Real Numbers
Real numbers include all the rational and irrational numbers. They can be represented on the number line and are used in various mathematical calculations and operations.
Types of Real Numbers
- Rational Numbers: These are numbers that can be expressed as a fraction of two integers, where the denominator is not equal to zero. Examples include 1/2, 3/4, 5, and -2.
- Irrational Numbers: These are numbers that cannot be expressed as a fraction, and their decimal expansions are non-repeating and non-terminating. Examples include √2, π, and e.
- Integers: These are whole numbers, including positive and negative numbers, as well as zero. Examples include -3, -2, -1, 0, 1, 2, 3.
- Natural Numbers: Also known as counting numbers, these are positive integers starting from 1. Examples include 1, 2, 3, 4, 5.
- Whole Numbers: These are non-negative integers, including zero. Examples include 0, 1, 2, 3, 4.
Properties of Real Numbers
Real numbers have certain properties that govern their behavior in mathematical operations. These properties include:
- Commutative Property: a + b = b + a and a * b = b * a
- Associative Property: (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c)
- Distributive Property: a * (b + c) = a * b + a * c
- Identity Property: a + 0 = a and a * 1 = a
- Inverse Property: a + (-a) = 0 and a * (1/a) = 1
Study Guide
When studying real numbers, it's important to understand the classification of real numbers, their properties, and how they are used in mathematical operations. Here are some key points to focus on:
- Learn to classify numbers as rational, irrational, integers, natural, or whole numbers.
- Understand the properties of real numbers and how they apply to addition, subtraction, multiplication, and division.
- Practice representing real numbers on the number line and comparing their magnitudes.
- Work on solving problems involving real numbers, including word problems and mathematical expressions.
- Explore real-world applications of real numbers in various fields such as science, finance, and engineering.
By mastering the properties and classifications of real numbers, you will have a solid foundation for more advanced mathematical concepts and applications.
[Real Numbers] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Seventh Grade. Rational and Irrational Numbers
Study Guide
Rational and Irrational Numbers 
Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Connections to the Grade 7 Focal Points (NCTM)
Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.