Grade 7 Mathematics ALGEBRA – Algebraic expressions Notes
Mathematics — ALGEBRA
Subtopic: Algebraic expressions (Age ~12, Kenyan context)
An algebraic expression is a mathematical phrase made from numbers, letters (called variables) and operation signs (+, −, ×, ÷). Example: 3x + 5, 2a − 4b, 5 (a number alone is also an expression).
- Term: each part separated by + or −. In 3x + 5, the terms are 3x and 5.
- Coefficient: the number multiplied by the variable. In 3x, the coefficient is 3. In x alone, the coefficient is 1.
- Variable: a letter that stands for a number, e.g., x, y, a, b.
- Constant: a term without a variable, e.g., 5, −2.
- Like terms: terms that have the same variable(s) raised to the same power. Example: 4m and −2m are like terms.
3x + 5 (3 times x, then add 5)
2a − 4b (two a minus four b)
x2 + 2x + 1 (x squared + 2x + 1)
To evaluate, replace the variable with a number and calculate.
Example: Evaluate 3x + 5 when x = 4.
Replace x with 4: 3(4) + 5 = 12 + 5 = 17.
Kenyan example: If a pen costs KSh 15 and you buy x pens, total cost = 15x. For x = 3, cost = 15×3 = KSh 45.
Only like terms can be added or subtracted.
Example 1: 4m + 2m = (4 + 2)m = 6m
Example 2: 5x + 3 − 2x = (5x − 2x) + 3 = 3x + 3
Example 3: 2a + 3b − a + 4b = (2a − a) + (3b + 4b) = a + 7b
Multiply each term inside the bracket by the number outside.
Example: 3(x + 2) = 3×x + 3×2 = 3x + 6
Example: 2(3m − 4) = 2×3m − 2×4 = 6m − 8
- Don't add unlike terms (e.g., 2x + 3 is not 5x).
- Remember x = 1×x (so x alone has coefficient 1). −x means −1×x.
- Distribute correctly: 2(x + 3) ≠ 2x + 3 (it is 2x + 6).
- Evaluate 4x − 3 when x = 2.
- Simplify: 3p + 5p − 2.
- Simplify: 2(a + 3) + 4a.
- Write an expression: Ali has x mangoes. Each mango costs KSh 20. Total cost?
- Are 3x and 3x2 like terms?
Answers (click to view)
- 4(2) − 3 = 8 − 3 = 5.
- 3p + 5p − 2 = (3p + 5p) − 2 = 8p − 2.
- 2(a + 3) + 4a = 2a + 6 + 4a = (2a + 4a) + 6 = 6a + 6.
- Total cost = 20x (KSh 20 times x). For x = 4, cost = KSh 80.
- No. 3x and 3x2 are not like terms because the powers of x are different (x vs x2).
Algebraic expressions help us write and solve real-life problems (money, measures, counts). Practice by converting simple word problems into expressions and then simplifying or evaluating them.