Real-World Examples of Variables and Algebraic Expressions (Grade 8)

📚 Quick Study Guide

• 🧮 Variable: A symbol (usually a letter) that represents an unknown number or a quantity that can change. Think of it as a placeholder.
• ➕ Algebraic Expression: A combination of variables, numbers, and at least one arithmetic operation (+, -, ×, ÷). It does *not* include an equals sign (=).
• ✏️ Coefficient: The number multiplied by a variable in an algebraic expression. For example, in $3x$, 3 is the coefficient.
• 📏 Constant: A number in an algebraic expression that does not change. It's not attached to any variable.
• 💡 Terms: Parts of an algebraic expression that are separated by + or - signs.
• 🔑 Evaluating Expressions: Replacing the variables in an expression with numbers and simplifying the result.
• 🤝 Combining Like Terms: Simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, $2x + 5x = 7x$.

🧪 Practice Quiz

1. Which of the following is an algebraic expression?
   1. $5 + 7 = 12$
   2. $3x + 2y - 1$
   3. $15$
   4. $x = 4$
2. A taxi charges a flat fee of $3 plus $2 per mile. If 'm' represents the number of miles, which expression represents the total cost?
   1. $3 + m$
   2. $2 + 3m$
   3. $3 + 2m$
   4. $5m$
3. What is the coefficient of 'y' in the expression $7x - 4y + 9$?
   1. $7$
   2. $-4$
   3. $9$
   4. $4$
4. Simplify the expression: $5a + 3b - 2a + b$
   1. $3a + 4b$
   2. $7a + 2b$
   3. $3a + 2b$
   4. $7a + 4b$
5. Evaluate the expression $2x^2 - x + 3$ when $x = 2$.
   1. $7$
   2. $9$
   3. $11$
   4. $13$
6. A rectangle has a length of $(x + 5)$ and a width of 4. Which expression represents the area of the rectangle?
   1. $4x + 5$
   2. $x + 9$
   3. $4x + 20$
   4. $5x + 4$
7. Which term is a constant in the expression $8p - 2q + 6$?
   1. $8p$
   2. $-2q$
   3. $6$
   4. $p$