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Q1. The midpoint of the segment between 3 and 10 is

• 1) 6.5
• 2)
• 3) Both A and C
• 4) 6

Solution

The midpoint of a and b is . 

Q2. Between the rational numbers  and  there is/are ______ rational numbers.

• 1) Infinite
• 2) No
• 3) 2
• 4) 1

Solution

Between the rational numbers  and  there are no rational numbers. Since,  in its simplified form is .

Q3. Every terminating number can be represented as a ……….number. 

• 1) Whole
• 2) Natural
• 3) Rational
• 4) Integer

Solution

Every number can be represented as a rational number. 

Q4. Solve the following expression using properties of rational numbers:

Solution

(by commutativity) (by distributivity)

Q5. The mean of 6 and 0.6 is

• 1) None of the above
• 2) 3
• 3) 3.3
• 4) 6.6

Solution

Mean = (6+0.6) ÷ 2=3.3

Q6. Use the number line to work out .

Solution

Here, dividend is -8 and divisor is 4. So, the single jump of -8 can be split into 4 equal jumps of -2. Thus, = -2

Q7. The midpoint of the segment between -5 and -7 is 

• 1) Both B and C
• 2)
• 3) 6
• 4) -6

Solution

The midpoint of a and b is  

Q8. 0.0001 <...... <0.01

• 1) 0.011
• 2) 0.1
• 3) 0.001
• 4) 0.00001

Solution

The numbers should be more than 0.0001 and less than 0.01. 

Q9. The sum of a, b, c and d in the following figure is

• 1)
• 2) 24
• 3)
• 4) 23

Solution

Since each unit is divided into 5 equal parts, we have

Q10.  

• 1)
• 2) 4
• 3)
• 4)

Solution

The numbers should be more than 0 and less than. 

Q11. Reciprocal of any natural number lies between

• 1) 0 and 1
• 2) 1 and infinity
• 3) 0 and -1
• 4) 100 and 1000

Solution

A natural number is always equal to or greater than 1. The reciprocal of a number which is greater than 1 is always less than 1. Moreover, all natural numbers are positive and reciprocal of a positive number is always positive. Therefore, the reciprocal of any natural number lies between 0 and 1.

Q12. In the rational number , such that q≠0, p and q are ……………… 

• 1) Whole numbers
• 2) Integers
• 3) Natural numbers
• 4) p=1 and q=1

Solution

p and q can be any integers, such that q≠0. 

Q13. Which of the following is a rational number?

• 1) All of above
• 2) 2
• 3) 0
• 4) -3

Solution

A rational number is one which can be expressed as , where b≠0.

Q14. Which is the bigger set?

• 1) Integers
• 2) Whole numbers
• 3) Rational numbers
• 4) Natural numbers

Solution

Rational numbers include integers, natural numbers and whole numbers. 

Q15. If a is an integer and b is a rational number, then the number of rational numbers between a and b is

• 1) 100
• 2) 2
• 3) infinite
• 4) zero

Solution

All integers are rational numbers with denominator 1. We know that between any two rational numbers, there are infinite rational numbers. Thus, there are infinite rational numbers between a and b.

Q16. Verify that −(−x) = x for

Solution

The additive inverse of is Because, The equality shows that the additive inverse of is Or = Or -(-x) = x Hence Verified.

Q17. Rational numbers between  are

• 1)
• 2)
• 3)
• 4) All of the above

Solution

The numbers should be more than and less than . 

Q18. Insert a rational number between (x - y)^-1 and x^-1 - y^-1, where and

Solution

Given that Therefore,   Rational number between Which is the required number

Q19. The product of a non-zero rational number and its additive inverse always lie

• 1) at 1
• 2) on the right of 0.
• 3) on the left of 0.
• 4) at 0

Solution

A non-zero rational number and its additive inverse have opposite signs. Therefore, on multiplying them, the product will always have a negative sign, since product of a positive and a negative number is negative. Also, we know that all negative rational numbers lie on the left side of 0. Thus, the product of a non-zero rational number and its additive inverse always lie on the left of 0.

Q20. Rational numbers between 11 and 14 are

• 1) 14 and 15
• 2) 12 and 13
• 3) 10 and 11
• 4) 11 and 14

Solution

The numbers should be more than 11 and less than 14.

Q21. Find the 29 rational numbers between

Solution

And Now the 29 integers between -20 and 10 are -19, -18, -17, . . . . . . . 8, 9 . The corresponding 29 rational numbers between are

Q22. Use the number line to work out

Solution

On the number line means three jumps of 4 to left of 0. By making three jumps of 4 we move 12 spaces to left of 0 and reach at the point -12. Thus, .

Q23. Represent on the number line.

Solution

The number lie between 0 and 1. Draw a number line. Mark points O and A to represent 0 and 1 repectively. Divide OA into 5 equal parts (equal to the denominator of ). The second point, Q, represents the rational number .

Q24. Represent the rational number 0.5 on the number line.       

Solution