Equations

What is an Equation?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) and can have variables, constants, and operations.

Parts of an Equation

There are three main parts of an equation:

Left-hand side (LHS): This is the expression on the left side of the equal sign.
Right-hand side (RHS): This is the expression on the right side of the equal sign.
Equal sign (=): This symbol shows that the expressions on both sides of the equal sign are equal.

Types of Equations

Equations can be classified into various types based on their structure and the number of solutions they have. Some common types of equations include:

Linear Equations
Quadratic Equations
Cubic Equations
Exponential Equations
Logarithmic Equations

Solving Equations

To solve an equation means to find the value of the variable that makes the equation true. The solution of an equation is the value of the variable that satisfies the equation.

Steps for Solving Equations

When solving an equation, you can follow these general steps:

Identify the type of equation: Determine the type of equation based on its structure and the highest power of the variable.
Perform operations to isolate the variable: Use inverse operations (addition, subtraction, multiplication, division) to isolate the variable on one side of the equation.
Check your solution: After finding the value of the variable, substitute it back into the original equation to ensure that it satisfies the equation.

Practice Problems

Here are some practice problems to help you master solving equations:

Solve the following equations:

3x + 5 = 11
x² - 4x + 4 = 0
2(3x - 7) = 5x + 1

Remember to show your work and check your solutions!

Conclusion

Equations are fundamental in mathematics and are used to represent relationships and solve various problems. By understanding the types of equations and learning how to solve them, you can develop strong problem-solving skills that are valuable in many areas of mathematics and beyond.

◂Math Worksheets and Study Guides Fifth Grade. Whole Numbers to Millions

Study Guide

Whole Numbers to Millions

Worksheet/Answer key

Whole Numbers to Millions

Worksheet/Answer key

Whole Numbers to Millions

Worksheet/Answer key

Whole Numbers to Millions

Vocabulary/Answer key

Whole Numbers to Millions

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).