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🔢 Chapter 3: The World of Numbers • Exercise Set 3.4

Verified step-by-step solutions for your class notes.

Q1

Exercise Set 3.4

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

  • -5/4 (= -1 1/4): Divide the interval between -2 and -1 into 4 equal segments; mark the point 1 segment to the left of -1 (or 5 units left of 0).
  • 2/3: Divide the unit interval between 0 and 1 into 3 equal parts; mark the second tick mark to the right of 0.
  • 1 1/2 (= 3/2): Located exactly midway between 1 and 2.
-2 -1 0 1 2 -5/4 (-1¼) 2/3 1½ (3/2)
Number Line Representation of -5/4, 2/3, and 1½
Q2

Exercise Set 3.4

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

  • Convert both fractions to a common denominator:
    -1/2 = -4/8
    1/4 = 2/8
  • Pick any three rational numbers whose numerators lie strictly between -4 and 2:
    -1/4 (or -2/8), -1/8, and 0 (or 1/8).
Q3

Exercise Set 3.4

3. Simplify the expression: (-1/4) + (5/12)

  • LCM(4, 12) = 12
  • -1/4 = -3/12
  • (-3/12) + (5/12) = (-3 + 5) / 12 = 2/12 = 1/6
Q4

Exercise Set 3.4

4. 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?

  • Total silk available = 15 3/4 = 63/4 metres
  • Silk required per kurta = 2 1/4 = 9/4 metres
  • Number of kurtas = (63/4) ÷ (9/4) = (63/4) × (4/9) = 63/9 = 7 kurtas
Q6

Exercise Set 3.4

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

  • Method of Equivalent Fractions: Convert both rational numbers to equivalent fractions with a much larger common denominator, then select any intermediate integer numerator (e.g., between 1/3 = 10/30 and 2/3 = 20/30, choose 11/30, 12/30, etc.).
  • Mediant Method: For two positive rational numbers a/b and c/d, the mediant (a + c)/(b + d) always lies strictly between them.
  • Decimal Expansion Method: Write both rational numbers as decimals and pick any terminating decimal lying numerically between them.