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**Table of Content**

Use this proportion calculator to find missing values in proportional relationships. It uses two methods such as cross-multiplication and proportion formula to represent the equality between two ratios.

**Limitation:** This calculator only accepts numerical inputs (integers or decimals) for representing quantities. It can not handle non-numeric data like text or characters.

**“When two ratios are set equal to each other, then it is called a proportion”**

Two variables are said to be directly proportional if one is the product of the other variable and a constant(x/y is a constant ratio). If the product of the two variables is a constant, then they are said inversely proportional( x·y is a constant). The symbol of proportion is ‘::’ and ‘=’.

Proportion shows how two things change together. If one increases as the other increases, they are directly proportional. If one increases as the other decreases, they are inversely proportional.

It is widely used to solve the problems of changing numbers. For instance, suppose the price of the water bottle has increased 10% from the old price, you know the old price is $7. You can find the new prices such as:

\(\frac{old\ price}{100}=\frac{new\ price}{110}\)

\(\frac{old\ price}{100}=\frac{x}{110}\)

\(\ x=\frac{7}{100}\ \times 110 = $7.7\)

Also, it can be used in several sectors to perform tasks such as conversions of units, scaling or resizing of images, videos, etc.

The formula for proportion is stated as:

a:b::c:d=\(\frac{a}{b}=\frac{c}{d}\)

Two more formulas are used for direct and indirect proportion, which are:

- \(\ y = k\ \dot\ x\) (It means y is directly proportional to x with a constant of proportionality k)
- \(\ y = \frac{k}{x}\) (It shows that y is inversely proportional to x with a constant of proportionality k)

Where

- a, d are the extreme terms
- b, c are the mean terms
- K is the constant of proportionality

The constant of proportionality (k) is a value that shows how two proportional variables change together. In a proportional relationship, as one variable increases or decreases, the other variable changes by a constant factor (represented by k). This is applicable for both direct (one increases, the other increases) and indirect proportions (one increases, the other decreases).

There are two main and easiest ways to solve proportions:

- Cross Multiplication
- Proportion Formula

We have used both in the given example for better understanding:

The two ratios are 8:𝑥::6:4, solve for the unknown variable x

**Solution:**

**Using Cross Multiplication:**

Step 1: Construct a Proportion:

\(\frac{8}{x}=\frac{6}{4}\)

Step 2: Apply Cross Multiplication:

\(\ x\ \times\ 6=\ 8\ \times\ 4\)

\(\ 6x= 32\)

\(\ x=\frac{32}{6}\)

\(\ x=\frac{16}{3}= 5.33…\)

**Using The Proportion Formula:**

a:b::c:d=\(\frac{a}{b}=\frac{c}{d}\)

\(\frac{8}{x}=\frac{6}{4}\)

\(\frac{8}{x}=\ 1.5\)

\(\ x =\frac{8}{1.5} = 5.33..\)

\(\ x = 5.33..\)

In this example, we have found the proportion manually. But for more complex problems, you can use the above proportion calculator.

Ratios are considered proportional if they represent the same constant multiplier between two quantities. In simpler terms, if you increase or decrease one quantity by a certain factor, the other quantity must change by the same factor to maintain proportionality.

**References:**

From the source of Wikipedia: Understanding of direct & inverse

From the site of Mathisfun: Definition

Other Languages: Kalkulator Proporcji, Kalkulator Proporsi, Proportions Rechner, 比例計算, Calculo De Proporção, Calculadora De Proporciones, Calcolo Proporzioni, Калькулятор Пропорций, Mittasuhteet Laskin.