Podcast
Questions and Answers
What is the correct method to rationalize the fraction $rac{2}{ ext{root}(3x)}$?
What is the correct method to rationalize the fraction $rac{2}{ ext{root}(3x)}$?
- Divide by $ ext{root}(3x)$ in either the numerator or the denominator
- Multiply by $ ext{root}(3x)$ in the numerator and denominator (correct)
- Multiply by $ ext{root}(3x)$ in either the numerator or the denominator
- Divide by $ ext{root}(3x)$ in the numerator and denominator
Which of the following describes a correct step in simplifying $rac{12x}{18y}$?
Which of the following describes a correct step in simplifying $rac{12x}{18y}$?
- Divide both the numerator and denominator by 3
- Divide both the numerator and denominator by 6 (correct)
- Multiply both the numerator and denominator by 6
- Multiply both the numerator and denominator by 3
Which of the following is classified as a rational number?
Which of the following is classified as a rational number?
- $\sqrt{2}$
- $\frac{5}{2}$ (correct)
- 0.123456...
- $\pi$
Which type of number cannot be expressed as a simple fraction?
Which type of number cannot be expressed as a simple fraction?
What happens when you multiply $rac{2}{\sqrt{3x}}$ by $\frac{1}{\sqrt{3x}}$?
What happens when you multiply $rac{2}{\sqrt{3x}}$ by $\frac{1}{\sqrt{3x}}$?
What type of number is $rac{3}{5}$?
What type of number is $rac{3}{5}$?
Which of the following CANNOT be expressed as a simple fraction?
Which of the following CANNOT be expressed as a simple fraction?
To find the decimal form of an irrational number, we may need to:
To find the decimal form of an irrational number, we may need to:
How can we rationalize irrational numbers in algebraic expressions?
How can we rationalize irrational numbers in algebraic expressions?
Which of the following is an irrational number?
Which of the following is an irrational number?
Study Notes
Exploring Maths Class 9th: Number System, Rationalization, and Real Numbers with RD Sharma
In this comprehensive article, we will delve into the fascinating world of Maths Class 9th, focusing on topics such as Rationalization of Denominators, Simplification of Fractions, Real Numbers, Rational Numbers, and Irrational Numbers as presented in RD Sharma's celebrated textbooks.
Rationalization of Denominators
To rationalize a fraction containing a radical expression in the denominator, we multiply the fraction by a form of 1 that will eliminate the radical. For example, to rationalize the fraction, we write:
$$\frac{2}{\sqrt{3x}}$$
Multiply both the numerator and denominator by $\sqrt{3x}$:
$$\frac{2}{\sqrt{3x}} \cdot \frac{\sqrt{3x}}{\sqrt{3x}} = \frac{2\sqrt{3x}}{3x}$$
Simplification of Fractions
To simplify a fraction, we reduce the fraction to its lowest terms. To do this, the numerator and denominator must have common factors. For instance, consider the fraction $\frac{12x}{18y}$:
Divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 6:
$$\frac{12x}{18y} = \frac{2x}{3y}$$
Real Numbers
Real numbers include all numbers we use in everyday life, such as integers, fractions, and decimal numbers. Real numbers are classified as either rational numbers (fractions) or irrational numbers (numbers that cannot be expressed as a simple fraction).
Rational Numbers
Rational numbers are the sum of two integers divided by a nonzero integer. For instance, $\frac{3}{5}$ and $-\frac{2}{7}$ are both rational numbers. To find the decimal form of a rational number, we can use long division or a calculator.
Irrational Numbers
Irrational numbers are numbers that cannot be expressed as a simple fraction, such as $\pi$, $\sqrt{2}$, and $e$. As there is no repeating pattern in their decimal representation, these numbers can only be expressed as infinite decimals.
To rationalize irrational numbers or square roots in algebraic expressions, we may multiply both the numerator and denominator by a form of 1 that will eliminate the radical, as we saw in the Rationalization of Denominators section.
In conclusion, Maths Class 9th is a fruitful ground for learning about various number systems and methods for simplifying fractions. By understanding these concepts, we set the foundation for more advanced mathematics in the future. For further exploration and practice, refer to RD Sharma's textbooks and online resources. Happy learning!
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Description
Delve into Rationalization of Denominators, Simplification of Fractions, Real Numbers, Rational Numbers, and Irrational Numbers in Maths Class 9th with RD Sharma's textbooks. Learn how to rationalize fractions, simplify fractions, and differentiate between rational and irrational numbers.
