Finding Value of an Expression
The value of an algebraic expression is the number you get when you replace (substitute) each variable with a given number and calculate.
For example, if x = 3, the value of 2x + 5 is 2(3) + 5 = 6 + 5 = 11.
What is Finding Value of an Expression - Grade 7 Maths (Algebraic Expressions)?
Definition: Finding the value of an expression means substituting given numbers for the variables and simplifying.
Steps:
- Write the expression.
- Replace each variable with its given value.
- Follow BODMAS to calculate.
Finding Value of an Expression Formula
Substitute → Calculate → Simplify
Types and Properties
Cases:
- Single variable: Replace x with its value.
- Two variables: Replace x and y with their given values.
- Negative values: Be careful with signs when substituting negative numbers.
Solved Examples
Example 1: Single Variable
Problem: Find the value of 3x² − 2x + 1 when x = 2.
Solution:
- = 3(2)² − 2(2) + 1
- = 3(4) − 4 + 1
- = 12 − 4 + 1 = 9
Answer: 9.
Example 2: Two Variables
Problem: Find the value of 2a + 3b when a = 4, b = −1.
Solution:
- = 2(4) + 3(−1)
- = 8 − 3 = 5
Answer: 5.
Example 3: Negative Substitution
Problem: Find the value of x² + 2x − 3 when x = −3.
Solution:
- = (−3)² + 2(−3) − 3
- = 9 − 6 − 3 = 0
Answer: 0.
Example 4: Fraction Substitution
Problem: Find the value of 4x + 6 when x = 1/2.
Solution:
- = 4(1/2) + 6 = 2 + 6 = 8
Answer: 8.
Real-World Applications
Real-world uses:
- Formulas: Area = l × b. Substituting l = 5, b = 3 gives area = 15.
- Physics: Speed = distance/time. Substituting values gives the answer.
- Finance: Simple Interest formula: SI = PRT/100.
Key Points to Remember
- Substitute the given values for the variables.
- Follow BODMAS order of operations.
- Be careful with negative numbers: (−3)² = 9, not −9.
- A variable can take different values — each gives a different result.
Practice Problems
- Find the value of 5x − 3 when x = 4.
- Find the value of a² + b² when a = 3, b = 4.
- Find the value of 2x² − x + 1 when x = −2.
- Find the value of (x + y)(x − y) when x = 5, y = 3.
Frequently Asked Questions
Q1. What does 'find the value of an expression' mean?
Replace each variable with the given number and calculate the result.
Q2. What is BODMAS?
The order of operations: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction.
Q3. Can an expression have different values?
Yes. The value depends on what number is substituted for the variable. The expression 2x + 1 equals 5 when x = 2, and 7 when x = 3.
