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Year 7–8 · Year 7–8 Maths

Year 7–8 Maths — Number and Algebra

Number and algebra in Years 7 and 8 covers the transition from arithmetic to algebraic thinking — using letters to represent unknown values and solving equations. These skills are the foundation for every higher-level maths topic. Mastering them now prevents the gaps that compound into Year 10 and VCE.

Key Concepts & Formulas

  • Order of operations (BODMAS/PEMDAS): Brackets → Orders (powers/roots) → Division/Multiplication → Addition/Subtraction

  • Integers: positive and negative whole numbers; adding a negative = subtracting; multiplying two negatives = positive

  • Fractions: to add/subtract, find a common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal

  • Percentages: convert to a decimal by dividing by 100; percentage of a quantity = percentage × amount

  • Ratios: can be simplified like fractions; use equivalent ratios to share quantities

  • Algebra: a pronumeral (letter) represents an unknown or variable; 3x means 3 × x

  • Like terms: only terms with the same variable and power can be added or subtracted: 3x + 2x = 5x (but 3x + 2y cannot be simplified)

  • Expanding brackets: a(b + c) = ab + ac

  • Solving linear equations: perform the same operation to both sides to isolate the unknown

  • Substitution: replace the pronumeral with a number to evaluate an expression

Practice Questions

5 questions

Attempt each question before reading the hint. These are styled to match school assessment format.

Q1.Simplify: 3x + 5 − 2x + 7

1 mark

Q2.Solve for x: 4x − 3 = 13

2 marks

Q3.Expand and simplify: 2(3x − 4) + 5x

2 marks

Q4.Find 35% of $240.

1 mark

Q5.Share $180 between two people in the ratio 2 : 3.

2 marks

Common Mistakes to Avoid

These are the errors that students most frequently make in Number and Algebra — and that examiners are specifically watching for.

  • Ignoring order of operations — multiplication and division must be done before addition and subtraction

  • Adding unlike terms: 3x + 2 ≠ 5x (you cannot add a number to a term with x)

  • Sign errors with negative numbers — especially when subtracting: x − (−3) = x + 3

  • Dividing instead of multiplying by the reciprocal when dividing fractions

Still finding Number and Algebra difficult?

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