Ratio Calculator: Simplify, Scale & Solve with Step-by-Step Working
Free interactive ratio calculator for PSLE students. Simplify ratios, find equivalent ratios, solve word problems with total or difference given, and combine ratios with detailed working shown.
Ratio Calculator for PSLE & Singapore Math
Struggling with ratios? Use our free calculator to simplify, scale, and solve ratio problems with complete step-by-step working. Perfect for P5-P6 students!
Interactive Ratio Calculator
Enter your ratio below and select what you want to calculate. The calculator shows every step so you can learn the method, not just get the answer.
Ratio Calculator
3 : 5 or 2:3:4How to Use This Calculator
This ratio calculator helps with 6 common types of ratio problems you’ll encounter in PSLE Math:
| Calculation Type | When to Use It |
|---|---|
| Simplify Ratio | Reduce 12 : 18 to simplest form (2 : 3) |
| Equivalent Ratios | Scale 3 : 5 up by ×4 to get 12 : 20 |
| Find Value (Total Given) | Share $60 in ratio 3 : 2 |
| Find Value (Difference Given) | 8 more boys than girls, ratio 5 : 3 |
| Ratio to Fraction | Convert 3 : 5 to fractions of total |
| Combine Two Ratios | Combine A:B = 2:3 and B:C = 4:5 into A:B:C |
Understanding Ratios: The Basics
A ratio compares two or more quantities using the ”:” symbol. The order matters — boys : girls is different from girls : boys!
💡 Key Concept
When we say the ratio of apples to oranges is 3 : 5, it means:
- For every 3 apples, there are 5 oranges
- Apples are 3 “parts” and oranges are 5 “parts”
- This does NOT mean there are exactly 3 apples!
Simplifying Ratios
To simplify a ratio, divide all terms by their Greatest Common Factor (GCF).
Example: Simplify 18 : 24
Step 1: Find the GCF of 18 and 24
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
GCF = 6
Step 2: Divide both terms by 6
18 ÷ 6 : 24 ÷ 6 = 3 : 4
Solving Ratio Word Problems
Most PSLE ratio questions fall into two categories:
Type 1: Total Given
When the total is given, follow these steps:
- Add up all ratio parts → total units
- Divide the total by total units → value of 1 unit
- Multiply to find each part
Example: Total Given Problem
Problem:
Amy and Ben share $60 in the ratio 3 : 2. How much does Amy get?
Step 1: Total units = 3 + 2 = 5 units
Step 2: 1 unit = $60 ÷ 5 = $12
Step 3: Amy (3 units) = 3 × $12 = $36
Type 2: Difference Given
When you’re told “how many more” one part is than another:
- Find the difference in units = larger part - smaller part
- Divide the given difference by difference in units → value of 1 unit
- Multiply to find each part
Example: Difference Given Problem
Problem:
The ratio of boys to girls is 5 : 3. There are 8 more boys than girls. How many girls are there?
Step 1: Difference in units = 5 - 3 = 2 units
Step 2: 2 units = 8, so 1 unit = 4
Step 3: Girls (3 units) = 3 × 4 = 12 girls
⚠️ Common Mistake
Don’t confuse “total given” with “difference given”! Read the question carefully to identify which type you’re dealing with.
Converting Between Ratios and Fractions
Understanding the connection between ratios and fractions is crucial for harder PSLE questions.
Ratio to Fraction (Part-to-Whole)
From a ratio A : B, the fraction of the total that A represents is:
Example: Ratio to Fraction
If boys : girls = 3 : 5, what fraction of the class are boys?
Total = 3 + 5 = 8
Boys = of the class
Fraction to Ratio
When you see “A is of B”, this means A : B = 3 : 5
The numerator becomes the first term, denominator becomes the second term.
Combining Two Ratios
When you have two ratios that share a common term, you can combine them into a three-term ratio.
The Method:
- Identify the common term
- Make it equal in both ratios using LCM
- Combine into one ratio
Example: Combining Ratios
Problem:
A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.
Step 1: Common term is B
B = 3 in first ratio, B = 4 in second ratio
Step 2: Make B equal using LCM(3, 4) = 12
A : B = 2 : 3 → multiply by 4 → 8 : 12
B : C = 4 : 5 → multiply by 3 → 12 : 15
Step 3: Combine
A : B : C = 8 : 12 : 15
Quick Reference: Ratio Formulas
| What You Need | Formula |
|---|---|
| Simplest form | Divide all terms by GCF |
| Equivalent ratio | Multiply/divide all terms by same number |
| 1 unit (total given) | Total ÷ (sum of ratio parts) |
| 1 unit (difference given) | Difference ÷ (larger part - smaller part) |
| Part-to-whole fraction | Part ÷ Total parts |
| Combine A:B and B:C | Make B equal using LCM, then combine |
Practice Tips for PSLE
💡 Exam Strategy
- Always draw a bar model — it helps you visualize the problem
- Write the ratio in the correct order — the order in the question matters
- Find 1 unit first — this is the key to solving most ratio problems
- Check your answer — does it make sense? Does it match the given information?
Common Mistakes to Avoid
| Mistake | Why It’s Wrong | Correct Approach |
|---|---|---|
| Writing ratio in wrong order | ”Girls to boys” is different from “boys to girls” | Read the question carefully |
| Adding total when difference is given | Uses the wrong formula | Identify if it’s total or difference |
| Not simplifying final answer | PSLE expects simplest form | Always simplify at the end |
| Forgetting units | Answer needs proper units | Include $, cm, kg, etc. |
Related Topics
After mastering ratios, you’ll be ready for:
- Percentage problems — ratios and percentages are closely related
- Rate and speed problems — uses similar “per unit” thinking
- Proportion — extends ratio concepts further
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