Addition Property of Equality - Definition, Examples, Quiz, FAQ, Trivia
Learn how to solve equations by adding the same value to both sides
What is the Addition Property of Equality?
The Addition Property of Equality is a fundamental rule in algebra. It states that if you add the same number to both sides of an equation, the two sides remain equal. This property helps us solve equations while keeping them balanced.
Think of an equation like a balanced scale. Whatever you add to one side, you must add to the other to keep it balanced. This property is essential for solving equations and finding unknown values.
Key Definition: If a = b, then a + c = b + c for any number c.
Key Concept
The Addition Property of Equality keeps equations balanced when we add the same value to both sides.
The Formula
The Addition Property of Equality has a simple formula that we can use to solve equations:
Addition Property Formula
This formula shows that adding the same value (c) to both sides of an equation keeps it balanced.
- a and b represent the two sides of the equation that are equal
- c is the number we add to both sides
- The equal sign (=) means both sides have the same value
Remember
You can add any number to both sides - positive, negative, whole numbers, or fractions - as long as you add the same value to both sides.
Examples
Let's look at some examples to understand how the Addition Property of Equality works:
Basic Examples
| Equation | Operation | Result |
|---|---|---|
| x - 3 = 8 | Add 3 to both sides | x = 11 |
| y - 5 = 2 | Add 5 to both sides | y = 7 |
| z - 10 = 15 | Add 10 to both sides | z = 25 |
| a + 4 = 9 | Add -4 to both sides | a = 5 |
Step-by-Step Solution
Example Tip
Adding a negative number is the same as subtracting. This helps us solve equations like x + 5 = 3 by adding -5 to both sides.
Applications in Solving Equations
The Addition Property of Equality is essential for solving many types of equations. Here's how we use it:
1. Solving for Unknowns: When you have an equation like x - 4 = 10, add 4 to both sides to find x = 14.
2. Isolating Variables: To get a variable by itself, add the opposite of whatever is with it.
3. Real-World Problems: Use this property to solve problems like:
- "After giving away 5 stickers, I have 8 left. How many did I start with?" → x - 5 = 8
- "The temperature dropped 10°F and is now 65°F. What was the original temperature?" → x - 10 = 65
Problem Solving Tip
When solving word problems, first write the equation, then use the Addition Property of Equality to find the solution.
Practice Quiz
Test your understanding with these 5 questions. Choose the correct answer for each.
Frequently Asked Questions
Here are answers to common questions about the Addition Property of Equality:
Math Trivia
Discover interesting facts about equations and algebra:
Ancient Equations
The earliest known equations date back to ancient Babylon around 1800 BC. Babylonian mathematicians solved quadratic equations on clay tablets!
The Equal Sign
The equal sign (=) was invented by Welsh mathematician Robert Recorde in 1557. He chose two parallel lines because "no two things can be more equal."
Algebra in Space
NASA engineers use algebra and equations daily to calculate spacecraft trajectories. A single mistake in an equation could send a spacecraft off course!
Longest Equation
The longest mathematical equation ever written is the Boolean Pythagorean Triples problem. Its solution required 200 terabytes of data - more than all the text in the Library of Congress!
