We know that Natural Numbers are closed under addition the sum of any two natural numbers Class 9

We know that Natural Numbers are closed under addition the sum of any two natural numbers Class 9

Question 1.

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. Class 9

Solution:

Natural numbers are not closed under subtraction.

Examples:

i. 3 - 5 = -2,

Here, -2 is not a natural number.

ii. 7 - 7 = 0

Here, 0 is not a natural number.

Since subtraction of natural numbers can result in zero or negative numbers, natural numbers are not closed under subtraction.

Question 2.

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? Class 9

Solution:

Each of the four fingers (index, middle, ring, and little finger) has 3 joints.

Total joints = 4 × 3 = 12

The thumb is used as a pointer to count these joints.

Thus, one can count to 12 on one hand.

This method leads to counting in groups of 12, forming the basis of the base-12 (duodecimal) system.

Examples of its use even today:

12 months in a year

12 inches in a foot

12 hours on a clock

24 hours in a day (2 × 12)