A fraction always represents part of a whole (part-to-whole).
A ratio can compare part-to-part or part-to-whole.
This means a part-to-whole ratio converts directly to a fraction, but a part-to-part ratio does not — you need an extra step.
Part-to-Whole Ratio → Fraction
5 out of 20 students passed → ratio 5:20
This is already part-to-whole
Write as fraction: 5/20
Simplify: 1/4
Part-to-Part Ratio → Fraction
Boys to girls = 3:2. What fraction are boys?
Find the total parts: 3 + 2 = 5
Boys are 3 out of 5 total
Fraction: 3/5
For part-to-part ratios, add the parts to get the whole, then write the part you want over the total.
Fraction → Ratio
3/8 of students are left-handed
Part-to-whole ratio: left-handed to total = 3:8
Part-to-part ratio: left to right = 3:5 (since 8−3=5)
💡 Always ask: Is the question asking for part-to-part or part-to-whole? This determines whether you write the ratio as-is or need to add/subtract to find the other part.
🎯 Practice Problems
1. The ratio of cats to total pets is 4:10. What fraction of pets are cats?
A) 10/4
B) 4/10
C) 4/6
D) 6/10
2. Boys to girls = 5:3. What fraction of the class are boys?
A) 5/3
B) 3/5
C) 5/8
D) 3/8
3. 2/7 of a bag is red marbles. What is the ratio of red to non-red?
A) 2:7
B) 7:2
C) 2:5
D) 5:2
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🎯 Bonus Practice
1. The ratio of wins to losses is 7:3. What fraction of games were won?
A) 7/3
B) 3/7
C) 7/10
D) 3/10
2. In a recipe, the ratio of flour to sugar is 4:1. What fraction of the dry mix is sugar?
A) 1/4
B) 4/1
C) 1/5
D) 4/5
3. 3/4 of the class passed. What is the ratio of pass to fail?
A) 3:4
B) 4:3
C) 3:1
D) 1:3
4. A paint mix is 2:3 (blue:white). What fraction is blue?
A) 2/3
B) 3/2
C) 2/5
D) 3/5
5. If 5/12 of items are defective, what is the part-to-whole ratio of non-defective items?