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Questions and Answers
What is the definition of a rational number?
What is the definition of a rational number?
- A real number that can be expressed as a repeating decimal
- A real number that can be expressed as the ratio of two integers (correct)
- A real number that can be expressed as an irrational number
- A real number that can be expressed as a finite decimal
What is the notation for rational numbers?
What is the notation for rational numbers?
- a / b (correct)
- a × b
- a - b
- a + b
Which of the following operations is not allowed on rational numbers?
Which of the following operations is not allowed on rational numbers?
- Multiplication
- Division by zero (correct)
- Subtraction
- Addition
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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