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Proportion Calculator

Proportion Calculator

Note: Enter 3 numbers and unknown variable (x) or any other letter into the given fields.

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Check our ratio calculator to learn more about the proportionality!
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An online proportion calculator allows you to solve proportion problems and find the missing variable value in a given proportion. The proportions calculator calculates the missing value by using the cross multiplication and proportion method.

Well, stick to the context to understand how to solve proportions (step-by-step) & with a calculator, basic tips & tricks on solving proportions, & more.

But, basic is essential before exploring the other related-terms, so let’s move to its mathematical definition.

What is Proportion?

Proportion is said to be a mathematical comparison between two numbers. More specifically, it two sets of the numbers are increasing/decreasing in the same ratio, then the ratios are referred to directly proportional to each other. Typically, proportions are represented with the symbol “\(::\)” or “\(=\)”.

Solving proportions is very simple as you simply need to state the ratios as fractions, representing the two fractions are equal to each other, cross multiplying as well as solving the resulting equation.

proportion calculator

Example of Proportion:

Remember that two ratios are referred to be in proportion when the two ratios are equal. For example, the time taken by train to cover \(40\) km per hour (kmph or km/hr) is exactly equal to the time that taken by it to cover the distance of 240 km for 6 hours. Such as \(40\) kmph \(= 240\) km/\(6\) hrs. To calculate proportion look at the given example below.

If you want to display the result in percent, simply use our online percentage calculator which is the best choice for you to get the proportion with 100 as denominator.

How to Solve a Proportion Manually (Step-by-Step):

If you want to know the missing variable in the proportion equation, then simply put the equal sign between them. Find the missing value by cross multiplication. Our proportion calculator generates the result with cross-multiplication as well as with the proportion method. Here we have a manual example for clarification.

Example:

The equation is given as \(\frac {8}{x} = \frac {6}{4}\), solve for the unknown \(x\)?

Solution:

By Cross Multiplication:

The equation is;

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

By cross multiplication,

\(6x = 8 \times 4\)

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

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

\(x = 5.33\)

By Proportion:

The equation is equal if,

8 / 6 = 1.33

So, it is true that,

x / 4 = 1.33

x = 1.33 × 4

x = 5.33

We urge you to use our free proportion calculator if you are going to solve proportions for large numbers or any decimal numbers.

If the term is connected the two variables without any further qualification, it is assumed as directly related. For example, c = y/x where c is the proportionality constant in the proportional equations, x & y are variables are directly related to each other.

If the product of two variables equal to a constant k, then the variables are inversely related to each other. The equation is written as, x*y = c. After using this proportional calculator you will be easily tell that whether two parameters are inversely related or directly related.

How Proportion Calculator Works:

This proportion solver gives the instant & accurate results of your problem related to proportions, just follow the given instructions:

Inputs:

  • Enter the values in the fields and replace the unknown value with any variable x, y or any other.
  • Then, hit on calculate button.

Outputs:

The Proportions calculator shows:

  • The value of a missing variable
  • Step-by –step solution of both methods (cross multiplication & proportion)

Tips and Tricks on Proportion:

  • a/b = c/d ⇒ ad = bc
  • a/b = c/d ⇒ b/a = d/c
  • a/b = c/d ⇒ a/c = b/d
  • a/b = c/d ⇒ (a + b)/b = (c + d)/d
  • a/b = c/d ⇒ (a – b/b = (c – d)/d
  • a/(b + c) = b/(c + a) = c/(a + b) and a + b + c ≠0, then a = b = c.
  • a/b = c/d ⇒ (a + b)/(a – b) = (c + d)/(c – d), which is said to be as componendo -dividendo rule
  • If “a” and “b” are multiplied or simply divided by the same number in the ratio a:b, then remember that the resulting ratio remains the same as the original ratio.

Frequently Ask Questions (FAQ’s):

What are 3 ways to solve a proportion?

The following are three ways to solve the proportions:

  • Vertical
  • Horizontal
  • Diagonal (Often called cross-product)

What are the types of proportion?

Basically, the two types of proportion exist:

  • Direct
  • Inverse

Wrapping it up:

Typically, the concepts of proportions are used in the field of geography, dietetics, cooking, comparing quantities in physics, etc. So, an online proportion calculator is the best way to calculate proportion within seconds.

References:

From the source of Wikipedia : Understanding of direct & inverse proportion

From the site of mathisfun : Definition of proportion

From the source of math.com : Manual calculations of proportions

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