill in the blank: \( \frac{3}{7} \) × \( \frac{5}{8} \) = ______ × \( \frac{3}{7} \).
Answer:
Multiplication is commutative, so 3/7 × 5/8 = 5/8 × 3/7.
The blank is \( \frac{5}{8} \).
In simple words: Order does not matter in multiplication.

Teacher's Note:
1. This is the commutative law of multiplication.
2. Check: both sides equal 15/56.

Question 5. Fill in the blank: \( \frac{3}{7} \) × (\( \frac{5}{8} \) + \( \frac{4}{7} \)) = \( \frac{3}{7} \) × \( \frac{5}{8} \) + \( \frac{3}{7} \) × ______.
Answer:
By the distributive law, 3/7 is multiplied by each term inside the bracket.
The blank is \( \frac{4}{7} \).
In simple words: Multiply 3/7 by both terms of the sum.

Teacher's Note:
1. This is the distributive law of multiplication over addition.
2. The same number multiplies each term.

Question 6. Fill in the blank: \( \frac{37}{58} \) × ______ = 1.
Answer:
The product of a number and its multiplicative inverse is 1.
The blank is \( \frac{58}{37} \).
In simple words: Flip the fraction to get the number that gives 1.

Teacher's Note:
1. The reciprocal of a/b is b/a.
2. 37/58 × 58/37 = 1.

Question 7. Fill in the blank: \( \frac{4}{9} \) × ______ = \( \frac{4}{9} \).
Answer:
Multiplying by 1 leaves a number unchanged.
The blank is 1 (the multiplicative identity).
In simple words: Only multiplying by 1 keeps the number the same.

Teacher's Note:
1. 1 is the multiplicative identity.
2. 0 is the additive identity, not this one.

Question 8. Fill in the blank: \( \frac{-5}{9} \) + ______ = 0.
Answer:
The number that adds to −5/9 to give 0 is its additive inverse.
The blank is \( \frac{5}{9} \).
In simple words: Add the opposite number to get zero.

Teacher's Note:
1. Additive inverse of a is −a.
2. −5/9 + 5/9 = 0.

Question 9. Fill in the blank: Additive inverse of 5 is ____ ___.
Answer:
The additive inverse of 5 is −5, because 5 + (−5) = 0.
In simple words: Change the sign to get the additive inverse.

Teacher's Note:
1. Additive inverse means 'the number that adds to zero'.
2. For −5 it would be 5.

Question 10. Fill in the blank: Product of 2/3 and −3/2 is ________.
Answer:
2/3 × (−3/2) = −6/6 = −1.
In simple words: The two numbers are reciprocals with opposite signs, so the product is −1.

Teacher's Note:
1. Cancel 2 and 3 before multiplying.
2. A number times its negative reciprocal is −1.

Question 11. State True or False: 91 is a prime number.
Answer:
False. 91 = 7 × 13, so it has factors other than 1 and 91.
In simple words: 91 can be divided by 7.

Teacher's Note:
1. Test small primes: 2, 3, 5, 7.
2. 91 is a favourite 'looks prime' number.

Question 12. State True or False: Prime number can also be negative integers.
Answer:
False. Prime numbers are natural numbers (greater than 1), so they cannot be negative.
In simple words: Primes are positive by definition.

Teacher's Note:
1. Prime numbers are a subset of natural numbers.
2. Negative integers are not natural numbers.

Question 13. State True or False: 2 is the only even prime number.
Answer:
True. Every other even number is divisible by 2 and so has at least three factors, but 2 has only 1 and 2.
In simple words: All other even numbers are divisible by 2.

Teacher's Note:
1. 2 is also the smallest prime.
2. All other primes are odd.

Question 14. State True or False: 0 is a rational number.
Answer:
True. 0 = 0/1, which has the form p/q with q ≠ 0.
In simple words: 0 can be written as 0/1.

Teacher's Note:
1. The numerator may be zero; only the denominator must not be.
2. 0 is neither positive nor negative.

Question 15. State True or False: Rational number can not be represented on real number line.
Answer:
False. Every rational number corresponds to a point on the number line.
In simple words: Rational numbers have exact places on the number line.

Teacher's Note:
1. Divide the unit lengths into equal parts as required.
2. Irrational numbers can also be shown, but that is a later topic.

Question 16. State True or False: \( \frac{3}{5} \) > \( \frac{2}{3} \).
Answer:
3/5 = 9/15 and 2/3 = 10/15. Since 9 < 10, 3/5 < 2/3.
So the statement is False.
In simple words: 3/5 is smaller than 2/3.

Teacher's Note:
1. Use a common denominator, here 15.
2. Decimals: 0.6 against 0.667.

Question 17. State True or False: The sum of 2 rational number is always a rational number.
Answer:
True. Rational numbers are closed under addition: a/b + c/d = (ad + bc)/bd, which is a ratio of integers.
In simple words: Adding two fractions always gives another fraction.

Teacher's Note:
1. This is the closure property of addition.
2. It holds for subtraction and multiplication as well.

Question 18. State True or False: Reciprocal of a positive rational number can either be negative or positive.
Answer:
False. The product of a number and its reciprocal is 1 (positive), so the reciprocal of a positive number is positive only.
In simple words: A positive number has a positive reciprocal.

Teacher's Note:
1. Reciprocal has the same sign as the number.
2. Neither can be zero.

Question 19. State True or False: There are only 4 integers between −3 and 2.
Answer:
The integers between −3 and 2 are −2, −1, 0 and 1, which are 4 integers.
The statement is True.
In simple words: List them: −2, −1, 0, 1.

Teacher's Note:
1. 'Between' leaves out −3 and 2 themselves.
2. Do not forget 0.

Question 20. State True or False: There exist infinite rational number between any 2 integers.
Answer:
True. Between any two rational numbers (and integers are rational) there are infinitely many rational numbers.
In simple words: There is always room for another fraction between two numbers.

Teacher's Note:
1. Take the average repeatedly.
2. Example between 1 and 2: 3/2, 5/4, 9/8, ...

Teacher's Note:
1. Simplify each item separately.
2. Each answer in Column-II is used exactly once.

Teacher's Note:
1. Look at what changes: order, grouping, or a special number 0 or 1.
2. Add 0 gives the additive identity; multiply by 1 gives the multiplicative identity.

Question 23. Smallest natural number is
Answer:
The smallest natural number is 1.
In simple words: Natural numbers begin at 1.

Teacher's Note:
1. 0 is a whole number but not a natural number.
2. Counting starts from 1.

Question 24. Smallest composite number is
Answer:
Composite numbers have more than two factors. 2 and 3 are prime, so the first composite is 4 (factors 1, 2, 4).
In simple words: 4 is the first number with three factors.

Teacher's Note:
1. 1 is neither prime nor composite.
2. Next composite numbers are 6, 8, 9, 10.

Question 25. Smallest prime number is
Answer:
The smallest prime number is 2.
In simple words: 2 is the first number with exactly two factors.

Teacher's Note:
1. 1 is not prime.
2. 2 is also the only even prime.