Example 1
Connect equivalent rational forms
- Begin with 7/20.
- Multiply numerator and denominator by 5 to obtain 35/100.
- Read 35/100 as decimal 0.35.
- Convert hundredths to 35%.
Final answer: 7/20 = 0.35 = 35%.
Check: Calculate 7 ÷ 20 = 0.35.
What students learn in AC9M7N04
We are learning to find equivalent representations of rational numbers and represent rational numbers on a number line.
A rational number can be written as a fraction of integers with a non-zero denominator. Equivalent fractions, decimals and percentages occupy the same point on a number line.
Conversion preserves value: 7/20 becomes 35/100, then 0.35 and 35%. A common representation makes comparison reliable when forms differ.
Signed rational numbers require attention to direction. Among negative values, a number with greater absolute value lies farther left and is therefore smaller.
Success criteria
- I can convert among fraction, decimal and percentage representations.
- I can justify that two rational representations are equivalent.
- I can locate and order positive and negative rational numbers on a number line.
Key vocabulary
- rational number
- number expressible as a fraction of integers with non-zero denominator.
- equivalent
- different representations with equal value.
- absolute value
- distance from zero on a number line.
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
Order signed rational numbers
- Convert −3/4 to −0.75.
- Keep −0.6 as a decimal.
- Convert 20% to 0.20.
- Order on a number line: −0.75 < −0.6 < 0.20.
Final answer: −3/4 < −0.6 < 20%.
Check: Values farther left on the number line are smaller.
Example 3
Application problem 1
Problem: Order −0.6, −5/8, 55% and 0.58 from least to greatest. Convert to a common representation and justify the order.
- Plan: Represent the information first, then calculate, interpret and independently check the result.
- Work: −5/8 = −0.625, so −0.625 < −0.6 < 0.55 < 0.58. Therefore −5/8, −0.6, 55%, 0.58.
- Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Final answer: −5/8 = −0.625, so −0.625 < −0.6 < 0.55 < 0.58. Therefore −5/8, −0.6, 55%, 0.58.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Application problem 2
Problem: Order 7/8, 0.86 and 87% and state the gap between greatest and least.
- Plan: Write 7/8 and 87% as decimals.
- Work: 0.86 < 87% < 7/8; the gap is 0.875−0.86=0.015.
- Interpret: Convert each value to a decimal.
Final answer: 0.86 < 87% < 7/8; the gap is 0.875−0.86=0.015.
Check: Convert each value to a decimal.
Common misconceptions
Common mistake: Percent sign removed without dividing by 100.
Correction: 60%=0.60, not 60.
Common mistake: Negative order reversed.
Correction: -0.8 is less than -0.3.
Common mistake: Equivalent numerator changed alone.
Correction: Scale numerator and denominator together.
10 important problems to solve
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Convert 3/4 to a decimal and percentage.
Check answer
Answer: 3/4 = 0.75 = 75%.
Hint: Divide 3 by 4, then multiply the decimal by 100.
Why: Equivalent forms name the same value.
2. Simplify 42/56.
Check answer
Answer: 42/56 = 3/4.
Hint: Find the highest common factor.
Why: Dividing both terms by 14 preserves value.
3. Write 0.6 as a fraction and percentage.
Check answer
Answer: 0.6 = 3/5 = 60%.
Hint: Write 0.6 as 6/10.
Why: Six tenths simplifies to three fifths.
4. Order −0.5, −2/3 and 25% from least to greatest.
Check answer
Answer: −2/3 < −0.5 < 25%.
Hint: Convert all three to decimals.
Why: Converting the three rational numbers to equivalent decimals reveals their number-line order.
5. Place 5/8 between two tenths on a number line.
Check answer
Answer: 5/8 = 0.625, so it lies between 0.6 and 0.7.
Hint: Calculate 5 ÷ 8.
Why: A decimal locates the fraction precisely.
6. Which is greater: 7/12 or 58%?
Check answer
Answer: 7/12 ≈ 58.33%, so 7/12 is greater.
Hint: Convert 7/12 to a percentage.
Why: A common representation permits comparison.
7. Correct the claim that −3/5 is greater than −1/2 because 3/5 > 1/2.
Check answer
Answer: −3/5 = −0.6, which is less than −0.5 = −1/2.
Hint: Plot both values left of zero.
Why: Negatives reverse the order of positive magnitudes.
8. A tank is 0.65 full. Express this as a simplified fraction and percentage.
Check answer
Answer: Dividing by 100 gives 0.65=65/100; simplifying by 5 gives 13/20, and multiplying the decimal by 100 gives 65%.
Hint: Simplify 65/100 by 5.
Why: All forms describe the same portion of the tank.
9. Order 7/8, 0.86 and 87% and state the gap between greatest and least.
Check answer
Answer: 0.86 < 87% < 7/8; the gap is 0.875−0.86=0.015.
Hint: Write 7/8 and 87% as decimals.
Why: Convert each value to a decimal.
10. Order −0.6, −5/8, 55% and 0.58 from least to greatest. Convert to a common representation and justify the order.
Check answer
Answer: −5/8 = −0.625, so −0.625 < −0.6 < 0.55 < 0.58. Therefore −5/8, −0.6, 55%, 0.58.
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 content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.
- Content description: find equivalent representations of rational numbers and represent rational numbers on a number line
- E1: investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as \frac23 is equivalent to \frac46 and \frac69 and therefore \frac23<\frac56
- E2: expressing a fraction in simplest form using common divisors
- E3: applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, 16\%, 0.16, \frac{16}{100} and \frac4{25}, using manipulatives, number lines or diagrams
- E4: representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7N04 — find equivalent representations of rational numbers and represent rational numbers on a number line |
| Victoria | Victorian Curriculum F-10 | Year 7 Maths: closest match in Number. Use this page as a VIC-aligned practice and homework reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Find equivalent representations of rational numbers and represent rational numbers on a number line and related outcomes. |
| United States | Common Core / NGSS | Grade 7 Common Core Mathematics/ELA closest topic match for Find equivalent representations of rational numbers and represent rational numbers on a number line. |
| England / UK | National Curriculum | Key Stage 3 / Year 7: closest programme-of-study match for Find equivalent representations of rational numbers and represent rational numbers on a number line. |
| Canada | Provincial and territory curricula | Grade 7 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 4 Maths: closest achievement-objective topic for Find equivalent representations of rational numbers and represent rational numbers on a number line. |
| India | NCERT / CBSE | Class 7 closest NCERT/CBSE topic match for Find equivalent representations of rational numbers and represent rational numbers on a number line. |
🎥 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: Comparing Fractions
Math Antics — Compare equivalent fractions and order their values; use the written lesson to extend to signed rational numbers.
As you watch: How does making equal-sized fractional parts help you compare values?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Place 1/2, 3/4 and 2/3 on a number line and justify the order.
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 Find equivalent representations of rational numbers and represent rational numbers...
Mapped skill: find equivalent representations of rational numbers and represent rational numbers on a number line
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 | AC9M7N04 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N04 · 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: AC9M7N04 — Equivalent 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.