Learn the 3-Step Method
1Total the parts.
3 : 2 → 5 parts in the whole.
2Each side over the total.
First amount = 3/5 of the whole; second = 2/5.
3Go backwards too.
If 3/5 of a class are girls, girls : boys = 3 : 2 (boys get the REST: 5 − 3 = 2).
Worked Example
In a box, the ratio of milk to dark chocolates is 5 : 3. What fraction are dark — and how many dark in a box of 24?
3 × 3 = 9
Watch Out! Common Mistakes
Over the TOTAL! 3 parts of 5 → 3/5.
Boys are the REST! 5 − 3 = 2 → girls : boys = 3 : 2.
Match the side! Dark is the 3: 3 × 3 = 9. (15 is the milk.)
⬇ Cheat Sheet
- Total the ratio parts.
- Fraction = that side's number over the total.
- Backwards: fraction a/b → ratio a : (b − a).
- Then use fraction-of-amount to get counts.
📖 Continue Your Journey
Quick summary
- Total the parts: 3 : 2 makes 5.
- Each side becomes a fraction over the total: 3/5 and 2/5.
- Backwards: 3/5 girls means girls : boys = 3 : 2 — the other side is the rest.
- Combine with fraction-of-amount for counts: 3/8 of 24 = 9.
Frequently asked questions
How do you turn a ratio into fractions?
Add the parts for the total, then put each side over it: 3 : 2 has 5 parts, so the sides are 3/5 and 2/5 of the whole.
How do you turn a fraction into a ratio?
The fraction's top is one side; the rest of the whole is the other: 3/5 girls means 3 : 2 against the remaining 2/5 boys.
Why is 3 : 2 not the same as 3/2?
Because the ratio compares part to part, while the fraction of the whole compares part to total — and the total is 5, not 2.
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