Q1. Represent the rational numbers 2/3, −5/4 and 1/2 on a single number line.

Answer:

Solution:

To represent these numbers on the number line, divide the intervals appropriately:

• 2/3: divide the interval between 0 and 1 into 3 equal parts and move 2 parts from 0 to the right.
• 1/2: divide the interval between 0 and 1 into 2 equal parts and move 1 part from 0 to the right.
• −5/4 = −1.25: divide the interval between −1 and −2 into 4 equal parts and move 1 part from −1 to the left.

Note: The number line should show these points as described.

Q2. Find three distinct rational numbers that lie strictly between −1/2 and 1/4.

Answer:

Solution:

We need rational numbers between −0.5 and 0.25.

Possible rational numbers: −0.4, 0, 0.1

In fraction form: −2/5, 0, 1/10

We can also find them by taking averages.

Answer: Three rational numbers between −1/2 and 1/4 are −2/5, 0, and 1/10. (Answers may vary.)

Q3. Simplify the expression: (−1/4) + (5/12).

Answer:

Solution:

LCM of 4 and 12 = 12

= (−3/12) + (5/12)

= 2/12 = 1/6

Answer: 1/6

Q4. A tailor has 15 3/4 metres of fine silk. If making one kurta requires 2 1/4 metres of silk, exactly how many kurtas can he make?

Answer:

Solution:

Total silk = 15 3/4 = 63/4 metres

Silk per kurta = 2 1/4 = 9/4 metres

Number of kurtas = (63/4) ÷ (9/4)

= 63/4 × 4/9 = 63/9 = 7

Answer: He can make exactly 7 kurtas.

Q5. Find three rational numbers between 3.1415 and 3.1416.

Answer:

Solution:

We need numbers between 3.1415 and 3.1416.

We can express them as fractions: 3.1415 = 31415/10000 and 3.1416 = 31416/10000

Possible rational numbers: 3.14151, 3.14155, 3.14159

As fractions: 314151/100000, 314155/100000, 314159/100000

Answer: Three rational numbers are 3.14151, 3.14155, and 3.14159 (or any other numbers between the given values).

Q6. Can you think of other way(s) to find a rational number between any two rational numbers?

Answer:

Solution:

Yes, there are multiple ways:

• Average method: The average of two rational numbers always lies between them. For a and b, (a + b)/2 is a rational number between a and b.
• Decimal method: Write both numbers in decimal form and insert a decimal between them. For example, between 0.12 and 0.13, we can take 0.125.
• Numerator/denominator adjustment: If a = p/q and b = r/s, we can find a rational number by cross-multiplication or by finding a common denominator and taking an intermediate numerator.

Answer: Other methods include using averages, decimal representation, or finding a common denominator and choosing an intermediate numerator.