Solved Questions on Rational Numbers
1. What is the difference between the additive inverse and multiplicative inverse of 5/7?
a) 72/35
b) 74/35
c) −72/35
d) −74/35
Answer: d) −74/35
Explanation: Additive inverse of 5/7 = − 5/7
Multiplicative inverse of 5/7 = 7/5
Difference between the additive inverse and multiplicative inverse of 5/7
= −5/7 − 7/5
= (−25 −49)/35 [LCM of 7 and 5]
= −74/35
2. Which of the following is a rational number?
a) 7 − √2
b) 7 − √3
c) 7 − √4
d) 7 − √5
Answer: c) 7 − √4
Explanation: The root of the numbers like √2 , √3 and √5 are irrational numbers.
The difference between a rational number and an irrational number is an irrational number. Hence, 7 − √2 , 7 − √3 and 7 − √5 are irrational numbers.
The difference between two rational numbers is a rational number.
Number: 7 − √4 = 7 − √(2 × 2) = 7 − 2 = 5 = 5⁄1
7 − √4 is a rational number which is in the form 5⁄1 where both ‘5’ and ‘1’ are integers and ‘1’ is not equal to zero.
3. What is the result obtained when the additive inverse of 23/11 is multiplied by the multiplicative inverse of the sum of 2/5 and 8/3?
a) − 15⁄11
b) − 15⁄22
c) 15⁄11
d) 15⁄22
Answer: b) − 15⁄11
Explanation: Additive inverse of 23/11 = − 23/11
Sum of 2/5 and 8/3 = 2/5 + 8/3
= (6 + 40)/15
= 46/15
Multiplicative inverse of the sum of 2/5 and 8/3 = 15/46
Result obtained when the additive inverse of − 23/11 is multiplied by the multiplicative inverse of the sum of 2/5 and 8/3 = − 23⁄11 × 15⁄46
= − 15⁄22
4. What are the next three rational numbers in the following pattern?
a) 
b) 
c) 
d) 
Answer: a) 
Explanation: Multiply the rational number by 2 and divide by 2 to get the next term.
5. The points A, P, Q, R, S, T, U, V, W and B on the number line. If AP = PQ = QR = RS = ST = TU = UV = VW = WB . which rational number is represented by U?
a) -1⁄3
b) -5⁄3
c) -1⁄9
d) -5⁄9
Answer: b) -5⁄3
Explanation: 
Rational number is represented by U = −16⁄9
= −12⁄3
= −1 − 2⁄3
= -5⁄3
