Example 1
Combine a percentage and fraction
- Find 25% of 64 as 1/4×64=16.
- Find 3/8 of 64 as 24.
- Add the two parts: 16+24=40.
- Check that 5/8×64=40.
Final answer: 25% of 64 plus 3/8 of 64 equals 40.
Check: The combined fraction is 1/4+3/8=5/8.
What students learn in AC9M7N06
We are learning to use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.
Positive rational numbers include positive fractions, decimals and percentages. Choosing an equivalent form can make one of the four operations more efficient without changing the value.
Addition and subtraction of fractions require common-sized parts, while multiplication and division can often be interpreted as scaling or sharing. Percentage problems require a clearly identified base quantity.
Multi-step calculations follow operation order and must be interpreted in context. An estimate, inverse operation or equivalent representation provides an independent reasonableness check.
Success criteria
- I can choose useful fraction, decimal or percentage forms for a calculation.
- I can apply the four operations to positive rational numbers accurately.
- I can follow operation order and verify a contextual result.
Key vocabulary
- positive rational number
- positive number expressible as a ratio of integers.
- percentage
- rate per hundred.
- operation order
- convention determining calculation sequence.
Visual models and representations
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
4 worked numerical & application examples
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 2
Apply operation order
- Evaluate 3+2.5×4.
- Multiply first: 2.5×4=10.
- Add 3 to obtain 13.
- Check by repeated addition: 3+2.5+2.5+2.5+2.5=13.
Final answer: 3+2.5×4=13.
Check: Multiplication precedes addition.
Example 3
Application problem 1
Problem: A jacket costs $80. It is reduced by 15%, then a $6 delivery fee is added. Find the final cost and explain why adding 15 to 80 would be incorrect.
- Plan: Represent the information first, then calculate, interpret and independently check the result.
- Work: 15% of $80 is $12, so the discounted price is $68; adding $6 gives $74. A percentage is a proportion of the original amount, not a raw dollar amount.
- Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Final answer: 15% of $80 is $12, so the discounted price is $68; adding $6 gives $74. A percentage is a proportion of the original amount, not a raw dollar amount.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Application problem 2
Problem: A 2.5 L drink is shared equally among 8 people after 10% spills. How much each?
- Plan: Find 90% of 2.5 L, then divide.
- Work: 2.25 L remains; 2.25÷8=0.28125 L, or 281.25 mL each.
- Interpret: Apply the percentage loss before division.
Final answer: 2.25 L remains; 2.25÷8=0.28125 L, or 281.25 mL each.
Check: Apply the percentage loss before division.
Common misconceptions
Common mistake: Fractions added by adding denominators.
Correction: Rename with common-sized parts.
Common mistake: Decimal division leaves divisor unchanged.
Correction: Scale both dividend and divisor equally.
Common mistake: Percentage change confused with percentage points.
Correction: Compare rates carefully.
10 important problems to solve
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Calculate 2/3 + 1/6.
Check answer
Answer: 5/6.
Hint: Rename 2/3 as sixths.
Why: Common sixths make the parts comparable.
2. Calculate 4.8−1.75.
Check answer
Answer: 3.05.
Hint: Line up decimal points.
Why: Aligned place values support decimal subtraction.
3. Find 30% of 90.
Check answer
Answer: 27.
Hint: Multiply 90 by 0.3.
Why: Thirty percent is 0.30 of the quantity.
4. Evaluate 3+2.5×4.
Check answer
Answer: 13.
Hint: Calculate 2.5×4 first.
Why: Operation order requires the multiplication to be completed before the addition.
5. A recipe uses 3/4 cup twice. How much altogether?
Check answer
Answer: 3/2 cups, or 1 1/2 cups.
Hint: Double 3/4.
Why: Two equal fraction amounts are added.
6. A $120 jacket is discounted by 15%. Find the sale price.
Check answer
Answer: Discount $18; sale price $102.
Hint: Find 0.15×120 first.
Why: Subtract the percentage amount from the original price.
7. Calculate 2.4÷0.6 and justify by multiplication.
Check answer
Answer: 4 because 0.6×4=2.4.
Hint: Ask how many 0.6s fit into 2.4.
Why: Multiplication checks division.
8. Mia spends 35% of $80, then 1/4 of the remainder. How much remains?
Check answer
Answer: After $28, $52 remains; 1/4 of $52 is $13, so $39 remains.
Hint: Update the base after the first spend.
Why: The second fraction uses the remainder, not the original amount.
9. A 2.5 L drink is shared equally among 8 people after 10% spills. How much each?
Check answer
Answer: 2.25 L remains; 2.25÷8=0.28125 L, or 281.25 mL each.
Hint: Find 90% of 2.5 L, then divide.
Why: Apply the percentage loss before division.
10. A jacket costs $80. It is reduced by 15%, then a $6 delivery fee is added. Find the final cost and explain why adding 15 to 80 would be incorrect.
Check answer
Answer: 15% of $80 is $12, so the discounted price is $68; adding $6 gives $74. A percentage is a proportion of the original amount, not a raw dollar amount.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Curriculum coverage and elaborations
The original AC9M7N06 curriculum coverage remains intact.
- Content description: use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.
- E1: solve addition and subtraction problems involving fractions and decimals using arrays, algebra tiles, digital tools or informal jottings.
- E2: choose an efficient representation such as 12.5%, 1/8, 0.125 or 125/1000.
- E3: use properties, place value, patterns and facts for multiplication and division with fractions and decimals.
- E4: solve multiplicative problems using models, calculators or informal jottings.
- E5: use regrouping, partitioning and properties for additive problems.
- E6: solve practical problems efficiently, including land use, nutrition and energy-account contexts.
International curriculum mapping
AC9M7N06 is the exact Australian Curriculum v9.0 code. Broad equivalents sit in Victorian Year 7 Number, NSW Stage 4, US Grade 7 rational-number operations, England Key Stage 3, Canadian Grade 7 Number, New Zealand Level 4 and Indian Class 7 rational numbers.
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Adding and Subtracting Fractions
Math Antics — Review addition and subtraction with fractions as part of the four-operation outcome.
As you watch: Why must denominators agree before numerators are added?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Work out 3/4 + 2/3, then check whether your answer is reasonable.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
About these videos
Videos are curated from trusted independent educational creators and played through YouTube. Rights remain with their respective owners. Inclusion does not imply that a creator or YouTube endorses SkillrHub.
YouTube’s terms and privacy policy apply to its player. Advertising, recommendations and external links may appear, and videos may change or become unavailable. SkillrHub’s written lessons and practice resources remain available separately.
To report a content, suitability or rights concern, email skillrhublearning@gmail.com with the lesson code and video link. Please do not include personal student information.
Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for The 4 operations with positive rational numbers including fractions, decimals...
Mapped skill: use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7N06 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N06 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-FRC-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
Help improve SkillrHub
Questions or feedback?
Ask about this lesson, suggest an improvement or report an error. Facebook opens only when you choose an option below.
Topic reference: AC9M7N06 — Four Operations with Positive Rational Numbers
Privacy: Please don’t share personal student or school information. Younger students should ask a parent, guardian or teacher to post on their behalf.