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🔢 Chapter 3: The World of Numbers • Exercise Set 3.1

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Exercise Set 3.1 4Exercise Set 3.2 4Exercise Set 3.3 8Exercise Set 3.4 5Exercise Set 3.5 5End-of-Chapter Exercises 14All Exercises 40
Q1

Exercise Set 3.1

1. A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with?

  • Rate of exchange: 2 bags of spices = 15 copper ingots.
  • Number of sets of 2 bags in 12 bags: 12 / 2 = 6 sets.
  • Total copper ingots received: 6 × 15 = 90 copper ingots.
Q2

Exercise Set 3.1

2. Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.

  • Common Property: They are all consecutive prime numbers (numbers greater than 1 with no positive divisors other than 1 and themselves). Specifically, they are the prime numbers between 10 and 20.
  • Next Three Numbers: The next three prime numbers following 19 are 23, 29, and 31.
Q3

Exercise Set 3.1

3. We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.

No, natural numbers are not closed under subtraction.

  • Subtracting a larger natural number from a smaller one or subtracting a number from itself does not yield a natural number:
    • 3 - 5 = -2 (which is a negative integer, not a natural number).
    • 4 - 4 = 0 (zero is a whole number/integer, not a natural number).
Q4

Exercise Set 3.1

4. Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?

  • Count on one hand: The four fingers (index, middle, ring, pinky) each have 3 distinct segments/joints. Using the thumb as a pointer gives:
    4 fingers × 3 joints = 12 distinct counts on a single hand.
  • Relation to base-12 system: This physiological method is the natural foundation for duodecimal (base-12) systems. It explains the historical division of days and nights into 12 hours each (total 24 hours), the 12 signs of the zodiac, and units like dozens (12) and grosses (144).