The properties of equality are rules that allow you to manipulate equations while keeping them balanced. This means that if you perform the same operation on both sides of an equation, the equation remains true. These properties are essential for solving algebraic equations and simplifying expressions. Key properties include the addition, subtraction, multiplication, and division properties of equality. Understanding these properties will make solving equations much easier! ๐
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Addition Property of Equality | A. If $a = b$, then $a \div c = b \div c$ (where $c \neq 0$) |
| 2. Subtraction Property of Equality | B. If $a = b$, then $a - c = b - c$ |
| 3. Multiplication Property of Equality | C. If $a = b$, then $a + c = b + c$ |
| 4. Division Property of Equality | D. If $a = b$, then $a \times c = b \times c$ |
| 5. Reflexive Property of Equality | E. $a = a$ |
Complete the following paragraph using the words: equation, equal, both sides, property, same.
The properties of equality help us solve an __________. To keep the equation balanced, we must do the __________ thing to __________ of the equation. Each __________ of equality allows us to manipulate the equation while keeping the two sides __________.
Explain, in your own words, why it is important to maintain balance when solving equations using the properties of equality. Provide an example to support your explanation.
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