Rational Numbers Study Guide

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be written in the form a/b, where a and b are integers and b is not equal to 0.

Examples of Rational Numbers

• 3/4
• -5/2
• 1

Properties of Rational Numbers

Rational numbers have the following properties:

1. Closure: The sum, difference, or product of any two rational numbers is also a rational number.
2. Commutative Property: For addition and multiplication, the order of the rational numbers does not change the result.
3. Associative Property: For addition and multiplication, the grouping of rational numbers does not change the result.
4. Identity Property: The sum of a rational number and 0 is the number itself, and the product of a rational number and 1 is the number itself.
5. Inverse Property: Every rational number has an additive inverse and a multiplicative inverse, except for 0.

Operations with Rational Numbers

There are four basic operations that can be performed with rational numbers:

1. Addition: To add two rational numbers, find a common denominator, add the numerators, and simplify the fraction if necessary.
2. Subtraction: To subtract two rational numbers, find a common denominator, subtract the numerators, and simplify the fraction if necessary.
3. Multiplication: To multiply two rational numbers, multiply the numerators together and the denominators together, and simplify the fraction if necessary.
4. Division: To divide two rational numbers, multiply the first number by the reciprocal of the second number, and simplify the fraction if necessary.

Real World Applications

Rational numbers are used in various real-world situations such as calculating distances, measurements, and financial transactions.

Study Tips

To master rational numbers, it's important to practice solving problems involving operations with fractions and decimals. Understanding the concept of equivalent fractions and knowing how to simplify fractions will also be helpful.

Remember to always check your work by verifying that the result is indeed a rational number. Practice and repetition will build confidence and proficiency in working with rational numbers.