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Online Ratio Calculator
A fast and accurate online tool for simplifying, scaling, and comparing ratios using exact integer arithmetic.
Answer
3 : 4 = 600 : 800
Answer
250:280 * 2.5 = 625:700
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What Is This Tool?
This calculator helps you simplify ratios by dividing both terms by their greatest common divisor (GCD), scale ratios by a factor, and check for equivalent ratios. It is designed to provide precise and accurate results for any numeric ratio inputs.
How to Use This Tool?
- Enter the two numbers representing the ratio (a and b)
- Click calculate to simplify the ratio by dividing both terms by gcd(a, b)
- Optionally input a scaling factor k to multiply both terms for scaling
- Compare ratios by entering two sets of numbers and checking equivalency
- Review the output ratio displayed in its simplest form or scaled form
Key Features
- Simplifies ratios using the greatest common divisor method
- Scales ratios by a multiplicative factor
- Checks equivalence between two ratios
- Uses exact integer arithmetic for accurate calculations
- Supports only numeric inputs for ratio terms
Examples
- Simplify the ratio 42:56 by finding gcd(42, 56) = 14, then divide both terms: 42/14:56/14 = 3:4
- Scale the ratio 3:4 by a factor of 2 to get 6:8
- Verify that ratios 3:4 and 6:8 are equivalent by confirming 3/4 = 6/8
Common Use Cases
- Simplifying ingredient proportions in cooking recipes
- Comparing map scales or model building dimensions
- Solving math problems involving proportions
- Designing engineering components with specific ratios
- Adjusting quantities in comparative measurements
Tips & Best Practices
- Always input numeric values for accurate calculation results
- Use the tool to confirm equivalency before scaling ratios
- Double-check inputs to avoid errors in proportion calculations
- Use integer values for ratio terms to maintain precision
- Apply scaling factors carefully to adjust quantities correctly
Limitations
- Supports only numeric values and does not process algebraic or symbolic ratio expressions
- Cannot simplify or compare ratios involving variables or formulas
- Does not handle non-integer or decimal ratios directly
Frequently Asked Questions
- How does the calculator simplify ratios?
- The calculator finds the greatest common divisor (GCD) of the two terms and divides both numbers by this GCD to give the simplest form of the ratio.
- Can this tool scale a ratio by any factor?
- Yes, you can multiply both terms of the ratio by any integer multiplicative factor to scale the ratio accordingly.
- Does the calculator accept algebraic expressions as inputs?
- No, it only supports numeric values and cannot handle algebraic or symbolic ratio expressions.
Key Terminology
- a
- First number in the ratio
- b
- Second number in the ratio
- k
- Multiplicative factor used to scale ratios
- gcd(a,b)
- Greatest common divisor of a and b used for simplifying ratios