Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to 0. In other words, a rational number is any number that can be written in the form p/q, where p and q are integers and q is not zero.

Examples of Rational Numbers

2/3
-5/7
1
-3

Properties of Rational Numbers

Closure Property: The sum, difference, or product of any two rational numbers is also a rational number.
Commutative Property: For addition and multiplication, the order of the rational numbers does not matter.
Associative Property: For addition and multiplication, the grouping of rational numbers does not matter.
Identity Property: The sum of any rational number and 0 is the rational number itself.
Inverse Property: Every rational number has an additive inverse (its negative) and a multiplicative inverse (reciprocal).

Operations with Rational Numbers

Rational numbers can be operated on using the following operations:

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

Study Guide

When studying rational numbers, make sure to understand the concept of fractions and how to perform operations with fractions. Practice finding common denominators and simplifying fractions. Familiarize yourself with the properties of rational numbers and how they apply to different operations. Additionally, work on word problems involving rational numbers to apply your knowledge in real-life situations.

Remember to always check your work and simplify your answers whenever possible.

Feel free to ask if you have any more questions or need further clarification on rational numbers!

◂Math Worksheets and Study Guides Eighth Grade. Real numbers

The resources above cover the following skills:

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]

Expressions and Equations

Work with radicals and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. [8-EE2]