IB MYP 4-5 Maths- Changing the subject of an equation - Study Notes - New Syllabus
IB MYP 4-5 Maths- Changing the subject of an equation – Study Notes
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- Changing the subject of an equation
IB MYP 4-5 Maths- Changing the subject of an equation – Study Notes – All topics
Changing the Subject of an Equation
Changing the Subject of an Equation
To change the subject of a formula or equation means to rearrange it so that a different variable is on its own on one side of the equation.
This is an essential skill in algebra and is commonly used in physics, geometry, and other real-world applications where formulas must be adapted for different variables.
Steps:
- Identify the new subject (which variable to make the subject).
- Use inverse operations to isolate that variable on one side.
- Work step by step: undo addition/subtraction, then multiplication/division.
- If the subject appears more than once, factor it or use other algebraic techniques.
Important Note: Changing the subject is just like solving an equation – you apply the same operation to both sides to keep the equation balanced.
Example:
Make \( x \) the subject: \( y = 3x + 5 \)
▶️ Answer/Explanation
Step 1: Subtract 5 from both sides:
\( y – 5 = 3x \)
Step 2: Divide both sides by 3:
\( x = \frac{y – 5}{3} \)
Example:
Make \( r \) the subject: \( A = \pi r^2 \)
▶️ Answer/Explanation
Step 1: Divide both sides by \( \pi \):
\( \frac{A}{\pi} = r^2 \)
Step 2: Take square root of both sides:
\( r = \sqrt{\frac{A}{\pi}} \)
Example:
Make \( a \) the subject: \( s = \frac{u + v}{2} \cdot t \)
▶️ Answer/Explanation
Step 1: Multiply both sides by 2:
\( 2s = (u + v)t \)
Step 2: Divide both sides by \( t \):
\( \frac{2s}{t} = u + v \)
Step 3: Rearranged for \( v \):
\( v = \frac{2s}{t} – u \)
Example:
Make \( x \) the subject: \( \frac{2x – 1}{3} = 5 \)
▶️ Answer/Explanation
Step 1: Multiply both sides by 3:
\( 2x – 1 = 15 \)
Step 2: Add 1 to both sides:
\( 2x = 16 \)
Step 3: Divide by 2:
\( x = 8 \)
Example:
Make \( x \) the subject: \( A = 3(x – 2) \)
▶️ Answer/Explanation
Step 1: Divide both sides by 3:
\( \frac{A}{3} = x – 2 \)
Step 2: Add 2 to both sides:
\( x = \frac{A}{3} + 2 \)
Tips to Remember:
- Undo operations in the reverse order of PEMDAS (Parentheses, Exponents, Multiply/Divide, Add/Subtract).
- Always perform the same operation on both sides of the equation.
- When dealing with square roots or powers, isolate the term before applying root or exponent.
Operations and Their Mathematical Inverses
When changing the subject of an equation, you must “undo” operations using their inverse operations. This helps isolate the required variable step by step.
Inverse operations are pairs of mathematical operations that cancel each other out. For example, addition is undone by subtraction, and squaring is undone by taking a square root.
| Operation | Inverse Operation | Example |
|---|---|---|
| Addition (\( + \)) | Subtraction (\( – \)) | \( x + 4 = 10 \Rightarrow x = 10 – 4 \) |
| Subtraction (\( – \)) | Addition (\( + \)) | \( x – 7 = 5 \Rightarrow x = 5 + 7 \) |
| Multiplication (\( \times \)) | Division (\( \div \)) | \( 3x = 15 \Rightarrow x = 15 \div 3 \) |
| Division (\( \div \)) | Multiplication (\( \times \)) | \( \frac{x}{4} = 6 \Rightarrow x = 6 \times 4 \) |
| Squaring (\( x^2 \)) | Square Root (\( \sqrt{x} \)) | \( x^2 = 49 \Rightarrow x = \sqrt{49} \) |
| Square Root (\( \sqrt{x} \)) | Squaring (\( x^2 \)) | \( \sqrt{x} = 5 \Rightarrow x = 5^2 \) |
Understanding and applying inverse operations is essential for changing the subject accurately.