Rational Numbers Properties Quiz

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).