Year 8 Mathematics · AC9M8N04

Operations with Integers and Rational Numbers

Use meaning and number structure—not isolated sign slogans—to calculate with integers, fractions and decimals efficiently. Track signs, choose exact representations…

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Key conceptTeach from the board

Signed operations should make sense in context and patterns. Subtracting a negative reverses a downward change: −6−(−9)=−6+9. For multiplication/division, extending patterns shows same signs produce a positive result and unlike signs a negative result.

For rational numbers, choose an efficient representation. Fractions are often best kept exact with common denominators; decimals may be convenient for measurement/money. Use commutative, associative and distributive properties where they reduce work.

Parentheses determine the base of a power: −3²=−9 because exponentiation occurs before the leading negative, while (−3)²=9.

Worked examplesWe do

Worked examples

AC9M8N04 - Operations with Integers and Rational Numbers
Example 1

Calculate −8+13 and −8−13.

Example 2

Explain why (−4)(−6)=24 using a sign pattern.

Example 3

Signed operations should make sense in context and patterns. Subtracting a negative reverses a downward change: −6−(−9)=−6+9. For multiplication/division, extending patterns shows same signs produce a positive result and unlike signs a negative result.

Example 4

For rational numbers, choose an efficient representation. Fractions are often best kept exact with common denominators; decimals may be convenient for measurement/money. Use commutative, associative and distributive properties where they reduce work.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8N04: use the 4 operations with integers and rational numbers, choosing efficient strategies and digital tools where appropriate.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8N04:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-INT-C-01; MA4-FRC-C-01; MAO-WM-01:Exact.

FrameworkMappingRelationship
Australian CurriculumAC9M8N04Canonical
VictoriaVC2M8N04Exact
NSW Stage 4MA4-INT-C-01; MA4-FRC-C-01; MAO-WM-01Exact
Questions and answersWith answers
  1. Why does negative×negative give positive? Extending multiplication patterns consistently requires it.
  2. Why use common denominators? They express fractions in equal-sized parts before adding/subtracting.
  3. When are decimals useful? In measurement/money or when a decimal result is natural.
  4. How do brackets affect powers? They determine whether the negative sign is part of the base.
Practice and reviewReady for practice
  • Two negatives always make a positive. That applies to multiplication/division; addition/subtraction require interpretation.
  • Adding denominators. Fraction addition/subtraction requires equivalent denominators.
  • Ignoring operation order. Multiplication/division precede addition/subtraction unless grouping changes it.
  • −3²=(−3)². Brackets change the base.
Curriculum alignmentStart here
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