Ratio tables and double number lines
Scale two linked quantities together and represent their relationship.
Before you begin
- Multiplication and division
- Part-to-part ratios
Preserve the multiplicative relationship
Equivalent ratios describe the same relative amounts. If a drink uses 2 cups of concentrate for 5 cups of water, multiplying both quantities by three gives 6:15. Adding the same amount to both does not usually preserve the mixture. A ratio table places matching amounts in each row, making it easier to scale up, scale down or combine whole batches.
Connect a table, diagram and graph
A double number line puts matching amounts at the same positions on two parallel scales. Both scales begin at zero, but their tick labels differ according to the ratio. Plotting table pairs as (concentrate, water) puts them on one straight line through the origin. Use the same order for every pair, and explain the units on each axis.
Worked example
A paint mixture uses blue:white = 3:4. Complete matching amounts for 6, 9 and 12 cups of blue paint.
Show the worked solution
- One batch has 3 cups blue and 4 cups white.
- 6, 9 and 12 cups blue are two, three and four batches, so multiply the white amount by the same factors.
- The pairs (6, 8), (9, 12) and (12, 16) all simplify to 3:4.
8, 12 and 16 cups of white paint.
Try it yourself
Which ratio is equivalent to 4:7?
Common mistakes
- Additive changes usually do not preserve a ratio.
- Label what each column, line or coordinate represents.
What can you explain now?
A recipe uses 5 cups of flour for 2 cups of milk. How much milk matches 15 cups of flour? State the graph point with flour first.
Compare with the explanation
6 cups of milk; (15, 6).
15 ÷ 5 = 3 batches, so milk is 2 × 3 = 6 cups. Scaling both amounts preserves the recipe.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗