# 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.
• A fraction with a zero numerator equals 0.

### 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 $$a + b : a – b = c + d : c – d$$

## Sample Proportion Calculator:

A sample proportion calculator is a tool used to calculate the proportion or percentage of a specific characteristic or attribute within a sample.

For example, if you have a sample of 100 students and you want to determine the proportion of female students in the sample, the sample proportion calculator would help you calculate that percentage.

## 3 Proportion Calculator:

The 3 proportion calculator is a tool that allows you to compare and calculate proportions between three different groups or categories. It can be used to determine the proportions of three different variables or attributes and compare them.

For example, if you have data on the proportion of people who prefer different types of ice cream flavors (chocolate, vanilla, and strawberry), the 3 proportion calculator can help you determine and compare those proportions.

## Population Proportion Calculator:

A population proportion calculator is used to estimate or calculate the proportion or percentage of a specific characteristic or attribute within a population. It is commonly used in statistical analysis to make inferences about a population based on a sample.

For example, if you want to estimate the proportion of adults in a country who own a car, you can use a population proportion calculator to determine that percentage.

## Proportion Calculator with Fractions:

A proportion calculator with fractions is a tool that allows you to solve proportions involving fractions. It is useful in various mathematical applications, such as solving word problems or calculating ratios and proportions with fractional values.

For example, if you have a proportion equation involving fractions, like “3/4 = x/12,” a proportion calculator with fractions can help you find the value of x.

## Ratio and Proportion Calculator:

A ratio and proportion calculator is a tool that helps you solve mathematical problems involving ratios and proportions. It can calculate unknown values or compare ratios and proportions between different quantities.

For instance, if you have a ratio such as 2:5 and want to determine the equivalent proportion, a ratio and proportion calculator can assist in finding the correct value.

## Proportion Calculator Ratio:

A proportion calculator ratio is specifically designed to calculate proportions using ratios. It can be used to solve proportion problems based on given ratios or to find equivalent ratios.

For example, if you have a ratio of 3:8 and want to determine the proportion it represents, a proportion calculator ratio can help you calculate the exact proportion.

## Percent Proportion Calculator:

A percent proportion calculator is a tool that calculates the proportion or percentage of a given value compared to the whole. It is commonly used in various fields, such as finance, statistics, and economics, to determine percentages.

For example, if you want to calculate the percentage increase in sales from one year to the next, a percent proportion calculator can assist you in finding the accurate percentage.

## Proportion Calculator with Variables:

A proportion calculator with variables is used to solve proportion problems involving unknown variables. It allows you to find the value of an unknown variable in a proportion equation.

For instance, if you have a proportion equation like “3/5 = x/15” and want to determine the value of x, a proportion calculator with variables can help you solve for x.

## Proportion Calculator Soup:

“Proportion Calculator Soup” does not appear to be a specific calculator or term commonly used in mathematics. It might refer to a website or platform that offers various proportion calculators for different purposes, similar to a recipe website that offers calculators for scaling recipes based on desired proportions.

## Inverse Proportion Calculator:

An inverse proportion calculator is used to solve problems involving inverse proportions or relationships. Inverse proportion occurs when one variable increases while the other decreases, or vice versa, in a specific pattern. The calculator helps determine the values of the variables in an inverse proportion equation.

For example, if you have an inverse proportion equation such as “y = k/x,” where y decreases as x increases, an inverse proportion calculator can assist in finding the corresponding values.

## Proportion Calculator with Decimals:

A proportion calculator with decimals is designed to solve proportion problems involving decimal values. It helps calculate the proportional relationship between different quantities expressed as decimals.

For instance, if you have a proportion equation with decimal values, like “0.75 = x/2,” a proportion calculator with decimals can help you find the value of x.

## 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.

How Do I Calculate Proportion?

To calculate a proportion, you need to compare two ratios or fractions and determine if they are equal. The general formula for a proportion is a/b = c/d, where a, b, c, and d are numbers. To calculate the missing value in a proportion, you can use cross-multiplication. For example, if you have the proportion 2/3 = x/9, you can cross-multiply and solve for x by multiplying 2 and 9 and then dividing by 3.

Is 1:4::4:16 a Proportion?

To determine if the ratios 1:4 and 4:16 form a proportion, you can cross-multiply and see if the products are equal. In this case, 1 x 16 is equal to 4 x 4, which gives 16 on both sides. Therefore, the ratios 1:4 and 4:16 form a proportion.

How to Do a Hypothesis Test for a Proportion on a Calculator?

To conduct a hypothesis test for a proportion on a calculator, you need to follow these steps:

a. Define the null hypothesis (H0) and the alternative hypothesis (Ha).

b. Collect your data and calculate the sample proportion.

c. Determine the test statistic, which depends on the specific hypothesis test you are conducting (e.g., one-sample z-test or one-sample t-test).

d. Use the calculator’s statistical functions or software to calculate the test statistic and corresponding p-value.

e. Compare the p-value to your significance level (e.g., 0.05) to make a decision about rejecting or failing to reject the null hypothesis.

How to Do a Two Proportion Z-Test on a Calculator?

To conduct a two-proportion z-test on a calculator, follow these steps:

a. Define the null hypothesis (H0) and the alternative hypothesis (Ha).

b. Collect data from two independent samples and calculate the sample proportions for each group.

c. Determine the test statistic, which is calculated using the formulas for the z-test for proportions.

d. Use the calculator’s statistical functions or software to calculate the test statistic and corresponding p-value.

e. Compare the p-value to your significance level (e.g., 0.05) to make a decision about rejecting or failing to reject the null hypothesis.

What Is Proportion with 2 Numbers?

A proportion with two numbers refers to a comparison between two ratios or fractions. It expresses the relationship between two quantities. A proportion can be written as a/b = c/d, where a, b, c, and d are numbers. It indicates that the ratio of a to b is equal to the ratio of c to d. Proportions are used in various mathematical calculations and comparisons.

How to Find Sample Proportion Calculator?

To find a sample proportion calculator, you can search online or use statistical software. Many websites and software tools offer sample proportion calculators where you can input the number of successes and the sample size to calculate the sample proportion. These calculators can be helpful for statistical analysis and hypothesis testing.

How to Solve a Proportion Using a Calculator?

To solve a proportion using a calculator, you can use the cross-multiplication method. Follow these steps:

a. Write the proportion equation with the known values and the variable you want to solve for.

b. Cross-multiply by multiplying the numerator of one fraction with the denominator of the other fraction.

c. Set the two cross-products equal to each other.

d. Solve the resulting equation for the unknown variable using your calculator’s arithmetic functions.

Do These Ratios Form a Proportion Using a Calculator?

To determine if a set of ratios forms a proportion using a calculator, you can cross-multiply and compare the products. For example, if you have the ratios 2:4 and 3:6, you can multiply 2 by 6 and 4 by 3. If the products are equal, such as 12 on both sides, then the ratios form a proportion.