Operations with Rational Numbers

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What is a rational number?
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A rational number is any number that can be expressed as the quotient or fraction of two integers, with a non-zero denominator.
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How do you add two rational numbers?
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To add two rational numbers, make sure they have a common denominator, then add their numerators.
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What is the additive inverse of a rational number?
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The additive inverse of a rational number is another rational number that, when added to the original, equals zero.
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How do you subtract rational numbers?
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To subtract rational numbers, change the sign of the number being subtracted and then add them using common denominators.
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How do you multiply two rational numbers?
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To multiply two rational numbers, multiply their numerators together and their denominators together.
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What is the reciprocal of a rational number?
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The reciprocal of a rational number is obtained by swapping its numerator and denominator.
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How do you divide one rational number by another?
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To divide by a rational number, multiply by its reciprocal.
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What is the result when a rational number is multiplied by zero?
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When a rational number is multiplied by zero, the result is zero.
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How do you find a common denominator for two rational numbers?
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Find the least common multiple (LCM) of the denominators to use as a common denominator.
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What is the associative property in the context of rational numbers?
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The associative property states that the way numbers are grouped does not affect their sum or product.
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What is the commutative property when working with rational numbers?
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The commutative property allows the order of addition or multiplication to be changed without affecting the result.
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What does simplifying a rational number mean?
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Simplifying a rational number means reducing it to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).
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How do you express a mixed number as a rational number?
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To express a mixed number as a rational number, convert the whole number to a fraction and add it to the fractional part.
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Can two rational numbers be equal? Give an example.
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Yes, for example, 1/2 is equal to 2/4.
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What happens when you add a rational number to its opposite?
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Adding a rational number to its opposite results in zero.
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