Worksheet on Rational Number for Class 7

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) −$\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{11}}{}}$
b) −$\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{22}}{}}$
c)$\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{11}}{}}$
d) $\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{22}}{}}$

Answer: b) −$\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{22}}{}}$

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 = − $\frac{\frac{\mathrm{23}}{}}{\frac{\mathrm{11}}{}}$ × $\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{46}}{}}$
                                                                                                                                                                                = − $\frac{\frac{\mathrm{15}}{}}{\frac{\mathrm{22}}{}}$

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: