What is the Ratio Formula
The ratio formula for any two quantities, such as a and b can be given by, a:b = \(\frac{a}{b}\)
Here, ‘a’ and ‘b’ are two different quantities with the same unit. As a result, the total quantity combined is (a + b).
As you can see, ‘a’ here is known as antecedent and ‘b’ is known as consequent.
The ratio a:b can be simplified by simplifying the fraction \(\frac{a}{b}\) in the usual way of dividing the fraction with common factors.
Solved Examples
Example 1: There are 55 students in a class. The number of boys are 27 and the remaining are girls. Find the ratio of the number of girls to the number of boys.
Solution:
As stated in the question,
The total number of students = 55
Number of boys in the class = 27
Hence, number of girls in the class = 55 – 27 = 28
Now, using the ratio formula,
The ratio of number of girls to the number of boys = Number of girls : Number of boys
= 28:27
Hence, the ratio of the number of girls to boys is 28:27.
Example 2: The ratio x:y = 2:3. If the value of x is 24, then find the value of y.
Solution: Here, x:y = 2:3
In order to find the value of y, we have to use the ratio formula.
So, by substituting x = 24 in the equation we get,
24:y = 2:3
\(\frac{24}{y}\) = \(\frac{2}{3}\) [Ratio formula]
y = \(\frac{24~\times~3}{2}\) [Solve for y]
y = 36 [Simplify]
Hence, the value of y is 36.
Example 3: Albert and Bob are partners in a company. The profit of the company is divided among the two in the ratio of 4:5. For the year 2021, Bob earned a profit of $3000. What is Albert’s profit share for the year 2021?
Solution: Details provided in the question,
Bob’s profit share for 2021 = $3000
The ratio of the profits shared between Albert and Bob = 4:5
Let Albert’s share of profit for the year 2021 be $x
So as per the question, 4:5 = x:3000
\(\frac{4}{5}\) = \(\frac{x}{3000}\) [Ratio formula]
x = \(\frac{4~\times~3000}{5}\) [Solve for x]
x = 2400 [Simplify]
Hence, Albert’s share of the profit for the year 2021 is $2400.
A ratio formula is either written by separating the two quantities using a colon (:), or, by writing the quantities in fractional form.
By learning about ratios, we can measure the relationship between two or more quantities by comparing them and understand the importance of the quantities being compared.
Ratio is the comparison between two or more quantities, while proportion is the equation in which two ratios are termed equal.
With the ratio formula, the simplest form of ratio can be expressed by further simplifying the fraction formed by the quantities in the ratio.