Proportional Reasoning: Advanced Ratio Problem Solving

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 17 | Questions: 15 | Updated: Jan 20, 2026
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1) The ratio 48:60 is the same as 4:5.

Explanation

Divide both by 12 → 48 ÷ 12 = 4, 60 ÷ 12 = 5.

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About This Quiz
Proportional Reasoning: Advanced Ratio Problem Solving - Quiz

When ratios go bigger, they turn into proportions — and that’s when problem-solving gets interesting! In this quiz, you’ll tackle advanced ratio challenges, from proportional relationships to multi-step reasoning. Take this quiz to level up your skills in making smart comparisons.

2) A recipe calls for 300 ml milk, 200 ml water, and 100 ml sugar. What is the simplified ratio of milk:water:sugar?

Explanation

Divide all by 100 → 300:200:100 = 3:2:1.

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3) If 40 students are boys and 60 students are girls, what is the ratio of boys to girls in its simplest form?

Explanation

Divide both by 20 → 40 ÷ 20 = 2, 60 ÷ 20 = 3.

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4) A box has 50 chocolates and 75 candies. Simplify the ratio of chocolates to candies.

Explanation

Divide both by 25 → 50 ÷ 25 = 2, 75 ÷ 25 = 3.

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5) A class has 20 students who like cricket, 30 who like football, and 50 who like basketball. Simplify the ratio cricket:football:basketball.

Explanation

Divide all by 10 → 20:30:50 = 2:3:5.

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6) The ratio of two numbers is 5:7. If their sum is 72, what are the two numbers?

Explanation

Parts = 12. Each part = 72 ÷ 12 = 6. Numbers = 5×6=30, 7×6=42.

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7) The angles of a triangle are in the ratio 2:3:4. What are the angles?

Explanation

Total parts = 9. Each part = 180 ÷ 9 = 20. Angles = 40°, 60°, 80°.

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8) The ratio of red balls to blue balls is 18:24. Simplify it to its lowest form.

Explanation

Divide both by 6 → 18 ÷ 6 = 3, 24 ÷ 6 = 4.

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9) A school has 120 boys and 150 girls. What is the simplified ratio of boys to total students?

Explanation

Total = 270. Ratio = 120:270. Divide both by 30 → 4:9.

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10) The ratio 84:126 simplifies to 2:3.

Explanation

Divide both by 42 → 84 ÷ 42 = 2, 126 ÷ 42 = 3.

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11) If the ratio of boys to girls is 7:9, and there are 126 girls, how many boys are there?

Explanation

Each part = 126 ÷ 9 = 14. Boys = 14 × 7 = 98.

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12) Simplify the ratio 126:189.

Explanation

Divide both by 63 → 126 ÷ 63 = 2, 189 ÷ 63 = 3.

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13) Simplify 275:330.

Explanation

Divide both by 55 → 275 ÷ 55 = 5, 330 ÷ 55 = 6.

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14) The simplest form of 64:80 is 4:5.

Explanation

Divide both by 16 → 64 ÷ 16 = 4, 80 ÷ 16 = 5.

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15) Simplify the ratio 96:144.

Explanation

Divide both by 48 → 96 ÷ 48 = 2, 144 ÷ 48 = 3.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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The ratio 48:60 is the same as 4:5.
A recipe calls for 300 ml milk, 200 ml water, and 100 ml sugar. What...
If 40 students are boys and 60 students are girls, what is the ratio...
A box has 50 chocolates and 75 candies. Simplify the ratio of...
A class has 20 students who like cricket, 30 who like football, and 50...
The ratio of two numbers is 5:7. If their sum is 72, what are the two...
The angles of a triangle are in the ratio 2:3:4. What are the angles?
The ratio of red balls to blue balls is 18:24. Simplify it to its...
A school has 120 boys and 150 girls. What is the simplified ratio of...
The ratio 84:126 simplifies to 2:3.
If the ratio of boys to girls is 7:9, and there are 126 girls, how...
Simplify the ratio 126:189.
Simplify 275:330.
The simplest form of 64:80 is 4:5.
Simplify the ratio 96:144.
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