Ratio Calculator

Solve ratios and proportions. Scale values proportionally, simplify ratios, and find missing values in proportional relationships.

Enter three values and leave one empty to solve.

A : B = C : D

About Ratio Calculator

Understanding Ratios

A ratio is a way of comparing two or more quantities by showing the relative size of one quantity to another. Written as A:B, it tells you that for every A units of one thing, there are B units of another. Ratios are one of the most fundamental concepts in mathematics and appear everywhere from cooking recipes to engineering blueprints.

Ratios can be expressed in several forms: using a colon (3:4), as a fraction (3/4), or with the word "to" (3 to 4). While these all represent the same relationship, the colon notation is the most common in everyday use.

Proportions and Cross-Multiplication

A proportion is an equation that states two ratios are equal, such as A:B = C:D. This is the foundation for solving unknown values in proportional relationships. The key technique is cross-multiplication: if A/B = C/D, then A × D = B × C.

For example, if you know that 2:3 = x:9, cross-multiplying gives 2 × 9 = 3 × x, so 18 = 3x, and x = 6. This method works for any proportion where exactly one value is unknown.

Simplifying and Scaling Ratios

Simplifying a ratio means reducing it to its smallest equivalent form by dividing both terms by their greatest common divisor (GCD). For instance, 24:36 simplifies to 2:3 because the GCD of 24 and 36 is 12. Simplified ratios are easier to understand and compare.

Scaling a ratio means multiplying both terms by the same factor to create an equivalent ratio with larger or smaller values. This is essential when adjusting recipes, resizing images, or creating scale models. A ratio of 1:4 scaled by 5 becomes 5:20.

Real-World Applications

Ratios are indispensable in daily life and professional fields. In cooking, a recipe might call for a 2:1 ratio of flour to sugar. In finance, the debt-to-income ratio helps lenders assess creditworthiness. Map scales use ratios like 1:50,000 to represent distances.

In science, ratios describe concentrations, gear ratios determine mechanical advantage, and aspect ratios define screen dimensions. Understanding ratios and proportions is a gateway skill that connects arithmetic to algebra, geometry, and beyond.

Frequently Asked Questions

What is a ratio?

A ratio is a comparison of two or more quantities that shows the relative size of one quantity to another. For example, 3:2 means for every 3 of one thing, there are 2 of another. Ratios can be written as 3:2, 3/2, or '3 to 2'.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (e.g., 3:4), while a proportion is an equation stating that two ratios are equal (e.g., 3:4 = 6:8). Proportions are used to find unknown values when one ratio is known and part of the equivalent ratio is given.

How do you simplify a ratio?

To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, the ratio 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4. Dividing both by 4 gives 3:2.

How do you solve for a missing value in a proportion?

Use cross-multiplication. For A:B = C:D, if D is unknown, multiply A × D = B × C, then solve for the missing value. For example, if 2:3 = 4:x, then 2x = 12, so x = 6.

What are common real-world uses of ratios?

Ratios are used in cooking (ingredient proportions), map scales, mixing paint colors, financial analysis (debt-to-income), architecture (scale models), photography (aspect ratios), and science (concentration solutions).

Can ratios have more than two terms?

Yes, ratios can compare three or more quantities. For example, a concrete mix ratio of 1:2:3 means 1 part cement, 2 parts sand, and 3 parts gravel. Each term is compared relative to all others.

Additional Resources

Math is Fun – Introduction to Ratios Khan Academy – Ratios, Rates, and Proportions Purplemath – Ratios and Proportions

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