richard832
richard832 8h ago โ€ข 0 views

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

Hey there! ๐Ÿ‘‹ Let's explore variables and algebraic expressions with real-world examples! This stuff might seem abstract, but it's used *everywhere*! I've created a quick study guide and some practice questions to help you ace it. Good luck! ๐Ÿ€
๐Ÿงฎ Mathematics

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โœ… Best Answer

๐Ÿ“š Quick Study Guide

  • ๐Ÿงฎ Variable: A symbol (usually a letter) that represents an unknown number or a quantity that can change. Think of it as a placeholder.
  • โž• Algebraic Expression: A combination of variables, numbers, and at least one arithmetic operation (+, -, ร—, รท). It does *not* include an equals sign (=).
  • โœ๏ธ Coefficient: The number multiplied by a variable in an algebraic expression. For example, in $3x$, 3 is the coefficient.
  • ๐Ÿ“ Constant: A number in an algebraic expression that does not change. It's not attached to any variable.
  • ๐Ÿ’ก Terms: Parts of an algebraic expression that are separated by + or - signs.
  • ๐Ÿ”‘ Evaluating Expressions: Replacing the variables in an expression with numbers and simplifying the result.
  • ๐Ÿค Combining Like Terms: Simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, $2x + 5x = 7x$.

๐Ÿงช 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. $p$
Click to see Answers
  1. B
  2. C
  3. B
  4. A
  5. B
  6. C
  7. C

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