Mastering Equation Transposition & Substitution

• Nieuwe lesbewerker

Mastering Equation Transposition & Substitution

What do you already know about transposing equations?

Learning Objective

At the end of the lesson you will be able to confidently transpose mathematical equations involving at least three letters, and substitute values to solve for unknowns.

What is Equation Transposition?

Equation transposition is the process of rearranging an equation to make a different variable the subject. This usually involves moving terms from one side to the other using inverse operations.

Example 1: Basic Transposition

Given the formula a = b + 3c, rearrange to make c the subject. Solution: 1. Subtract b from both sides: a - b = 3c 2. Divide both sides by 3: (a - b)/3 = c

Example 2: More Involved Transposition

Given the equation 4d = 2e - f, make e the subject. Solution: 1. Add f to both sides: 4d + f = 2e 2. Divide both sides by 2: (4d + f)/2 = e

Substituting Values and Solving

Replace each variable (except the unknown) with given values. For example, using F = ma, if m = 5 and a = 3, substitute to get F = 5 × 3.

Step 2: Solve

Step 1: Substitute

Carry out the calculation. In the example above, F = 15. If rearrangement is needed, make the unknown the subject first, then substitute.

Practice Examples

Try these yourself, rearrange if needed, then substitute values: 1. p = 2q + 5r; make q the subject. 2. h = (a + b)/c; make a the subject. 3. x = 3y - 4z; make z the subject. 4. s = ut + 0.5at^2; make a the subject. 5. V = IR; make R the subject. 6. y = mx + c; make x the subject. 7. w = (x + y)/z; make y the subject.

Top Tips for Transposition & Substitution

• Always perform the same operation on both sides. • Isolate the variable step-by-step. • Be careful with signs and brackets.

Check Your Understanding

Can you rearrange and solve equations with three or more letters? Try reviewing the practice problems if you need more practice.

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.