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Ratio Calculator

Simplify integer and decimal ratios, solve proportion equations, or divide values into specific parts.

Simplify Ratio

Supports integers and decimals. Separate terms with colons (:) or commas (,).

How Ratios and Proportions function

Ratios describe the relative size of two or more values. They are commonly written with a colon (e.g. 2:3) or as a fraction (2/3). Simplifying a ratio reduces the numbers to their lowest integers, making it easier to read and compare.

Understanding Proportions

A **proportion** states that two ratios are equal: A:B = C:D. If one value is missing, cross-multiplication solves the equation: A × D = B × C. This technique is useful in scaling recipes, map scales, screen dimensions, and camera aspect ratios.

Frequently Asked Questions (FAQ)

What is a mathematical ratio?

A ratio is a way of comparing two or more quantities to show how their sizes relate. For example, if you have 8 apples and 12 oranges, the ratio of apples to oranges is 8:12, which simplifies to 2:3.

How do you simplify a ratio?

To simplify a ratio, find the Greatest Common Factor (GCF) of all the numbers in the ratio. Then, divide each number by that GCF. For instance, for 15:20, the GCF is 5. Dividing both terms by 5 gives you 3:4.

What does it mean to solve a proportion?

A proportion is a statement that two ratios are equal, such as A:B = C:D (or A/B = C/D). If you know three of these numbers, you can solve for the fourth using cross-multiplication: A × D = B × C. For example, if 2:5 = X:15, then X = (2 × 15) / 5 = 6.

How do you divide an amount into a ratio?

First, sum all the parts of the ratio to find the total number of parts. Next, divide the total value by this sum to find the value of one single part. Finally, multiply each number in the ratio by the value of a single part to find the individual shares.

Can ratios contain decimal numbers?

Yes, ratios can contain decimals. To simplify a ratio with decimals, first multiply all terms by a power of 10 (like 10, 100, or 1000) to convert them all into integers. Then, simplify the resulting integers using their GCF as usual.

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About This Calculator

Target Audience: Students, educators, engineers & everyday problem solvers

What Does This Calculator Do?

The Ratio Calculator simplifies, scales, and compares proportions between numbers. It helps you find missing values in a ratio pair or scale a ratio up or down. This is extremely useful for scaling recipes, mixing fuel, resizing images, or calculating scale models in design projects.

How to Use It

  1. Enter Initial Ratio: Type in your starting ratio values (A : B).
  2. Enter Target Value: Input one value of your new scaled ratio (either C or D) to find the missing variable.
  3. Submit: Click calculate to find the missing proportion and see the simplified ratio.

The Logic Explained Simply

  • The Concept: A ratio compares the sizes of two or more values. Scaling a ratio keeps the relative proportions of the parts exactly the same even if the total amount increases or decreases.
  • The Formula: A / B = C / D
  • To solve for a missing value (e.g. D): D = (B * C) / A

Real-World Calculation Breakdown

Suppose you are mixing concrete where the required ratio of cement to sand is 1 : 3. You have 5 bags of cement and need to know how much sand to mix.

  1. Enter the starting ratio: A = 1, B = 3.
  2. Input the cement value you have: C = 5.
  3. Solve for the missing sand amount (D): D = (3 * 5) / 1 = 15.
  4. You need to mix exactly 15 bags of sand with your 5 bags of cement to keep the correct ratio!

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