Discover
A purple paint uses 2 cups of red for 3 cups of blue. To make the same color with 6 cups of red, how much blue?
- 9 cups
- 7 cups
Key idea
Equivalent ratios multiply both quantities by the same number.
A ratio compares two quantities in order. Equivalent ratios come from multiplying (or dividing) both parts by the same number: . Tables and double number lines show them.
Worked example
.
Multiply both by 4
5 × 4 = 20.
4 × 4.
Your turn, guided
Your turn: .
× 4.
Practice ★
- A recipe uses 7 cups of flour for every 6 cups of sugar. How many cups of sugar go with 42 cups of flour?
- A recipe uses 2 cups of flour for every 7 cups of sugar. How many cups of sugar go with 12 cups of flour?
- Which ratio is equivalent to ?
Watch out!
Practice ★★
- Complete the equivalent ratio .
- Complete the equivalent ratio .
Exit ticket
Three questions to check you have got it.
- A recipe uses 7 cups of flour for every 6 cups of sugar. How many cups of sugar go with 42 cups of flour?
- A recipe uses 2 cups of flour for every 7 cups of sugar. How many cups of sugar go with 12 cups of flour?
- A recipe uses 9 cups of flour for every 2 cups of sugar. How many cups of sugar go with 27 cups of flour?
Summary card
Equivalent ratios
Multiply both parts by the same number.
Watch out: adding the same amount changes the ratio.
End of the lesson
Next lesson: Part-part-whole ratio problems Back to the chapter