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Questions and Answers
What is a fundamental property of rational numbers?
What is a fundamental property of rational numbers?
- They always have a terminating decimal expansion.
- They are always prime numbers.
- They are never negative.
- They can be expressed as a quotient or fraction of two integers. (correct)
What is the first step in adding two rational numbers?
What is the first step in adding two rational numbers?
- Multiply the fractions together.
- Find a common denominator (LCD) for the two fractions. (correct)
- Add the numerators and keep the same denominator.
- Subtract the denominators and keep the same numerator.
How do you subtract two rational numbers?
How do you subtract two rational numbers?
- Multiply the fractions together and then subtract.
- Add the numerators and keep the same denominator.
- Divide the two fractions.
- Find a common denominator, convert both fractions, and then subtract the numerators. (correct)
What is the result of multiplying two rational numbers?
What is the result of multiplying two rational numbers?
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How do you divide two rational numbers?
How do you divide two rational numbers?
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Why is it essential to simplify the resulting fraction when performing arithmetic operations with rational numbers?
Why is it essential to simplify the resulting fraction when performing arithmetic operations with rational numbers?
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What is a key rule to keep in mind when adding or subtracting rational numbers?
What is a key rule to keep in mind when adding or subtracting rational numbers?
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What is true about the decimal expansion of rational numbers?
What is true about the decimal expansion of rational numbers?
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Study Notes
Properties of Rational Numbers
- A rational number is a number that can be expressed as the quotient or fraction of two integers (p/q), where q ≠0.
- Rational numbers can be expressed in decimal form, and the decimal expansion is finite or recurring.
- Rational numbers satisfy the usual rules of arithmetic, including commutativity, associativity, and distributivity.
Adding Rational Numbers
- To add two rational numbers, find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Add the numerators and keep the same denominator.
Subtracting Rational Numbers
- To subtract two rational numbers, find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Subtract the numerators and keep the same denominator.
Multiplying Rational Numbers
- To multiply two rational numbers, multiply the numerators.
- Multiply the denominators.
- Simplify the resulting fraction, if possible.
Dividing Rational Numbers
- To divide two rational numbers, invert the second fraction (flip the numerator and denominator).
- Multiply the fractions.
- Simplify the resulting fraction, if possible.
Important Note
- When performing arithmetic operations with rational numbers, it's essential to simplify the resulting fractions to their simplest form.
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