Year 7 Mathematics · AC9M7N08

Ratios and Equivalent Relationships

We are learning to recognise, represent and solve problems involving ratios

Ready to project and teach

Learning goalsSay it simply

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.

Success criteria

  • I can write and interpret ratios in a stated order.
  • I can generate and justify equivalent ratios using a common scale factor.
  • I can solve ratio scaling, sharing and rate problems.
Key conceptTeach from the board

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

Scale an equivalent ratio

  1. Use red:water = 2:5.
  2. To make red 10, multiply 2 by 5.
  3. Multiply water by the same factor: 5×5=25.
  4. Write the equivalent ratio 10:25.

Final answer: Ten parts red require 25 parts water.

Check: 10:25 simplifies by 5 to 2:5.

Example 2

Share a total in a ratio

  1. Share $84 in ratio 3:4.
  2. Total parts = 3+4=7.
  3. One part = $84÷7=$12.
  4. Shares are 3×$12=$36 and 4×$12=$48.

Final answer: The shares are $36 and $48.

Check: $36+$48=$84 and 36:48=3:4.

Example 3

Application problem 1

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?

  1. Plan: Represent the information first, then calculate, interpret and independently check the result.
  2. Work: 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.
  3. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.

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

Application problem 2

Problem: Recipe A uses 300 g flour to 180 mL milk; B uses 450 g to 260 mL. Are they equivalent?

  1. Plan: Match the flour, then test the milk.
  2. Work: No. Scaling A by 1.5 gives 450 g and 270 mL, not 260 mL.
  3. Interpret: Equivalent ratios require one common scale factor.

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M7N08 - Ratios and Equivalent Relationships
Example 1

Example 1 Scale an equivalent ratio Use red:water = 2:5. To make red 10, multiply 2 by 5. Multiply water by the same factor: 5×5=25. Write the equivalent ratio 10:25. Final answer: Ten parts red require 25 parts water. Check: 10:25 simplifies by 5 to 2:5.

Example 2

Example 2 Share a total in a ratio Share $84 in ratio 3:4. Total parts = 3+4=7. One part = $84÷7=$12. Shares are 3×$12=$36 and 4×$12=$48. Final answer: The shares are $36 and $48. Check: $36+$48=$84 and 36:48=3:4.

Example 3

Example 3 Application problem 1 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? Plan: Represent the information first, then calculate, interpret and independently check the result. Work: 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. Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills. 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

Example 4 Application problem 2 Problem: Recipe A uses 300 g flour to 180 mL milk; B uses 450 g to 260 mL. Are they equivalent? Plan: Match the flour, then test the milk. Work: No. Scaling A by 1.5 gives 450 g and 270 mL, not 260 mL. Interpret: Equivalent ratios require one common scale factor. 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.

Curriculum examplesCopied content

Content description: recognise, represent and solve problems involving ratios.

Questions and answersWith answers

Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.

  1. 1. Simplify 18:24.

    Check answer

    Answer: 3:4.

    Hint: Find the highest common factor.

    Why: Divide both parts by their common factor 6.

  2. 2. Write blue:orange when there are 6 blue and 4 orange counters.

    Check answer

    Answer: 6:4=3:2.

    Hint: Write blue first, then simplify.

    Why: Ratio order follows the named quantities.

  3. 3. Find an equivalent ratio to 3:5 with first part 12.

    Check answer

    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. 4. A cordial mix uses syrup:water=1:4. How much water for 250 mL syrup?

    Check answer

    Answer: 1000 mL water.

    Hint: Multiply 250 by 4.

    Why: The water amount is four times the syrup.

  5. 5. Share 72 stickers in ratio 5:3.

    Check answer

    Answer: 45 stickers and 27 stickers.

    Hint: Add ratio parts, then divide 72.

    Why: Eight total parts make each part 9.

  6. 6. Are 8:12 and 14:21 equivalent?

    Check answer

    Answer: Yes; both simplify to 2:3.

    Hint: Divide each pair by its common factor.

    Why: Equivalent ratios share a simplified form.

  7. 7. A map scale is 1 cm:5 km. What distance does 7.2 cm represent?

    Check answer

    Answer: 36 km.

    Hint: Calculate 7.2×5.

    Why: Scale factors multiply corresponding quantities.

  8. 8. A paint mix is red:blue:white=2:3:1 and totals 48 L. Find each amount.

    Check answer

    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. 9. Recipe A uses 300 g flour to 180 mL milk; B uses 450 g to 260 mL. Are they equivalent?

    Check answer

    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. 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?

    Check answer

    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.

Practice and reviewReady for practice

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.

Curriculum alignmentStart here

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.

Success criteria

  • I can write and interpret ratios in a stated order.
  • I can generate and justify equivalent ratios using a common scale factor.
  • I can solve ratio scaling, sharing and rate problems.
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.