Understanding Variable Expressions

1. Definition:
   • A variable expression (or algebraic expression) is a mathematical phrase that includes numbers, variables (letters representing unknown values), and operations.
2. Variables:
   • Variables are symbols (usually letters) that stand for unknown or changeable values.
   • Example: In the expression 3x+4, x is the variable.

Evaluating Variable Expressions

1. Substitution:
   • To evaluate a variable expression, substitute the given value(s) of the variable(s) into the expression and perform the arithmetic operations.
   • Example: Evaluate 3x+4 for x=2.
     • Substitute x=: 3(2)+4
     • Perform the operations: 6+4=10
2. Order of Operations (PEMDAS):
   • When evaluating expressions, always follow the order of operations:
     • Parentheses
     • Exponents (not typically covered in 6th grade, but good to be aware)
     • Multiplication and Division (from left to right)
     • Addition and Subtraction (from left to right)

Steps to Evaluate Variable Expressions

1. Step 1: Substitute the Values:
   • Replace the variables in the expression with their given values.
   • Example: For x=3, y=4, evaluate 2x+3y.
     • Substitute: 2(3)+3(4)
2. Step 2: Follow the Order of Operations:
   • Perform any calculations inside parentheses first.
   • Then, perform multiplication and division from left to right.
   • Finally, perform addition and subtraction from left to right.
   • Example: 2(3)+3(4)
     • Multiply: 6+12
     • Add: 18

Examples

1. Single Variable:
   • Evaluate 5x−7 for x=2
     • Substitute: 5(2)−7)
     • Calculate: 10−7=3
2. Multiple Variables:
   • Evaluate 3x+4y for x=1 and y=2
     • Substitute: 3(1)+4(2)
     • Calculate: 3+8=11
3. With Parentheses:
   • Evaluate 2(x+y) for x=3 and y=5
     • Substitute: 2(3+5)
     • Calculate inside parentheses: 2(8)=16

Tips for Students

• Substitute Carefully:
  • Ensure you replace each variable with the correct value.
• Follow Order of Operations:
  • Always use PEMDAS to avoid mistakes.
• Show Your Work:
  • Write each step to make your calculations clear and to check for errors.
• Practice Regularly:
  • Consistent practice with different types of expressions helps solidify understanding.