ganak.appRatio Calculator
Simplify ratios, solve proportions, scale ratios, and compare for equivalence. Supports 2-term and 3-term ratios with step-by-step solutions and visual bars.
Enter a ratio to simplify it to lowest terms
Step-by-Step Solution
See how the answer is calculated
What Is a Ratio?
Understanding the relationship between two or more quantities
A ratio is a way to compare two or more quantities by showing how many times one value contains or is contained within the other. Ratios are written using a colon, for example 3 : 2, meaning “for every 3 of the first, there are 2 of the second.”
Ratio Notation
A : B = “A to B”
Part-to-part ratio: Compares one part to another part (e.g., 3 boys to 2 girls = 3 : 2).
Part-to-whole ratio: Compares one part to the total (e.g., 3 boys out of 5 students = 3 : 5).
Multi-term ratio: Compares three or more quantities (e.g., flour : sugar : butter = 3 : 2 : 1).
How to Simplify a Ratio
Reduce a ratio to its simplest form using the GCD
Step-by-Step Method
- Find the Greatest Common Divisor (GCD) of all terms
- Divide every term by the GCD
- The result is the ratio in simplest form
Example: Simplify 12 : 8
GCD of 12 and 8 = 4
12 ÷ 4 = 3, 8 ÷ 4 = 2
12 : 8 = 3 : 2
Decimal Ratios
If the ratio contains decimals, multiply all terms by a power of 10 to make them whole numbers first, then simplify.
0.5 : 1.5 → 5 : 15 → 1 : 3
How to Solve Proportions
Find the missing value when two ratios are equal
A proportion states that two ratios are equal: A : B = C : D. If one value is unknown, you can solve for it using cross multiplication.
Cross Multiplication Formula
A × D = B × C
Example: 3 : 5 = 9 : ?
D = B × C / A = 5 × 9 / 3 = 15
3 : 5 = 9 : 15
You can verify by checking that the cross products are equal: 3 × 15 = 45 and 5 × 9 = 45.
Scaling Ratios Up and Down
Create equivalent ratios by multiplying or dividing
To scale a ratio, multiply (or divide) every term by the same number. The resulting ratio is equivalent to the original.
Scaling Up
2 : 3 × 4 = 8 : 12
Scaling Down
8 : 12 ÷ 4 = 2 : 3
This is useful in recipes, maps, models, and anywhere you need to maintain the same proportion at a different scale.
Real-World Examples
Where ratios appear in everyday life
Cooking & Recipes
A recipe uses flour and sugar in a 3 : 1 ratio. For 6 cups of flour, you need 2 cups of sugar.
3 : 1 = 6 : 2
Maps & Scale Models
A map scale of 1 : 50,000 means 1 cm on the map = 50,000 cm (500 m) in real life.
1 : 50000 → 2 cm = 1 km
Finance & Business
Two partners invest in a 3 : 2 ratio. On $50,000 profit, they get $30,000 and $20,000.
3 : 2 → 60% : 40%
Screen Aspect Ratios
A 16 : 9 display is the standard widescreen ratio. A 1920 × 1080 screen follows this ratio.
1920 / 1080 = 16 / 9 = 1.778
Common Mistakes with Ratios
Pitfalls to avoid for accurate results
Confusing ratio with fraction
3 : 5 means 3 parts to 5 parts (total 8 parts). As fractions of the whole: 3/8 and 5/8, not 3/5.
Wrong order matters
3 : 5 is not the same as 5 : 3. Order reflects which quantity is first. Always match the order to the context.
Not simplifying to lowest terms
Always divide all terms by their GCD. 12 : 8 should be written as 3 : 2 for clarity.
Adding or subtracting ratio terms
You cannot add ratios like fractions. 2 : 3 + 1 : 4 does not equal 3 : 7. Ratios require proportional reasoning.
Mixing units in a ratio
Both quantities must be in the same unit. Convert 2 hours : 30 minutes to 120 : 30, then simplify to 4 : 1.
Frequently Asked Questions
Common questions about ratios, proportions, and simplification
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Last updated Feb 19, 2026