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Questions and Answers
What is the set of rational numbers denoted by?
What is the result of multiplying a rational number with the sum of two rational numbers, according to the distributivity property?
What is an example of an improper fraction?
What is the property that states the order of the numbers in an operation does not change the result?
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What is an example of a mixed number?
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What is a fraction that represents the same value as another fraction?
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Study Notes
Definition of Rational Numbers
- A rational number is a number that can be expressed as the ratio of two integers, i.e., a fraction.
- It can be written in the form
a/b, whereaandbare integers, andbis non-zero. - The set of rational numbers is denoted by
Q.
Properties of Rational Numbers
- Closure: The sum, difference, product, and quotient of two rational numbers are always rational numbers.
- Commutativity: The order of the numbers in an operation does not change the result.
- Associativity: The order in which operations are performed does not change the result.
- Distributivity: The multiplication of a rational number with the sum of two rational numbers is equal to the sum of the products.
Types of Rational Numbers
-
Proper fractions: Fractions where the numerator is less than the denominator, e.g.,
1/2,3/4. -
Improper fractions: Fractions where the numerator is greater than or equal to the denominator, e.g.,
3/2,5/3. -
Mixed numbers: A combination of a whole number and a proper fraction, e.g.,
2 1/2,3 3/4. -
Equivalent ratios: Different fractions that represent the same value, e.g.,
1/2and2/4.
Operations on Rational Numbers
- Addition: To add two rational numbers, add the numerators and keep the denominator the same.
- Subtraction: To subtract one rational number from another, subtract the numerators and keep the denominator the same.
- Multiplication: To multiply two rational numbers, multiply the numerators and multiply the denominators.
- Division: To divide one rational number by another, invert the second number and multiply.
Important Concepts
- Simplifying rational numbers: Expressing a rational number in its simplest form by dividing both numerator and denominator by their greatest common divisor.
- Comparing rational numbers: Comparing two rational numbers by converting them to equivalent fractions with the same denominator.
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Description
Test your knowledge of rational numbers, including their definition, properties, types, operations, and important concepts like simplification and comparison.
