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Proportion Calculator + Online Solver With Free Steps
The Proportion Calculator calculates the value of an unknown variable, such as “x,” using the proportionality formula and three known values. You can enter three known constant values, then add a variable, and the calculator will find the value for that unknown variable.
You can also use this to find the value of an unknown variable in terms of other variables such as x = 33z/13. We are unaware of the value of z but this generalized formula can be used to find the value of x for any value of z.
What Is the Proportion Calculator?
The Proportion Calculator is an online tool that determines the value of an unknown variable by using the three known values and their proportionality between the four sets of values. Furthermore, the calculator will provide the answer in fractions instead of decimal values.
The calculator interface has four single-line text boxes to enter the three known values and the unknown variable. The boxes are divided vertically with a dashed line to denote the terms divided and a “=” sign denoting that the ratio of the terms is equal.
Moreover, there is no strict rule for using three known values. You can use two unknowns and show one unknown variable in terms of another.
Also, you can enter all four as unknown variables, and the calculator will provide you with a generalized formula with the first term as the subject in terms of the rest of the unknowns.
How To Use the Proportion Calculator?
You can use the proportion calculator by entering the values which you want to find. It is the value of the unknown “x,” into the four text boxes as required, and the calculator will determine the value of x. Let us take a case where we have the values: x, 10, 14, and 15.
Following are the detailed steps:
Step 1
Ensure that there are no infinity or 0 values in the text box, such as having the value “0” in the denominator.
Step 2
Enter the known and unknown values needed to calculate in the text boxes. In our example, we enter the values x, 10, 14, and 15 in the text boxes.
Step 3
Finally, press the Submit button to get the results.
Results
- Input: This is the input section as interpreted by the calculator in LaTeX syntax. You can verify the correct interpretation of your input values by the calculator.
- Result: The answer to the values that you have entered. This can be in the form of an equation as well with the subject being the first unknown value entered in the text boxes. The result is in fractional form and can be converted to an approximate form by clicking on the “approximate form” button on the top-right-hand side of the section.
How Does the Proportion Calculator Work?
The Proportion Calculator works by using the equality between the ratios of the known values to find the unknown values. This is done by the algorithm used by the calculator, which is based on the proportionality equation, to form an equation that shows the correct answer based on the data provided to the calculator.
Furthermore, this answer can either be in the form of a general equation or an exact value that fully satisfies the proportionality equations.
Definition
The general idea behind the calculator’s working is the proportionality equation:
\[\frac{\text{a}}{\text{b}} = \frac{\text{c}}{\text{d}}\]
Given that the variables a, b, c, and d can be either known values or expressions.
The resulting equation can be of any type. If it comes out as a polynomial, the result of the unknown will be its roots, which can be either real or in complex form, depending on the polynomial.
Types of Proportionality
In mathematics, two sequences of numbers, typically experimental data, are proportional or directly proportional if their corresponding components have a linear ratio, which is termed the coefficient of proportionality or proportionality constant. two sequences are inversely proportional if corresponding elements have a constant product, conjointly called the coefficient of proportionality.
This definition is often extended to related varying quantities that are often called variables. This means of variable is not the common meaning of the term in mathematics; these two different ideas share a similar name for historical reasons.
If several pairs of variables have equivalent proportionality constant “k, they are governed by the equation that compares the equality of their ratio known as proportion.
Directly Proportional
Given that two variables, “a” and “b,” are directly proportional to each other, their proportionality can be shown by:
x = ky
Or
x $\thicksim$ y, x $\varpropto$ y
Thus, for x is NOT equal to zero,
k = y/x
where “k” denotes the proportionality constant expressed as the ratio between “y” and “x.” This is also called the constant of variation. Two directly proportional variables can be explained by a linear equation with a y-intercept of 0 and a slope equal to “k.”
Examples of such proportionality include:
- Diameter and circumference of the circle with “π” being the proportionality constant
- Distance and time with a constant speed as proportionality constant
- Acceleration and force on an object, where the object’s mass is the proportionality constant.
Inversely Proportional
Inverse proportionality differs from direct proportionality. Consider two variables, which are “inversely proportional” to one another. If all other variables are maintained constant, the magnitude or absolute value of one inversely proportional variable drops as the other variable rises, and their product (the constant of proportionality k) remains constant.
For example, the length of a journey is inversely proportional to the speed of movement.
Furthermore, two variables are inversely proportional if each variable reciprocal is directly proportional to the reciprocal of the other variable such that:
y = k/x
or
xy = k
where k is the proportionality constant and “x” and “y” are proportional variables.
Inverse proportionality can be depicted as a rectangular hyperbola on the cartesian coordinate plane. The product of the values of “x” and “y” are constant on each point of the curve and the curve never intercepts the axis as neither “x” nor “y” can be equal to 0
Examples of Inverse proportionality are as follows:
- Speed and time to complete a journey, where the distance is the proportionality constant.
- The number of workers to complete the task and time, where the task is the proportionality constant.
- More people means less time it takes to complete a job.
Solved Examples
Example 1
A company constructs 4 buildings in 2 years. How many buildings will they construct in 5 years?
Solution
In the above example, there are three known quantities and one unknown quantity of buildings constructed. We can denote this unknown by “x.” Thus, using the proportionality formula:
x-buildings/ 5 years = 4 buildings / 2 years
x-buildings = 5 x 4 / 2
x-buildings = 10
Hence, The company will construct 10 buildings in 5 years.
Example 2
For the proportionality equation:
\[\frac{\text{a}}{\text{b}} = \frac{\text{c}}{\text{d}}\]
Let:
a = (y-10),
b = 3,
c = 12,
d = 4
Find the value of “y” for the given values.
Solution
An expression is given in this example, which we can solve using the proportionality rule.
(y-10)/3 = 12/4
y-10 = (12 x 3) / 4
y = 36 / 4 + 10
y = 9+10
y = 19
Thus, by simply making “y” as the subject and solving accordingly, we determined y to be equal to 19
Example 3
For the following proportionality equation:
\[\frac{\text{a}}{\text{b}} = \frac{\text{c}}{\text{d}}\]
Let:
a = (y-15),
b = 1,
c = 10,
d = y
Find the value of “y” for the given values
Solution
In this example, the values, when organized, provide us with a quadratic equation. This equation will have two roots of “y,” i.e. there will be two answers for y.
(y-15)/1 = 10/y
y(y-15) = 10
y$^2$ – 15y = 10
y$^2$ – 15y – 10 = 0
Finding the roots of the quadratic equation using the quadratic formula that is:
\[y = \frac{-b \pm \sqrt{ b^2-4ac }}{2a}\]
\[y = \frac{15 \pm \sqrt{15^2-4(1)(-10)}}{2}\]
\[y = \frac{15 \pm \sqrt{225+40}}{2}\]
\[y = \frac{15 \pm \sqrt{265}}{2}\]
\[\therefore \quad y = \frac{1}{2} (15 \pm \sqrt{265}) \]
This value can be approximated to 4 significant figures.
y $\approx$ -0.6394\]
y $\approx$ 15.63