Algebra — Grade 5 Mathematics
Algebra uses letters (variables) to represent unknown numbers. In Grade 5 we write expressions, solve one-step and two-step equations, and substitute values into formulae.
Key Vocabulary
VariableA letter that represents an unknown, e.g. x, y, n.
ExpressionCombination of numbers and variables, e.g. 3x + 5. No equals sign.
EquationStates that two expressions are equal, e.g. 3x + 5 = 20.
CoefficientThe number multiplied by the variable: in 7y, the coefficient is 7.
Writing Expressions
- "5 more than x" → x + 5
- "3 times a number n, then subtract 4" → 3n − 4
- "A number divided by 6" → n ÷ 6 or n/6
Solving Equations — Balance Method
Whatever you do to one side of the equation, do the same to the other.
One-step equation
x + 9 = 25
→ −9 both sides →
x = 16
Two-step equation
3x + 4 = 22
→ −4 →
3x = 18
→ ÷3 →
x = 6
Substitution
Evaluate the expression 4a − 2b for different values:
| a | b | 4a − 2b |
|---|---|---|
| 5 | 3 | 4(5) − 2(3) = 20 − 6 = 14 |
| 0 | 7 | 0 − 14 = −14 |
| 3 | 0 | 12 − 0 = 12 |
Worked Examples
Example 1 — Write and Solve
I think of a number, multiply by 4 then add 7. The result is 35. Find the number.
- Let the number = n
- 4n + 7 = 35
- 4n = 28
- n = 7
Example 2 — Two-step with division
Solve: (x / 5) − 3 = 9
- Add 3 to both sides: x/5 = 12
- Multiply both sides by 5: x = 60
Example 3 — Formula Substitution
The perimeter of a rectangle: P = 2(l + w). Find P when l = 8 cm and w = 5 cm.
- P = 2(8 + 5) = 2 × 13 = 26 cm
Practice Questions
1. Solve: y + 13 = 30
✅ y = 30 − 13 = 17
2. Solve: 5m − 3 = 22
✅ 5m = 25 → m = 5
3. Evaluate 3x − y when x = 6 and y = 4.
✅ 3(6) − 4 = 18 − 4 = 14
4. Write an expression: "a number k halved then increased by 9".
✅ k/2 + 9
5. Solve: n/4 + 6 = 14
✅ n/4 = 8 → n = 32
Key Points to Remember
- A variable is a letter standing for an unknown number.
- An expression has no equals sign; an equation does.
- Solve equations using the balance method: same operation to both sides.
- For two-step equations: undo the addition/subtraction first, then undo the multiplication/division.
- Substitution: replace each variable with its given value and calculate carefully.