expressions and equations review sheet grade 7 pdf

📚 Understanding Expressions and Equations

In mathematics, expressions and equations are fundamental concepts. An expression is a combination of numbers, variables, and operations (like addition, subtraction, multiplication, and division) that represents a quantity. An equation, on the other hand, is a statement that two expressions are equal.

📜 A Brief History

The use of symbols to represent unknown quantities dates back to ancient civilizations. Egyptians and Babylonians used hieroglyphs and cuneiform to solve basic algebraic problems. However, the systematic use of variables and equations as we know them today developed gradually through the work of mathematicians like Diophantus, Al-Khwarizmi, and later European mathematicians during the Renaissance.

🔑 Key Principles

• ➕ Combining Like Terms: Only terms with the same variable and exponent can be added or subtracted. For example, $3x + 2x = 5x$.
• ⚖️ Maintaining Equality: When solving an equation, any operation performed on one side must also be performed on the other side to keep the equation balanced.
• ➗ Inverse Operations: Use inverse operations to isolate the variable. For example, to solve $x + 5 = 10$, subtract 5 from both sides.
• 🌱 Distributive Property: Distribute a term across parentheses. For example, $a(b + c) = ab + ac$.
• 🔢 Order of Operations: Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

💡 Real-world Examples

Expressions and equations are used in many real-world scenarios:

• 💰 Budgeting: Creating a budget involves using expressions to represent income and expenses, and equations to ensure that income equals or exceeds expenses.
• 📏 Geometry: Calculating the area and perimeter of shapes involves using expressions and equations. For example, the area of a rectangle is given by $A = lw$, where $l$ is the length and $w$ is the width.
• 🌡️ Science: Converting temperature from Celsius to Fahrenheit uses the equation $F = \frac{9}{5}C + 32$.

📝 Practice Quiz

Solve the following equations and simplify the expressions:

1. Simplify: $4x + 7 - 2x + 3$
2. Solve for $x$: $x - 8 = 12$
3. Simplify: $3(2y - 5) + 4y$
4. Solve for $a$: $5a + 10 = 25$
5. Simplify: $2(m + 3) - m + 1$
6. Solve for $z$: $\frac{z}{4} = 6$
7. Simplify: $-2(3n - 4) + 5n$

✅ Solutions

1. $2x + 10$
2. $x = 20$
3. $10y - 15$
4. $a = 3$
5. $m + 7$
6. $z = 24$
7. $-n + 8$

🔑 Conclusion

Mastering expressions and equations is crucial for success in algebra and beyond. By understanding the key principles and practicing regularly, you can build a strong foundation in mathematics. Keep practicing and you'll become more confident in your abilities. Good luck!