# Proportion Calculator

A Proportion Calculator is a free online tool that displays a proportion of a given expression. STUDYQUERIES’S online proportion calculator tool makes the calculations faster and easier where it shows the proportion in a fraction of seconds.

## How to Use a Proportion Calculator?

Solve for an unknown value $$x$$ with this fractions calculator. Find the missing fraction variable in the proportion using cross multiplication to calculate the unknown variable $$x$$. Solve the proportion between 2 fractions and calculate the missing fraction variable inequalities.

## Proportion Calculator

Enter 3 values and 1 unknown. For example, enter $$\mathbf{\frac{x}{45} = \frac{1}{15}}$$. The proportion calculator solves for $$x$$.

### How to Solve for x in Fractions

Solve for $$x$$ by cross multiplying and simplifying the equation to find x.

Example: Given the equation $$\mathbf{\frac{4}{10} = \frac{x}{15}}$$ solve for $$x$$.

Cross multiply the fractions

$$\mathbf{4 \times 15 = 10 \times x}$$

Solve the equation for $$x$$

$$\mathbf{x = \frac{(4 \times 15)}{10}}$$

Simplify for $$x$$

$$x = 6$$

To check the work put the result, 6 back into the original equation

$$\mathbf{\frac{4}{10} = \frac{6}{15}}$$

Cross multiply the fractions and you get

$$\mathbf{4 \times 15 = 10 \times 6}$$

$$60 = 60$$

Since $$60 = 60$$ is true, you can be sure that $$x = 6$$ is the correct answer.

• A fraction with a zero denominator is undefined.

### Why Does the Cross Multiplication Calculator for Fractions Work?

Cross multiplying works because you’re just multiplying both sides of the equation by 1. Since multiplying anything by 1 doesn’t change its value you’ll have an equivalent equation.

For example, look at this equation:

$$\mathbf{\frac{a}{b} = \frac{c}{d}}$$

If you multiply both sides by $$1$$ using the denominators from the other side of the equation you get:

$$\mathbf{\frac{a}{b}\times \frac{d}{d}= \frac{c}{d}\times \frac{b}{b}}$$

Note that this doesn’t change anything, because multiplying anything by $$1$$ doesn’t change its value. So now you have:

$$\mathbf{\frac{a×d}{b×d}=\frac{b×c}{b×d}}$$

Since the denominators are also the same here, b × d, you can remove them and say that:

$$a\times d=b\times c$$

This is the result of cross multiplying the original equation:

$$\mathbf{\frac{a}{b} = \frac{c}{d}}$$

## Proportion

Proportion is explained majorly based on ratios and fractions. A fraction, represented in the form of $$\mathbf{\frac{a}{b}}$$, while ratio $$a:b$$, then a proportion states that two ratios are equal. Here, $$a$$ and $$b$$ are any two integers. The ratio and proportion are key foundations to understand the various concepts in mathematics as well as in science.

Proportion finds application in solving many daily life problems such as in business while dealing with transactions or while cooking, etc. It establishes a relation between two or more quantities and thus helps in their comparison.

### What is Proportion?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

#### Definition

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol $$”::”\ or\ “=”$$.

Example

Two ratios are said to be in proportion when the two ratios are equal. For example, the time taken by train to cover $$50km\ per\ hour$$ is equal to the time taken by it to cover the distance of $$250\ km\ for\ 5\ hours$$. Such as $$50km/hr = \frac{250\ km}{5\ hrs}$$.

#### Continued Proportions

Any three quantities are said to be in continued proportion if the ratio between the first and the second is equal to the ratio between the second and the third. Similarly, four quantities in continued proportion will have the ratio between the first and second equal to the ratio between the third and fourth.

For example, consider two ratios to be a:b and c:d. In order to find the continued proportion for the two given ratio terms, we will convert their means to a single term/number. This in general, would be the LCM of means, and for the given ratio, the LCM of b & c will be bc. Thus, multiplying the first ratio by c and the second ratio by b, we have

• First ratio- $$ca:bc$$
• Second ratio- $$bc:bd$$

Thus, the continued proportion for the given ratios can be written in the form of $$ca:bc:bd$$.

### Ratios and Proportions

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers $$a$$ and $$b$$ is given by $$a:b$$ or $$\mathbf{\frac{a}{b}}$$. Multiply and divide each term of a ratio by the same number (non-zero), which doesn’t affect the ratio.

When two or more such ratios are equal, they are said to be in proportion.

#### Fourth, Third and Mean Proportional

If $$a : b = c : d$$, then:

• $$d$$ is called the fourth proportional to $$a, b, c$$.
• $$c$$ is called the third proportional to $$a$$ and $$b$$.
• The mean proportion between $$a$$ and $$b$$ is $$\sqrt(ab)$$.

#### Tips and Tricks on Proportion

• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc}$$
• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{b}{a} = \frac{d}{c}}$$
• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a}{c} = \frac{b}{d}}$$
• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a + b}{b} = \frac{c + d}{d}}$$
• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a – b}{b} = \frac{c – d}{d}}$$
• $$\mathbf{\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b}\ and\ a + b + c \neq0, then\ a = b = c}$$
• $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a + b}{a – b} = \frac{c + d}{c – d}}$$, which is known as componendo -dividendo rule
• If both the numbers a and b are multiplied or divided by the same number in the ratio $$a:b$$, then the resulting ratio remains the same as the original ratio.

### Proportion Formula with Examples

A proportion formula is an equation that can be solved to get the comparison values. To solve proportion problems, we use the concept that proportion is two ratios that are equal to each other. We mean this in the sense of two fractions being equal to each other.

#### Ratio Formula

Assume that we have any two quantities (or two entities) and we have to find the ratio of these two, then the formula for ratio is defined as $$a:b \Rightarrow \frac{a}{b}$$, where

• $$a$$ and $$b$$ could be any two quantities.
• $$“a”$$ is called the first term or antecedent.
• $$“b”$$ is called the second term or consequent.

For example, in ratio $$5:9$$, is represented by $$\frac{5}{9}$$, where $$5$$ is antecedent and $$9$$ is consequent. $$5:9 = 10:18 = 15:27$$

#### Proportion Formula

Now, let us assume that, in proportion, the two ratios are $$a:b$$ and $$c:d$$. The two terms $$‘b’$$ and $$‘c’$$ are called $$‘means\ or\ mean\ terms’$$, whereas the terms $$‘a’$$ and $$‘d’$$ are known as ‘extremes or extreme terms.’

$$\mathbf{\frac{a}{b} = \frac{c}{d} or a:b::c:d$$

For example, let us consider another example of the number of students in $$2$$ classrooms where the ratio of the number of girls to boys is equal. Our first ratio of the number of girls to boys is $$2:5$$ and that of the other is $$4:8$$, then the proportion can be written as $$2:5::4:8$$ or $$\mathbf{\frac{2}{5} = \frac{4}{8}$$. Here, $$2$$ and $$8$$ are the extremes, while $$5$$ and $$4$$ are the means.

### Types of Proportions

Based on the type of relationship two or more quantities share, the proportion can be classified into different types. There are two types of proportions.

• Direct Proportion
• Inverse Proportion

#### Direct Proportion

This type describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases and vice-versa. For example, if the speed of a car is increased, it covers more distance in a fixed amount of time. In notation, the direct proportion is written as y ∝ x.

#### Inverse Proportion

This type describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases and vice-versa. In notation, an inverse proportion is written as y ∝ 1/x. For example, increasing the speed of the car will result in covering a fixed distance in less time.

### Difference Between Ratio and Proportion

Ratio and proportion are closely related concepts. Proportion signifies the equal relationship between two or more ratios. To understand the concept of ratio and proportion, go through the difference between ratio and proportion given here.

1. The ratio is used to compare the size of two things with the same unit. The proportion is used to express the relation of the two ratios.
2. It is expressed using a colon (:) or slash (/). It is expressed using the double colon (::) or equal to the symbol (=)
3. It is an expression. It is an equation.
4. The keyword to distinguish ratio in a problem is “to every”. The keyword to distinguish proportion in a problem is “out of”.

## Important Notes

• Proportion is a mathematical comparison between two numbers.
• Basic proportions are of two types: direct proportions and inverse proportions.
• We can apply the concepts of proportions to geography, comparing quantities in physics, dietetics, cooking, etc.
Properties of Proportion
• Proportion establishes equivalent relation between two ratios. The properties of proportion that is followed by this relation :

Addendo – If $$a : b = c : d$$, then value of each ratio is $$a + c : b + d$$
Subtrahendo – If $$a : b = c : d$$, then value of each ratio is $$a – c : b – d$$
Dividendo – If $$a : b = c : d$$, then $$a – b : b = c – d : d$$
Componendo – If $$a : b = c : d$$, then $$a + b : b = c + d : d$$
Alternendo – If $$a : b = c : d$$, then $$a : c = b: d$$
Invertendo – If $$a : b = c : d$$, then $$b : a = d : c$$
Componendo and dividendo – If $$a : b = c : d$$, then $$a + b : a – b = c + d : c – d$$

## FAQs

How do I calculate proportion?

The Formula for Percent Proportion is Parts /whole = percent/100. This formula can be used to find the percent of a given ratio and to find the missing value of a part of a whole.

What is a proportion in a math calculator?

A proportion is two ratios that have been set equal to each other, for example, 1/4 equals 2/8.

What is the proportion of 3 : 5 = x : 40?

Complete this proportion: 3 : 5 = x : 40. (3 out of 5 is how many out of 40?) “5 goes into 40 eight times.

How do you know if a relationship is proportional?

You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are, all the same, the table shows a proportional relationship.

What is the ratio of 1 to 10?

So just as a fraction of 3/30 can be simplified to 1/10, a ratio of 3:30 (or 4:40, 5:50, 6:60, and so on) can be simplified to 1:10.