# Proportion Calculator

The proportion calculator will help compute identical proportions. Before we can use the calculator, it's important to understand what a proportion is and how to solve proportions by hand.

## What is a proportion?

A proportion is the relationship between two quantities. It displays what portion of one part is contained in the whole. The result is typically seen as a fraction, but can also be represented with a colon, or as a decimal or percent.

Just as a fraction is made up of two parts, a numerator and a denominator, the same holds true for a proportion. The number number of a proportion is the numerator and the bottom part of the proportion is the denominator. To illustrate this, let's look at an example.

Suppose there is a cake cut into 12 slices and 5 of the 12 slices have been eaten. If we want to know what the proportion of slices remaining compared to the entire cake, we have `12-5 = 7`

slices remaining, so the proportion `7/12`

. If you wish to write this proportion using a colon, you would write it as `7:12`

. Note that the proportion calculator will not represent the proportion in the latter form. What process is involved if you want to simplify or scale the proportion up to a larger, yet equivalent proportion? The next section on how to solve proportions will explain the process.

## How to solve proportions

Suppose we have the same proportion of `7/12`

but we want to scale it up to a larger, equivalent ratio with a denominator of `96`

. To do this we set up two equivalent proportions and solve for the missing part. The process to solve the proportion is as follows:

- Set up both fractions, labeling the missing part with any variable of your choice.
- Put an equal sign between the two ratios. Note that ratio and proportion are the same thing.
- Isolate the variable by using cross multiplication, which is multiply the denominator of one proportion by the numerator of the other and vice versa.
- Solve for the variable.
- Use the proportion calculator to check your answer.

Solving the above example, we get

`7/12 = x/96`

`12 * x = 96 * 7`

`12x = 672`

`x = 56`

I urge you to use the proportion calculator if you are solving proportions with larger numbers or those involving decimals. Note that the ratio calculator accomplishes the same task since ratio is a synonym for proportion.

## The golden ratio

There is a special ratio that occurs in nature and construction that is achieved when two quantities have the same proportion as the proportion of their sum to the larger of the two quantities. This is known as the golden ratio, which has a value of approximately 1.618. The formula for the golden ratio, given two quantities `a`

and `b`

is `(a+b)/a = a/b`

. The golden ratio calculator is handy to compute this ratio.

The golden ratio is seen in architecture and in general with shapes such as the rectangle. A rectangle is golden if, given the width `a`

and length `a + b`

, the ratio `(a+b)/a = a/b`

yields the value of approximately 1.618. There golden ratio is the limit of the ratio of consecutive Fibonacci numbers and is a non-terminating decimal, thus we use the approximate value of 1.618. The golden rectangle calculator will compute the length and width that achieves the golden rectangle.