6 Questions
What is a rational number?
A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
What is an example of the commutative property of rational numbers?
2/3 × 3/2 = 1
How do you add or subtract rational numbers?
You need to have the same denominator.
How do you multiply rational numbers?
You multiply the numerators and multiply the denominators.
What is the standard form of a rational number?
A rational number where the numerator and denominator have no common factors except 1.
Can rational numbers be represented on the number line?
Yes, rational numbers can be represented on the number line.
Study Notes
Rational Numbers
- A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Examples: 3/4, 22/7, -3/5
Properties of Rational Numbers
- Commutativity: The order of the numbers does not change the result. (e.g., 2/3 × 3/2 = 1)
- Associativity: The order in which we multiply rational numbers does not change the result. (e.g., (2/3 × 3/4) × 4/5 = 2/3 × (3/4 × 4/5))
- Distributivity: The multiplication of rational numbers distributes over addition. (e.g., 2/3 × (3/4 + 2/5) = 2/3 × 3/4 + 2/3 × 2/5)
Addition and Subtraction of Rational Numbers
- To add or subtract rational numbers, we need to have the same denominator.
- Like fractions: Fractions with the same denominator.
- Unlike fractions: Fractions with different denominators.
Multiplication and Division of Rational Numbers
- To multiply rational numbers, multiply the numerators and multiply the denominators.
- To divide rational numbers, invert the second number and then multiply.
Representation of Rational Numbers on the Number Line
- Rational numbers can be represented on the number line.
- Every rational number corresponds to a unique point on the number line.
Standard Form of Rational Numbers
- A rational number is said to be in standard form if the numerator and denominator have no common factors except 1.
- Example: 2/3 is in standard form, but 4/6 is not (it can be simplified to 2/3).
Rational Numbers
- A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Examples of rational numbers include 3/4, 22/7, and -3/5.
Properties of Rational Numbers
Commutativity
- The order of the numbers does not change the result of a multiplication operation.
- Example: 2/3 × 3/2 = 1.
Associativity
- The order in which we multiply rational numbers does not change the result.
- Example: (2/3 × 3/4) × 4/5 = 2/3 × (3/4 × 4/5).
Distributivity
- The multiplication of rational numbers distributes over addition.
- Example: 2/3 × (3/4 + 2/5) = 2/3 × 3/4 + 2/3 × 2/5.
Operations on Rational Numbers
Addition and Subtraction
- To add or subtract rational numbers, they must have the same denominator.
- Like fractions are fractions with the same denominator.
- Unlike fractions are fractions with different denominators.
Multiplication
- To multiply rational numbers, multiply the numerators and multiply the denominators.
Division
- To divide rational numbers, invert the second number and then multiply.
Representation of Rational Numbers
- Rational numbers can be represented on the number line.
- Every rational number corresponds to a unique point on the number line.
Standard Form of Rational Numbers
- A rational number is in standard form if the numerator and denominator have no common factors except 1.
- Example: 2/3 is in standard form, but 4/6 is not (it can be simplified to 2/3).
Test your understanding of rational numbers, including their definition and properties such as commutativity, associativity, and distributivity.
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