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Questions and Answers
What is the definition of a rational number?
What is the definition of a rational number?
What is the notation for rational numbers?
What is the notation for rational numbers?
Which of the following operations is not allowed on rational numbers?
Which of the following operations is not allowed on rational numbers?
Which of the following numbers is a rational number?
Which of the following numbers is a rational number?
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What is the condition for two ratios to be equivalent?
What is the condition for two ratios to be equivalent?
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How can a rational number be simplified?
How can a rational number be simplified?
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Study Notes
Definition
A rational number is a real number that can be expressed as the ratio of two integers, i.e., a fraction.
Notation
Rational numbers can be written in the form:
a/b
where a and b are integers, and b is non-zero.
Properties
- The set of rational numbers is denoted by Q.
- Rational numbers can be added, subtracted, multiplied, and divided (except by zero).
- Rational numbers are closed under these operations, meaning that the result of performing these operations on rational numbers is always a rational number.
Examples
- 3/4 is a rational number.
- 22/7 is a rational number.
- 0.5 is a rational number, since it can be written as 1/2.
- π (pi) is not a rational number, since it cannot be expressed as a finite decimal or fraction.
Equivalent Ratios
- Two ratios a/b and c/d are equivalent if ad = bc.
- For example, 1/2 and 2/4 are equivalent ratios.
Simplification
- A rational number can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
- For example, 6/8 can be simplified to 3/4.
Ordering
- Rational numbers can be compared and ordered using the usual rules for fractions.
- For example, 1/2 < 2/3, since 3(1) < 2(2).
Definition of Rational Numbers
- A rational number is a real number that can be expressed as a ratio of two integers, or a fraction.
Notation of Rational Numbers
- Rational numbers can be written in the form a/b, where a and b are integers and b is non-zero.
Properties of Rational Numbers
- The set of rational numbers is denoted by Q.
- Rational numbers can be added, subtracted, multiplied, and divided (except by zero).
- Rational numbers are closed under these operations, meaning the result is always a rational number.
Examples of Rational Numbers
- 3/4 is a rational number.
- 22/7 is a rational number.
- 0.5 is a rational number, since it can be written as 1/2.
- π (pi) is not a rational number, since it cannot be expressed as a finite decimal or fraction.
Equivalent Ratios
- Two ratios a/b and c/d are equivalent if ad = bc.
- For example, 1/2 and 2/4 are equivalent ratios.
Simplification of Rational Numbers
- A rational number can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
- For example, 6/8 can be simplified to 3/4.
Ordering of Rational Numbers
- Rational numbers can be compared and ordered using the usual rules for fractions.
- For example, 1/2 < 2/3, since 3(1) < 2(2).
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Description
Learn about rational numbers, their notation, and properties, including their ability to be added, subtracted, multiplied, and divided.
