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Enter three known numbers and one unknown (x) to calculate the proportional relationship between two ratios instantly.
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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.
“When two ratios are set equal to each other, then it is called a proportion”
The symbol of proportion is ‘::’ and ‘=’.
Two variables are said to be directly proportional if one variable is equal to the product of the other variable and a constant. If the product of the two variables is a constant, then they are said inversely proportional ( x·y is a constant).
The formula for proportion is stated as:
a:b :: c:d ⇔ \(\frac{a}{b} = \frac{c}{d}\)
There are two main and easiest ways to solve proportions:
We have used both in the given example for better understanding:
The two ratios are 8:?::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.
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