Rational Numbers Properties and Definition

Questions and Answers

A number that can be expressed as the product of two integers

A number that can be expressed as the sum of two integers

A number that can be expressed as the difference of two integers

A number that can be expressed as the quotient or fraction of two integers (correct)

Associativity

Closure

Distributivity

Commutativity (correct)

Add the denominators

Subtract the numerators

Convert both numbers to have the same denominator (if necessary) (correct)

Multiply the numerators

The product of the numerators and the product of the denominators Signup and view all the answers

Convert both numbers to have the same denominator (if necessary) Signup and view all the answers

They are closed under addition, subtraction, multiplication, and division (except by zero) Signup and view all the answers

To express the fraction in its simplest form Signup and view all the answers

A fraction with the same denominator Signup and view all the answers

Study Notes

A rational number is a number that can be expressed as the quotient or fraction of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
It can also be defined as a finite decimal or a ratio of two integers.

Closure: The set of rational numbers is closed under addition, subtraction, multiplication, and division (except by zero).
Commutativity: The order of rational numbers does not change the result of addition and multiplication.
Associativity: The order in which rational numbers are added or multiplied does not change the result.
Distributivity: Multiplication of rational numbers distributes over addition.

To add two rational numbers, follow these steps:
1. Convert both numbers to have the same denominator (if necessary).
2. Add the numerators.
3. Keep the same denominator.

To multiply two rational numbers, follow these steps:
1. Multiply the numerators.
2. Multiply the denominators.
3. Simplify the resulting fraction (if possible).

To subtract one rational number from another, follow these steps:
1. Convert both numbers to have the same denominator (if necessary).
2. Subtract the numerators.
3. Keep the same denominator.

A rational number is a number that can be expressed as the quotient or fraction of two integers (p/q), where p and q are integers and q ≠ 0.
It can also be defined as a finite decimal or a ratio of two integers.

The set of rational numbers is closed under addition, subtraction, multiplication, and division (except by zero).
The order of rational numbers does not change the result of addition and multiplication (commutativity).
The order in which rational numbers are added or multiplied does not change the result (associativity).
Multiplication of rational numbers distributes over addition (distributivity).