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

Short Answer Questions

Question 1. Find the greater number in the following pairs of rational numbers :- (a) \( \frac{9}{11} \) and \( \frac{10}{12} \) (b) \( \frac{-5}{8} \) and \( \frac{12}{16} \)
Answer:
(a) LCM of 11 and 12 is 132. 9/11 = 108/132 and 10/12 = 110/132. Since 110 > 108, 10/12 is greater.
(b) −5/8 is negative and 12/16 is positive, so 12/16 is greater.
In simple words: Use a common denominator, or note that a positive number beats a negative one.

Teacher's Note:
1. Compare numerators after making denominators equal.
2. Check the signs first.

Question 2. Write the following rational numbers in descending order \( \frac{2}{9} \), \( \frac{5}{12} \), \( \frac{7}{15} \), \( \frac{10}{14} \)
Answer:
Decimals: 2/9 ≈ 0.222, 5/12 ≈ 0.417, 7/15 ≈ 0.467, 10/14 ≈ 0.714.
Descending order: 10/14, 7/15, 5/12, 2/9.
In simple words: Write the largest first.

Teacher's Note:
1. Convert to decimals for a fast comparison.
2. Descending means greatest to smallest.

Question 3. The sum of two rational numbers is \( \frac{-8}{9} \). If one of the numbers is \( \frac{-5}{7} \), find the other.
Answer:
Other number = −8/9 − (−5/7) = −8/9 + 5/7.
= (−56 + 45)/63 = −11/63.
In simple words: Subtract the known number from the sum.

Teacher's Note:
1. Sum − one number = the other number.
2. LCM of 9 and 7 is 63.

Question 4. What should be subtracted from \( \frac{-4}{9} \) so as to get \( \frac{5}{12} \) ?
Answer:
Let the number be x: −4/9 − x = 5/12.
x = −4/9 − 5/12 = (−16 − 15)/36 = −31/36.
In simple words: Form the equation and solve for x.

Teacher's Note:
1. Minuend − x = result.
2. LCM of 9 and 12 is 36.

Question 5. The product of two rational numbers is \( \frac{-25}{49} \). If one of the numbers is \( \frac{5}{8} \), find the other?
Answer:
Other number = (−25/49) ÷ (5/8) = −25/49 × 8/5.
= −40/49.
In simple words: Divide the product by the known number.

Teacher's Note:
1. Product ÷ one factor = the other factor.
2. Cancel 5 with 25 first.

Question 6. Divide the sum of \( \frac{-7}{6} \) and \( \frac{4}{5} \) by their product .
Answer:
Sum = −7/6 + 4/5 = (−35 + 24)/30 = −11/30.
Product = −7/6 × 4/5 = −28/30 = −14/15.
Quotient = (−11/30) ÷ (−14/15) = (−11/30) × (−15/14) = 11/28.
In simple words: Find the sum, then the product, then divide.

Teacher's Note:
1. Dividing by a fraction means multiplying by its reciprocal.
2. Negative ÷ negative is positive.

Question 7. Write any 5 rational numbers between \( \frac{-5}{6} \) and \( \frac{7}{8} \).
Answer:
LCM of 6 and 8 is 24: −5/6 = −20/24 and 7/8 = 21/24.
Any numerators from −19 to 20 can be used.
Five such numbers: −19/24, −10/24, 0, 5/24, 20/24 (many answers are possible; for example −3/24, 4/24 also work).
In simple words: Use the common denominator 24 and pick numerators in between.

Teacher's Note:
1. Many correct answers exist.
2. Keep the chosen numerators strictly between −20 and 21.

Question 8. Arrange the following rational number in ascending order : \( \frac{1}{3} \), \( \frac{5}{8} \), \( \frac{23}{24} \), \( \frac{5}{6} \).
Answer:
LCM of 3, 8, 24, 6 is 24: 1/3 = 8/24, 5/8 = 15/24, 23/24, 5/6 = 20/24.
8 < 15 < 20 < 23.
Ascending order: 1/3 < 5/8 < 5/6 < 23/24.
In simple words: Make all denominators 24 and compare numerators.

Teacher's Note:
1. Ascending order means smallest first.
2. LCM keeps the numbers small.

Question 9. Standard form of \( \frac{205}{82} \).
Answer:
HCF of 205 and 82: 205 = 5 × 41 and 82 = 2 × 41, so HCF = 41.
205/82 = (205 ÷ 41)/(82 ÷ 41) = 5/2.
In simple words: Divide both numbers by 41.

Teacher's Note:
1. Standard form means lowest form with positive denominator.
2. Factorise both to find the HCF.

Question 10. The product of two rational numbers is \( \frac{-5}{7} \), if one of the number is \( \frac{2}{9} \), find the other.
Answer:
Other number = (−5/7) ÷ (2/9) = −5/7 × 9/2.
= −45/14.
In simple words: Divide the product by the given number.

Teacher's Note:
1. Multiply by the reciprocal 9/2.
2. One negative sign gives a negative answer.

Question 11. Find the number which when divided by \( \frac{8}{21} \) gives 1.
Answer:
Let the number be x: x ÷ 8/21 = 1, so x = 1 × 8/21.
The number is 8/21.
In simple words: A number divided by something gives 1 only if it equals that something.

Teacher's Note:
1. a ÷ b = 1 means a = b.
2. Check: (8/21) ÷ (8/21) = 1.

Question 12. Give three rational numbers between – 2 and – 1.
Answer:
Write −2 = −8/4 and −1 = −4/4. Numbers between: −7/4, −6/4 = −3/2, −5/4.
Three rational numbers: −7/4, −3/2, −5/4.
In simple words: Take quarters between −2 and −1.

Teacher's Note:
1. Use a denominator bigger than the gap needs.
2. Many other answers are right.

Question 13. Give three rational numbers between 3 and 4.
Answer:
Write 3 = 30/10 and 4 = 40/10. Numbers between: 31/10, 33/10, 37/10, ...
Three rational numbers: 31/10, 33/10, 37/10.
In simple words: Write both numbers over 10 and pick numerators between 30 and 40.

Teacher's Note:
1. Any numerators from 31 to 39 work.
2. The average 7/2 also lies between 3 and 4.

Question 14. Find three different rational numbers between \( \frac{5}{7} \) and \( \frac{9}{11} \).
Answer:
LCM of 7 and 11 is 77: 5/7 = 55/77 and 9/11 = 63/77.
Numbers in between: 56/77, 57/77, 58/77, ...
Three rational numbers: 56/77, 57/77, 58/77.
In simple words: Use the common denominator 77 and take numerators between 55 and 63.

Teacher's Note:
1. Numerators 56 to 62 all work.
2. Equivalent fractions give the same values.