Compare two quantities with a ratio, understand part-to-part vs part-to-whole, and find equivalent ratios.
A ratio compares two quantities. You can write it three ways:
Part-to-whole ratios compare one part to the total.
Equivalent ratios name the same comparison — just scaled up or down (like equivalent fractions).
| Multiply both by 2 | Multiply both by 3 | Multiply both by 4 |
|---|---|---|
| 1:2 | 1:2 | 1:2 |
| 2:4 | 3:6 | 4:8 |
1. A bag has 4 green marbles and 6 yellow marbles. What is the ratio of green to yellow?
Green to yellow — list green first. There are 4 green and 6 yellow, so the ratio is 4:6.
2. Using the same bag (4 green, 6 yellow, 10 total), what is the part-to-whole ratio of yellow marbles to total marbles?
Part-to-whole: yellow (the part) to total. Yellow = 6, total = 10, so 6:10.
3. A recipe uses 2 cups of flour for every 3 cups of oats. Which ratio correctly describes flour to oats?
Flour comes first in "flour to oats." 2 cups flour : 3 cups oats = 2:3.
4. Which ratio is equivalent to 2:5?
Multiply both parts of 2:5 by the same number. 2×2 = 4, 5×2 = 10, so 4:10 is equivalent to 2:5.
5. A class has 12 boys and 15 girls. What is the ratio of boys to the total number of students?
Total = 12 + 15 = 27. Boys to total = 12:27.
6. A fruit bowl has 5 apples and 3 oranges. What is the ratio of oranges to apples?
Oranges to apples: oranges first = 3, apples = 5. So 3:5.
7. Fill in the blank: 3:4 = ___:8 (What number goes in the blank?)
4 was multiplied by 2 to get 8, so multiply 3 by 2 as well: 3 × 2 = 6.