Proportion Calculator
Solve proportions: a/b = c/d
Proportion Formula
How to Solve Proportions
Set Up the Proportion
Write the proportion as a/b = c/d and identify the missing value.
Cross Multiply
Multiply diagonally: a × d = b × c
Solve for Unknown
Isolate the variable by dividing both sides.
Verify
Check that cross products are equal.
Examples
Example 1: Solve 3/4 = 6/x
Cross multiply: 3 × x = 4 × 6
3x = 24
x = 8
Verify: 3 × 8 = 24, 4 × 6 = 24 ✓
Answer: x = 8
Example 2: Recipe scaling - If 2 cups serve 4 people, how many cups for 10 people?
Set up: 2/4 = x/10
Cross multiply: 2 × 10 = 4 × x
20 = 4x
x = 5
Answer: 5 cups
Example 3: Map scale - If 1 inch = 50 miles, how many miles is 3.5 inches?
Set up: 1/50 = 3.5/x
Cross multiply: 1 × x = 50 × 3.5
x = 175
Answer: 175 miles
About Proportions
A proportion is an equation that states two ratios are equal. Proportions are fundamental in mathematics and appear constantly in real-world applications like cooking, construction, business, and science.
What is a Proportion?
A proportion shows that two fractions or ratios are equivalent: a/b = c/d. This means the relationship between a and b is the same as the relationship between c and d.
Cross Multiplication Rule
The cross products of a proportion are always equal: if a/b = c/d, then a × d = b × c. This is the key to solving proportions.
Real-World Applications
- Cooking: Scale recipes up or down for different serving sizes
- Shopping: Compare unit prices to find best deals
- Maps: Convert between map distances and real distances
- Construction: Maintain correct ratios for mixing materials
- Medicine: Calculate proper dosages based on weight
- Photography: Maintain aspect ratios when resizing images
- Business: Calculate profit margins and pricing
Types of Proportion Problems
- Direct Proportion: As one increases, the other increases (speed and distance)
- Inverse Proportion: As one increases, the other decreases (workers and time)
- Part-to-Part: Comparing two parts of a whole (boys to girls)
- Part-to-Whole: Comparing a part to the total (wins to games)
How to Use This Calculator
1Enter Your Values
Input the required values in the calculator fields above. Make sure all inputs are valid numbers.
2Click Calculate
Press the "Calculate" button to perform the calculation and see your results.
3Review Results
Review the calculated results displayed below. Use these values for your needs.
Formula
Formula will be calculated based on the inputs provided.
Example:
Example: Enter your values above and click Calculate to see the formula in action.
About Proportion Calculator
The Proportion Calculator is a useful tool for calculating proportion values. This calculator helps you quickly and accurately determine the results you need for your calculations.
When to Use This Calculator
- Quick Calculations: Get instant results without manual computation
- Accuracy: Ensure precise calculations every time
- Planning: Use for project planning and estimation
- Verification: Double-check your manual calculations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works on all devices
- ✅ Accurate: Precise mathematical calculations
Tips for Best Results
- Double-Check Inputs: Verify all values before calculating
- Use Valid Numbers: Ensure inputs are valid numbers
- Review Results: Check results for reasonableness
- Clear and Retry: Clear inputs if you need to recalculate
Frequently Asked Questions
How to Use This Calculator
Enter Your Values
Input the required values in the calculator fields above. Make sure all inputs are valid numbers.
Click Calculate
Press the "Calculate" button to perform the calculation and see your results.
Review Results
Review the calculated results displayed below. Use these values for your needs.
Formula
Formula will be calculated based on the inputs provided.
Example:
Example: Enter your values above and click Calculate to see the formula in action.
About Proportion Calculator
The Proportion Calculator is a useful tool for calculating proportion values. This calculator helps you quickly and accurately determine the results you need for your calculations.
When to Use This Calculator
- Quick Calculations: Get instant results without manual computation
- Accuracy: Ensure precise calculations every time
- Planning: Use for project planning and estimation
- Verification: Double-check your manual calculations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works on all devices
- ✅ Accurate: Precise mathematical calculations
Tips for Best Results
- Double-Check Inputs: Verify all values before calculating
- Use Valid Numbers: Ensure inputs are valid numbers
- Review Results: Check results for reasonableness
- Clear and Retry: Clear inputs if you need to recalculate
What is cross multiplication?
Cross multiplication means multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. For a/b = c/d, you multiply a×d and b×c.
How do I know if two ratios are proportional?
Two ratios are proportional if their cross products are equal. For example, 2/3 and 4/6 are proportional because 2×6 = 3×4 = 12.
Can proportions have negative numbers?
Yes! The same rules apply. Just be careful with signs when cross multiplying and solving.
What is the difference between a ratio and a proportion?
A ratio compares two quantities (3:4), while a proportion states that two ratios are equal (3:4 = 6:8 or 3/4 = 6/8).
How are proportions used in real life?
Everywhere! Scaling recipes, reading maps, comparing prices, calculating speeds, mixing paint colors, determining medication doses, and countless other daily situations.