🧱 See It
Picture a pile of colored tiles: 3 red tiles and 2 blue tiles, sitting side by side. A ratio just describes how many of one thing you have compared to how many of another.
3 red tiles for every 2 blue tiles.
✏️ Draw It
Now double every tile — 2 red groups become... well, watch what happens to the counts. The relationship between red and blue stays exactly the same, even though there are more tiles.
3 red to 2 blue.
6 red to 4 blue — twice as many of each, but still the same "3-to-2" relationship.
🔢 Write It
Mathematicians write the same red-to-blue ratio a few different ways — they all mean the exact same thing:
3 to 2
3 : 2
3/2
💡 Worked Examples
Example 1 — Scaling Up: A recipe uses 2 cups flour to 1 cup sugar. If you use 6 cups flour, how much sugar do you need?
- Write the original ratio:
2 flour : 1 sugar - Find the scale factor: how did flour change?
6 ÷ 2 = 3, so everything scales ×3. - Apply the same ×3 to the sugar side:
1 × 3 = 3 - Answer: 3 cups of sugar.
Example 2 — Scaling Down: A trail mix uses 9 raisins to 6 almonds. You only have 3 almonds — how many raisins should you use?
- Write the original ratio:
9 raisins : 6 almonds - Find the scale factor: almonds went from
6to3, so3 ÷ 6 = ½— everything scales ×½ (divide by 2). - Apply the same ÷2 to the raisins side:
9 ÷ 2 = 4.5 - Answer: 4.5 raisins.