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Understanding Formulas | Year 7 | Substitute Values & Rearrange Formulas Easily
Year 7 & 8 • Algebra
Lesson: Formulas
Learn how to work with formulas: understand what a formula is, substitute values correctly, evaluate answers, and rearrange simple formulas – perfect for Year 7 & 8 students.
Lesson Objectives
- Understand what a formula is and where formulas are used.
- Substitute values into formulas accurately.
- Evaluate formulas step-by-step, using the correct order of operations.
- Rearrange simple formulas to make a different variable the subject.
1. What Is a Formula?
A formula is a rule or equation that shows how different quantities are related.
It usually uses letters (variables) to represent numbers that can change.
Examples of common formulas:
Perimeter of a rectangle: P = 2l + 2w
Area of a rectangle: A = l × w
Distance travelled: d = s × t
Perimeter of a rectangle: P = 2l + 2w
Area of a rectangle: A = l × w
Distance travelled: d = s × t
2. Substituting Values into Formulas
To substitute means to replace a letter with a given number and then work out the value.
Example 1:
Formula: A = l × w
Find A when l = 8 cm and w = 3 cm.
Formula: A = l × w
Find A when l = 8 cm and w = 3 cm.
A = 8 × 3 = 24 cm²
Example 2:
Formula: d = s × t
Find d when s = 5 m/s and t = 10 s.
d = 5 × 10 = 50 m
3. Evaluating Formulas (Order of Operations)
When substituting into formulas, we must follow the correct order of operations (BIDMAS/BODMAS).
Example:
Formula: C = 2a + 3b
Find C when a = 4 and b = 5.
Formula: C = 2a + 3b
Find C when a = 4 and b = 5.
Step 1: Substitute values: C = 2(4) + 3(5)
Step 2: Multiply first: 2 × 4 = 8, 3 × 5 = 15
Step 3: Add: 8 + 15 = 23
So C = 23.
4. Rearranging Simple Formulas
Sometimes we know the answer and want to find a different variable.
We can rearrange the formula using inverse operations, similar to solving equations.
Example 1:
Formula: d = s × t
Make s the subject (solve for s).
Formula: d = s × t
Make s the subject (solve for s).
d = s × t → divide both sides by t:
s = d ÷ t
Example 2:
Formula: P = 2l + 2w
If we know P and w, and want to find l:
P = 2l + 2w
P − 2w = 2l
l = (P − 2w) ÷ 2
5. Real-Life Example
A taxi company charges according to the formula:
C = 3m + 5, where C is the total cost in pounds (£) and m is the number of miles.
(a) Find the cost of a 4-mile journey.
(b) A journey costs £26. How many miles was the journey?
(Answers are in the Answer Key section below.)
Practice Questions
A. Substitute and Evaluate
Substitute the given values into the formulas and find the answer.
- Formula: A = l × w
Find A when l = 9 cm and w = 4 cm. - Formula: d = s × t
Find d when s = 12 m/s and t = 3 s. - Formula: C = 2a + 3b
Find C when a = 5 and b = 2.
B. Use BIDMAS/BODMAS
Carefully evaluate each formula using the correct order of operations.
- Formula: P = 4n − 3
Find P when n = 7. - Formula: T = 3x²
Find T when x = 4. - Formula: K = 5p − 2q
Find K when p = 6 and q = 3.
C. Rearranging Simple Formulas
Make the indicated letter the subject of the formula.
- d = s × t → make s the subject.
- A = l × w → make l the subject.
- V = 3h + 2 → make h the subject.
D. Word Problems with Formulas
-
The area of a triangle is given by the formula A = ½bh,
where b is the base and h is the height.
Find A when b = 10 cm and h = 6 cm. -
The temperature in degrees Fahrenheit (F) is related to degrees Celsius (C) by the formula:
F = (9/5)C + 32.
Find F when C = 20.
E. Taxi Cost Formula
Use the formula C = 3m + 5, where C is the cost in pounds and m is the number of miles.
- Find C when m = 4.
- Find C when m = 10.
- If C = 26, find the value of m.
✅ Show Answer Key
A. Substitute and Evaluate
- A = l × w = 9 × 4 = 36 cm²
- d = s × t = 12 × 3 = 36 m
- C = 2a + 3b = 2(5) + 3(2) = 10 + 6 = 16
B. Use BIDMAS/BODMAS
- P = 4n − 3 = 4(7) − 3 = 28 − 3 = 25
- T = 3x² = 3 × 4² = 3 × 16 = 48
- K = 5p − 2q = 5(6) − 2(3) = 30 − 6 = 24
C. Rearranging Simple Formulas
- d = s × t
→ divide both sides by t → s = d ÷ t - A = l × w
→ divide both sides by w → l = A ÷ w - V = 3h + 2
Subtract 2 from both sides: V − 2 = 3h
Divide by 3: h = (V − 2) ÷ 3
D. Word Problems with Formulas
- A = ½bh = ½ × 10 × 6 = 5 × 6 = 30 cm²
- F = (9/5)C + 32
= (9/5)×20 + 32 = 36 + 32 = 68°F
E. Taxi Cost Formula
- C = 3m + 5 = 3(4) + 5 = 12 + 5 = £17
- C = 3(10) + 5 = 30 + 5 = £35
- C = 26 → 26 = 3m + 5
26 − 5 = 3m → 21 = 3m → m = 21 ÷ 3 = 7 miles
Real-Life Example (from Section 5)
- (a) C = 3m + 5 with m = 4 → C = 3(4) + 5 = 12 + 5 = £17
- (b) C = 26 → same as above → m = 7 miles
© Aviate Learning – Formulas (Year 7 & 8)