Equal To

In math, the concept of "equal to" refers to the relationship between two quantities that have the same value. The symbol used to denote equality is "=", and it is used to compare two expressions or values to determine if they are the same.

Understanding Equality

When we say that two quantities are equal, it means that they represent the same amount or value. For example, 5 = 5, which reads "5 is equal to 5," indicates that both 5s are representing the same quantity.

Equality is a fundamental concept in mathematics and is used in various operations such as addition, subtraction, multiplication, division, and equations.

Examples of Equality

Here are some examples of equality in math:

2 + 3 = 5
10 - 4 = 6
3 × 4 = 12
20 ÷ 5 = 4

Properties of Equality

When working with equality, it's important to understand the properties that govern the relationship between two equal quantities:

Reflexive Property: Any quantity is equal to itself. For example, a = a.
Symmetric Property: If a = b, then b = a.
Transitive Property: If a = b and b = c, then a = c.
Addition Property of Equality: If a = b, then a + c = b + c.
Subtraction Property of Equality: If a = b, then a - c = b - c.
Multiplication Property of Equality: If a = b, then a × c = b × c.
Division Property of Equality: If a = b and c ≠ 0, then a ÷ c = b ÷ c.

Study Guide

When studying the concept of "equal to," it's important to practice solving equations and understanding the properties of equality. Here are some key points to focus on:

Practice writing and solving equations using the "=" symbol.
Understand the reflexive, symmetric, and transitive properties of equality.
Work on applying the addition, subtraction, multiplication, and division properties of equality when solving equations.
Review real-life examples of equality to understand its practical applications.
Complete practice problems to reinforce your understanding of equality in math.

By mastering the concept of "equal to" and its properties, you'll be well-equipped to tackle more advanced mathematical concepts and problem-solving tasks.

◂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]