Ratios and Proportions
Solve proportional relationships and simplify mathematical ratios. Get instant step-by-step solutions — completely free, no signup required.
Free Ratios and Proportions Calculator
Enter your problem below to get an instant step-by-step solution.
About Ratios and Proportions
Solve proportional relationships and simplify mathematical ratios. Pre-algebra builds the foundation for all higher math. Understanding order of operations, percentages, and basic number properties is essential before moving to algebra.
Our Ratios and Proportions calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any ratios and proportions expression and receive a complete, verified solution with every step shown.
Ratios and Proportions Formula
a / b = c / d ⇔ a·d = b·c
A ratio compares two quantities; a proportion states that two ratios are equal. To find a missing value, cross-multiply and divide. Simplify ratios by dividing every part by the greatest common factor.
Worked Example
If 3 notebooks cost $7.50, how much do 8 cost?
- Set up the proportion: 3 / 7.50 = 8 / x
- Cross-multiply: 3x = 8 × 7.50 = 60
- Divide: x = 60 / 3 = 20
Answer: $20.00
Common Mistakes to Avoid
- Setting the proportion up with inconsistent units on each side.
- Cross-multiplying across the same fraction instead of diagonally.
- Simplifying a ratio by subtracting instead of dividing.
How to Use the Ratios and Proportions Calculator
- 1
Type your Ratios and Proportions problem into the input field above
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Press Enter or click the Solve button to run the calculation
- 3
Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Ratios and Proportions formula?
a / b = c / d ⇔ a·d = b·c. A ratio compares two quantities; a proportion states that two ratios are equal. To find a missing value, cross-multiply and divide. Simplify ratios by dividing every part by the greatest common factor.
Can you show a worked Ratios and Proportions example?
If 3 notebooks cost $7.50, how much do 8 cost?: Set up the proportion: 3 / 7.50 = 8 / x; Cross-multiply: 3x = 8 × 7.50 = 60; Divide: x = 60 / 3 = 20. Answer: $20.00.
Is this Ratios and Proportions calculator free to use?
Yes — the Ratios and Proportions calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Ratios and Proportions homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.