AC9M7N08 • Year 7 Maths • Number • Learn
recognise, represent and solve problems involving ratios.
We are learning to recognise, represent and solve problems involving ratios.
A ratio is an ordered multiplicative comparison. The statement red:blue = 3:2 differs from blue:red = 3:2, so the named quantities and their order must remain visible.
Equivalent ratios are created by multiplying or dividing every part by the same factor. Adding the same amount to each part does not generally preserve the relationship.
Ratio tables and a unit ratio support scaling, sharing and map problems. For a total shared in a ratio, add the parts, find the value of one part and scale each share.
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 1
Final answer: Ten parts red require 25 parts water.
Check: 10:25 simplifies by 5 to 2:5.
Example 2
Final answer: The shares are $36 and $48.
Check: $36+$48=$84 and 36:48=3:4.
Example 3
Problem: A sports drink uses concentrate and water in the ratio 2:7. How much of each is needed to make 3.6 L, and how do you know the ratio is preserved?
Final answer: There are 9 equal parts, so each part is 3.6÷9 = 0.4 L. Concentrate = 0.8 L and water = 2.8 L; 0.8:2.8 simplifies to 2:7.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Problem: Recipe A uses 300 g flour to 180 mL milk; B uses 450 g to 260 mL. Are they equivalent?
Final answer: No. Scaling A by 1.5 gives 450 g and 270 mL, not 260 mL.
Check: Equivalent ratios require one common scale factor.
Common mistake: Ratio order ignored.
Correction: 3:2 differs from 2:3.
Common mistake: Same number added to both parts.
Correction: Use equal multiplication or division.
Common mistake: Part-to-part and part-to-whole confused.
Correction: Name quantities explicitly.
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Simplify 18:24.
Answer: 3:4.
Hint: Find the highest common factor.
Why: Divide both parts by their common factor 6.
2. Write blue:orange when there are 6 blue and 4 orange counters.
Answer: 6:4=3:2.
Hint: Write blue first, then simplify.
Why: Ratio order follows the named quantities.
3. Find an equivalent ratio to 3:5 with first part 12.
Answer: 12:20.
Hint: Multiply 3 and 5 by the same factor.
Why: Multiplying both parts by the common scale factor 4 creates the equivalent ratio 12:20.
4. A cordial mix uses syrup:water=1:4. How much water for 250 mL syrup?
Answer: 1000 mL water.
Hint: Multiply 250 by 4.
Why: The water amount is four times the syrup.
5. Share 72 stickers in ratio 5:3.
Answer: 45 stickers and 27 stickers.
Hint: Add ratio parts, then divide 72.
Why: Eight total parts make each part 9.
6. Are 8:12 and 14:21 equivalent?
Answer: Yes; both simplify to 2:3.
Hint: Divide each pair by its common factor.
Why: Equivalent ratios share a simplified form.
7. A map scale is 1 cm:5 km. What distance does 7.2 cm represent?
Answer: 36 km.
Hint: Calculate 7.2×5.
Why: Scale factors multiply corresponding quantities.
8. A paint mix is red:blue:white=2:3:1 and totals 48 L. Find each amount.
Answer: There are 6 parts, each 8 L: red 16 L, blue 24 L, white 8 L.
Hint: Add ratio parts before finding one part.
Why: All three parts must total 48 L.
9. Recipe A uses 300 g flour to 180 mL milk; B uses 450 g to 260 mL. Are they equivalent?
Answer: No. Scaling A by 1.5 gives 450 g and 270 mL, not 260 mL.
Hint: Match the flour, then test the milk.
Why: Equivalent ratios require one common scale factor.
10. A sports drink uses concentrate and water in the ratio 2:7. How much of each is needed to make 3.6 L, and how do you know the ratio is preserved?
Answer: There are 9 equal parts, so each part is 3.6÷9 = 0.4 L. Concentrate = 0.8 L and water = 2.8 L; 0.8:2.8 simplifies to 2:7.
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.
Content description: recognise, represent and solve problems involving ratios.
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
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:
Math Antics — Represent a comparison between quantities using a ratio and apply it to a practical model.
As you watch: Why does the order of the quantities in a ratio matter?
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Try it: A drink uses cordial and water in the ratio 1:5. Model enough for 18 equal measures and explain the quantities you choose.
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Mapped skill: recognise, represent and solve problems involving ratios
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 | AC9M7N08 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7N08 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-RAT-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.
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Topic reference: AC9M7N08 — Ratios and Equivalent Relationships
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