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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.
Natural numbers are not closed under the operation of subtraction because the result of subtracting one natural number from another is not always a natural number itself. For instance, subtracting a smaller number from a larger one like 5 minus 2 gives 3, which is a natural number. However, reversinRead more
Natural numbers are not closed under the operation of subtraction because the result of subtracting one natural number from another is not always a natural number itself. For instance, subtracting a smaller number from a larger one like 5 minus 2 gives 3, which is a natural number. However, reversing the order to 2 minus 5 results in negative 3. Since negative numbers are integers and not natural numbers, closure does not hold true.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessAncient 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?
Each of the four fingers has three distinct joints, allowing you to count up to 12 on a single hand by using your thumb as a pointer to touch each joint. This practical method is the foundation of ancient base-12 counting systems, known as duodecimal systems. It explains why historical cultures settRead more
Each of the four fingers has three distinct joints, allowing you to count up to 12 on a single hand by using your thumb as a pointer to touch each joint. This practical method is the foundation of ancient base-12 counting systems, known as duodecimal systems. It explains why historical cultures settled on twelve as a primary mathematical grouping, which influenced modern measurements like twelve inches in a foot and twelve hours on a clock face.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessThe temperature in the high-altitude desert of Ladakh is recorded as 4 °C at noon. By midnight, it drops by 15 °C. What is the midnight temperature?
The recorded temperature at noon in the high-altitude desert of Ladakh starts at 4 degrees Celsius. To find the new temperature after a drop of 15 degrees Celsius by midnight, we must subtract 15 from the initial value. Setting up the arithmetic expression gives 4 minus 15. Calculating this integerRead more
The recorded temperature at noon in the high-altitude desert of Ladakh starts at 4 degrees Celsius. To find the new temperature after a drop of 15 degrees Celsius by midnight, we must subtract 15 from the initial value. Setting up the arithmetic expression gives 4 minus 15. Calculating this integer operation yields a final value of -11. Therefore, the temperature at midnight is -11 degrees Celsius.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessA spice trader takes a loan (debt) of rupees 850. The next day, he makes a profit (fortune) of rupees 1,200. The following week, he incurs a loss of rupees 450. Write this sequence as an equation using integers and calculate his final financial standing.
We can represent financial transactions using signed integers where debts and losses are negative, and profits are positive. The trader starts with a loan of -850 rupees, adds a profit of +1200 rupees, and adds a loss of -450 rupees. The complete sequence forms the integer equation -850 + 1200 - 450Read more
We can represent financial transactions using signed integers where debts and losses are negative, and profits are positive. The trader starts with a loan of -850 rupees, adds a profit of +1200 rupees, and adds a loss of -450 rupees. The complete sequence forms the integer equation -850 + 1200 – 450. Adding the numbers together gives 350 – 450, which equals -100. His final financial standing is a net debt of 100 rupees.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessHow is it different from the algebraic expression in Example 1?
The algebraic expression in Example 1 is 4x + 5y + 3, where the variables x and y appear separately in different terms. In Example 2, the expression is 200l + 160w + 50lw. The important difference is that the term 50lw contains two variables multiplied together. Example 1 includes a constant term 3,Read more
The algebraic expression in Example 1 is 4x + 5y + 3, where the variables x and y appear separately in different terms. In Example 2, the expression is 200l + 160w + 50lw. The important difference is that the term 50lw contains two variables multiplied together. Example 1 includes a constant term 3, but Example 2 has no constant term. Also, Example 1 is about counting pens and pencils, while Example 2 is related to the cost of fencing and seeds.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-2/
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