Keep a mix in the same ratio
Use equivalent ratios to scale a fictional mixture.
Supplied materials
- Paper or a note app; no actual mixing is required.
- Fictional paint recipe: 2 cups blue to 3 cups white. One batch is 5 cups altogether.
Learn the idea
A ratio compares quantities in a stated order. Blue:white = 2:3 does not mean that blue is 2/3 of the whole mixture; blue is 2 of the 5 total parts.
An equivalent ratio multiplies both amounts by the same factor. Scaling only one amount changes the recipe. Check a result by adding the two amounts and comparing each amount with the original.
- Write blue:white = 2:3 and label the total as 5 cups.
- For 10 cups, divide 10 by 5 to find the scale factor.
- Multiply both ingredient amounts by that factor.
- Repeat the method for the 20-cup question below.
See the method in action
For 10 cups, the factor is 10 ÷ 5 = 2. Blue = 2 × 2 = 4 cups; white = 3 × 2 = 6 cups. The total is 10 and the ratio 4:6 simplifies to 2:3.
Check your reasoning
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See the answer and explanation
8 cups blue and 12 cups white
20 ÷ 5 = 4, so both amounts increase fourfold: 8 blue and 12 white. Equal quantities would change the ratio; reversing the amounts would reverse the recipe.
Take it further
Plan a 15-cup batch and explain why blue is 2/5, rather than 2/3, of the total. Check: 6 blue and 9 white.
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Longer courses for learners ages 14+
These related courses have their own preparation and projects. They are not early-grade assignments.
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