Mathematics Class IX

Number Systems
Polynomials
Coordinate Geometry
Lines and Angles
Triangles
Circles
Constructions
Heron’s Formula
Surface Areas and Volumes
Statistics
Probability

Operations on Real Numbers

1. The sum, difference, product and quotient of two rational numbers will be rational.

Example:

2. If we add or subtract a rational number with an irrational number then the result will be irrational.

Example:

If is a rational number and is an irrational number then and are irrational numbers.

3. If we multiply or divide a non-zero rational number with an irrational number then the result will be irrational.

Example:

If is a rational number and is an irrational number then and are irrational numbers.

4. The sum, difference, product and quotient of two irrational numbers could be rational or irrational.

Example:

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