Podcast
Questions and Answers
A rational number is a real number that can be expressed as the ratio of two ______, i.e., a fraction.
A rational number is a real number that can be expressed as the ratio of two ______, i.e., a fraction.
integers
Rational numbers can be ______, subtracted, multiplied, and divided (except by zero).
Rational numbers can be ______, subtracted, multiplied, and divided (except by zero).
added
Rational numbers can be expressed in ______ form, which may be finite or infinite.
Rational numbers can be expressed in ______ form, which may be finite or infinite.
decimal
Irrational numbers cannot be expressed as a finite ______ or fraction.
Irrational numbers cannot be expressed as a finite ______ or fraction.
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To add or subtract rational numbers, find a common ______ and then add or subtract the numerators.
To add or subtract rational numbers, find a common ______ and then add or subtract the numerators.
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To multiply rational numbers, multiply the ______ and denominators separately.
To multiply rational numbers, multiply the ______ and denominators separately.
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To divide rational numbers, invert the second number and then ______.
To divide rational numbers, invert the second number and then ______.
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Two ratios a/b and c/d are equivalent if ad = b______.
Two ratios a/b and c/d are equivalent if ad = b______.
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A rational number can be simplified by dividing both the numerator and ______ by their greatest common divisor (GCD).
A rational number can be simplified by dividing both the numerator and ______ by their greatest common divisor (GCD).
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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.
- It can be written in the form
a/b, whereaandbare integers, andbis non-zero.
Properties
- Rational numbers can be added, subtracted, multiplied, and divided (except by zero).
- The result of these operations is always a rational number.
- Rational numbers can be expressed in decimal form, which may be finite or infinite.
Examples
- 3/4, 22/7, 1/2 are all rational numbers.
- Integers, such as 5, can be written as rational numbers (5/1).
- Finite decimals, such as 0.5, are also rational numbers.
Irrational Numbers vs. Rational Numbers
- Irrational numbers cannot be expressed as a finite decimal or fraction.
- Examples of irrational numbers include π, e, and the square root of 2.
Operations with Rational Numbers
- Addition and Subtraction: To add or subtract rational numbers, find a common denominator and then add or subtract the numerators.
- Multiplication: To multiply rational numbers, multiply the numerators and denominators separately.
- Division: To divide rational numbers, invert the second number and then multiply.
Equivalent Ratios
- Two ratios
a/bandc/dare equivalent ifa*d = b*c. - Equivalent ratios have the same value, but may not have the same form.
Simplifying Rational Numbers
- A rational number can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
- The resulting simplified form is an equivalent ratio.
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Description
This quiz covers the definition, properties, and operations of rational numbers, including equivalent ratios and simplification. Test your knowledge of these fundamental math concepts.
