Mathematics Class 9: Frequently Asked Questions

 

Below are some commonly asked questions and their answers related to Class 9 Mathematics. This should help provide clarity on key concepts and problem-solving techniques.

1. What are Rational Numbers?

Rational Numbers

: A rational number is any number that can be expressed as the quotient or fraction (\frac{p}{q}), where (p) and (q) are integers and (q \neq 0). For example, (\frac{1}{2}), (-3), and (0.75) (which is (\frac{3}{4})) are all rational numbers.

2. How do you find the Least Common Multiple (LCM) of two numbers?

Finding the LCM

: The LCM of two numbers is the smallest number that is a multiple of both. To find the LCM:

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in any of the numbers.

For instance, to find the LCM of 12 and 15:

• Prime factors of 12: (2^2 \times 3)

• Prime factors of 15: (3 \times 5)

LCM = (2^2 \times 3 \times 5 = 60).

3. What is the Pythagorean Theorem?

Pythagorean Theorem

: This theorem applies to right-angled triangles. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, if (c) is the hypotenuse, and (a) and (b) are the other two sides, then: [ c^2 = a^2 + b^2 ]

4. How do you solve a linear equation in one variable?

Solving Linear Equations

: A linear equation in one variable is of the form (ax + b = 0).

To solve:

1. Isolate the variable (x) by performing inverse operations.

2. Simplify the equation until (x) is on one side and the constants are on the other.

Example: Solve (3x + 5 = 11).

• Subtract 5 from both sides: (3x = 6).

• Divide by 3: (x = 2).

5. What are the properties of parallel lines and a transversal?

Properties

:

• Alternate Interior Angles

  are equal.

• Corresponding Angles

  are equal.

• Co-interior (Consecutive Interior) Angles

  are supplementary (add up to 180°).

If two parallel lines are cut by a transversal, these properties help in solving various angle-related problems.

6. How do you calculate the area of a triangle?

Area of a Triangle

: The area (A) can be calculated using the formula: [ A = \frac{1}{2} \times \text{base} \times \text{height} ]

For example, for a triangle with a base of 5 cm and a height of 4 cm: [ A = \frac{1}{2} \times 5 \times 4 = 10 , \text{cm}^2 ]

These answers highlight important concepts and problem-solving methods essential for Class 9 Mathematics. If you have more specific questions or need further assistance, feel free to ask!