CBSE Class 8 Maths Advanced Rational Numbers Very Short Answer Questions Set 02

Very Short Answer Questions

Question 1. Only even prime number is
Answer:
The only even prime number is 2.
In simple words: Any other even number can be divided by 2 and so is composite.

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

Question 2. Represent \( \frac{13}{5} \) and \( \frac{-13}{5} \) on the number line.
Answer:
13/5 = \( 2\frac{3}{5} \) = 2.6, so it lies 3 fifths beyond 2. Similarly −13/5 = −2.6 lies 3 fifths to the left of −2.
Divide each unit into 5 equal parts. Count 13 parts to the right of 0 to reach 13/5, and 13 parts to the left of 0 to reach −13/5.

In simple words: Split each unit into 5 parts and count 13 steps each way from 0.

Teacher's Note:
1. Mixed form: 13/5 = 2 and 3/5.
2. The two points are the same distance from 0, on opposite sides.

Question 3. Represent –17.5 on the number line.
Answer:
−17.5 lies exactly half-way between −18 and −17.
Mark −18 and −17 on the line, then halve the gap to locate P = −17.5.

In simple words: It is the mid-point of −18 and −17.

Teacher's Note:
1. Negative numbers go to the left of 0, so −17.5 is further left than −17.
2. −17.5 = −35/2.

Question 4. Find the additive inverse of the following : (a) \( \frac{1}{3} \) (b) 0 (c) 5 (d) \( \frac{5}{-7} \)
Answer:
(a) −1/3
(b) 0 (since 0 + 0 = 0)
(c) −5
(d) 5/(−7) = −5/7, so its additive inverse is 5/7.
In simple words: Flip the sign of each number; 0 stays 0.

Teacher's Note:
1. Additive inverse of a is −a.
2. Write (d) with a positive denominator first.

Question 5. Find the multiplicative inverse of the following : (a) \( \frac{7}{5} \) (b) 0 (c) – 8 (d) \( \frac{-2}{5} \)
Answer:
(a) 5/7
(b) Does not exist, because no number multiplied by 0 gives 1.
(c) −1/8
(d) −5/2
In simple words: Take the reciprocal; zero has none.

Teacher's Note:
1. The sign stays the same in a reciprocal.
2. Write −8 as −8/1 and flip.

Question 6. Check 972 a prime number ?
Answer:
972 is an even number, so it is divisible by 2 (972 = 2 × 486).
It has factors other than 1 and itself, so 972 is not a prime number.
In simple words: 972 can be divided by 2, so it is composite.

Teacher's Note:
1. Even numbers greater than 2 are never prime.
2. For other numbers, test primes up to the square root.

Question 7. Express 0.88 into \( \frac{p}{q} \) form ?
Answer:
0.88 = 88/100 = 22/25 (dividing by 4).
In simple words: Write 88 over 100 and reduce.

Teacher's Note:
1. Two decimal places mean denominator 100.
2. 22 and 25 have no common factor.

Question 8. Show that \( \frac{-8}{12} \) = \( \frac{24}{-36} \) ?
Answer:
−8/12: HCF of 8 and 12 is 4, so −8/12 = −2/3.
24/(−36) = −24/36, and HCF of 24 and 36 is 12, so it equals −2/3.
Both have the same lowest form −2/3, so −8/12 = 24/(−36).
Cross-check: (−8) × (−36) = 288 and 12 × 24 = 288.
In simple words: Both fractions reduce to −2/3.

Teacher's Note:
1. Equal rational numbers have the same lowest form.
2. Cross-multiplication gives a second check.

Question 9. \( |-138| - |-243| \) = ?
Answer:
|−138| = 138 and |−243| = 243.
138 − 243 = −105.
In simple words: Remove the signs inside the bars, then subtract.

Teacher's Note:
1. Absolute value is never negative.
2. The final answer can still be negative.

Question 10. Find two rational numbers whose absolute value is \( \frac{1}{5} \).
Answer:
A number and its negative have the same absolute value.
The two numbers are 1/5 and −1/5.
In simple words: Both 1/5 and −1/5 are 1/5 away from zero.

Teacher's Note:
1. Absolute value means distance from 0.
2. There are always two such numbers (except for 0).