VARIABLE EXPRESSION
Definition Of Variable Expression
A variable expression is a combination of numbers (or constants), operations, and variables.
Examples of Variable Expression
- The following are examples of variable expressions.
Video Examples: Variables Expressions and Equations
Solved Example on Variable Expression
Ques: Charles and Dennis fired 20 shots each to hit a target. Each person gets p points for a hit and loses q points for a miss. Charles hits the mark 14 times and Dennis hits the mark 12 times. Identify the variable expressions for their individual scores.
Choices:
A. 12p, 14q
B. 14p - 6q, 12p - 8q
C. 14p, 12q
D. 14p - 6, 12p - 8
Correct Answer: B
Solution:
Step 1: Points scored by each person = Number of hits 'p' - Number of missed hits 'q'.
Step 2: Number of hits that Charles missed = (20 - 14) = 6. [Subtract.]
Step 3: The variable expression for the points scored by Charles is 14p - 6q.
Step 4: Number of hits that Dennis missed = (20 - 12) = 8. [Subtract.]
Step 5: The variable expression for the points scored by Dennis is 12p - 8q.
Step 6: So, the variable expressions for the points scored by Charles and Dennis are 14p - 6q and 12p - 8q respectively.
Quick Summary
- Variable expressions combine numbers, operations, and variables.
- Examples include: 2x + 3, y - 5, a/4
⚠️ Common Mistakes
- Incorrectly applying the order of operations (PEMDAS/BODMAS).
- Combining unlike terms (e.g., adding a constant to a variable term).
🌍 Real-World Uses
- Calculating the total cost of items: If 'x' is the price of an apple and you buy 3, and 'y' is the price of a banana and you buy 2, the expression '3x + 2y' represents the total cost.
- Determining the area of a rectangular garden: If 'l' is the length and 'w' is the width, the area is represented by the expression 'l * w'.
- Calculating the distance traveled: If 'r' is the rate of speed and 't' is the time traveled, the distance is represented by the expression 'r * t'.
📋 Standards Alignment
CCSS.MATH.CONTENT.6.EE.A.2CCSS.MATH.CONTENT.7.EE.A.1
🔗 Related Links
🍎 Teacher Insights
Use real-world examples to illustrate variable expressions. Encourage students to translate word problems into variable expressions.🎓 Prerequisites
- Variables
- Constants
- Operations (Addition, Subtraction, Multiplication, Division)
Check Your Knowledge
Q1: Which of the following is a variable expression?
Q2: What does the expression 3y - 2 represent if y = 5?
Frequently Asked Questions
Q: What is the difference between a variable expression and an equation?
A: A variable expression does not have an equals sign, while an equation sets two expressions equal to each other.
Q: How do you simplify a variable expression?
A: Combine like terms by adding or subtracting their coefficients. Follow the order of operations.