Questions and Answers
Which of the following numbers is NOT a rational number?
What is the simplest form of the rational number 12/18?
Which of the following represents the result of adding 1/3 and 1/4?
What is the result of multiplying 2/5 by 3/7?
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Which of the following is equivalent to the ratio 4/6?
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What is the result of dividing 5/8 by 2/3?
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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., it can be written in the form:
a/b
where a and b are integers, and b is non-zero.
Properties
- A rational number can be expressed as a finite decimal or a repeating decimal.
- The set of rational numbers is denoted by Q.
- Rational numbers can be added, subtracted, multiplied, and divided (except by zero) using the same rules as integers.
- The result of any arithmetic operation on rational numbers is always a rational number.
Examples
- 3/4, 22/7, -1/2 are all rational numbers.
- 0.5, 0.25, 0.333... (repeating) are also rational numbers.
Equivalent Ratios
- Two ratios a/b and c/d are equivalent if ad = bc.
- Equivalent ratios represent the same rational number.
Simplification of Rational Numbers
- A rational number can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
- A rational number in its simplest form is said to be in lowest terms.
Operations on Rational Numbers
- Addition and subtraction:
- To add or subtract rational numbers, find a common denominator and then add or subtract the numerators.
- Example: 1/4 + 1/6 = (3+2)/12 = 5/12
- Multiplication:
- To multiply rational numbers, multiply the numerators and denominators separately.
- Example: 1/2 × 3/4 = (1×3)/(2×4) = 3/8
- Division:
- To divide rational numbers, invert the second number and then multiply.
- Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = (2×4)/(3×3) = 8/9
Definition of Rational Numbers
- A rational number is a real number that can be expressed as the ratio of two integers in the form a/b, where a and b are integers, and b is non-zero.
Properties of Rational Numbers
- Can be expressed as a finite decimal or a repeating decimal.
- Denoted by the set Q.
- Can be added, subtracted, multiplied, and divided (except by zero) using the same rules as integers.
- The result of any arithmetic operation on rational numbers is always a rational number.
Examples of Rational Numbers
- 3/4, 22/7, -1/2 are all rational numbers.
- 0.5, 0.25, 0.333...(repeating) are also rational numbers.
Equivalent Ratios
- Two ratios a/b and c/d are equivalent if ad = bc.
- Equivalent ratios represent the same rational number.
Simplification of Rational Numbers
- Can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
- A rational number in its simplest form is said to be in lowest terms.
Operations on Rational Numbers
Addition and Subtraction
- To add or subtract rational numbers, find a common denominator and then add or subtract the numerators.
- Example: 1/4 + 1/6 = (3+2)/12 = 5/12.
Multiplication
- To multiply rational numbers, multiply the numerators and denominators separately.
- Example: 1/2 × 3/4 = (1×3)/(2×4) = 3/8.
Division
- To divide rational numbers, invert the second number and then multiply.
- Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = (2×4)/(3×3) = 8/9.
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Description
Learn about the definition and properties of rational numbers, including their representation, arithmetic operations, and notation. Test your understanding of Q and its rules.