How To Calculate Ratios

Calculating ratios is an important part of Maths. We use the ratio formula while comparing the relationship between two numbers or quantities. Ratio is defined as the relation between the quantities of two or more objects and it indicates the amount of one object contained in the other. The general form of representing a ratio of two quantities say, a and b, is

a : b

where,

a = Antecedent
b = Consequent

What is the Ratio Formula?

The ratio is the relation between the quantities of two or more objects, indicating the amount of one object contained in the other. A ratio can be represented in the form of a fraction using the ratio formula. The ratio formula for any two quantities say, a and b, is given as, a:b = a/b

Example

Solving Ratio Problems

A ratio is a mathematical expression that compares two or more numbers, showing the relative sizes of the values. Ratios can be used in various real-life applications such as mixing ingredients, comparing quantities, and scaling models.

The general approach to solving ratio problems includes:

Understanding the given ratio and its meaning.
Writing the ratio in fraction form when needed.
Using multiplication or division to simplify or scale the ratio.

Simplifying a Ratio

To simplify a ratio, divide both terms by their greatest common divisor (GCD).

Example:

If the ratio is \( 12:18 \), the GCD is 6, so dividing both terms by 6 gives the simplified ratio \( 2:3 \).

Finding a Missing Value in a Ratio

To find a missing value in a ratio, set up a proportion and solve for the unknown value.

Example:

If the ratio of boys to girls is \( 3:4 \) and there are 15 boys, set up the proportion:

\[ \frac{3}{4} = \frac{15}{x} \]

Cross multiply: \( 3x = 60 \).
Solve for \( x \): \( x = 20 \).

So, there are 20 girls.

Converting a Ratio to a Fraction

To express a ratio as a fraction, write it with the first term as the numerator and the second term as the denominator.

Example:

The ratio \( 5:8 \) can be written as the fraction \( \frac{5}{8} \).

Using Ratios in Real-life Applications

Ratios are widely used in practical scenarios such as:

Scaling up or down a recipe (e.g., maintaining ingredient proportions).
Comparing financial investments (e.g., return on investment ratios).
Understanding population distributions (e.g., male-to-female ratios in a city).

Ratio Calculation Examples Table
Problem Type	Description	Steps to Solve	Example
Simplifying a Ratio	Reducing a given ratio to its simplest form.	Find the greatest common divisor (GCD) of both numbers. Divide both terms by the GCD to simplify.	For the ratio \( 12:18 \), the GCD is 6, so dividing both terms by 6 gives the simplified ratio \( 2:3 \).
Finding a Missing Value in a Ratio	Determining an unknown quantity in a given ratio.	Set up a proportion using the given ratio. Use cross-multiplication to solve for the missing value.	If the ratio of boys to girls is \( 3:4 \) and there are 15 boys, set up \( \frac{3}{4} = \frac{15}{x} \). Solving for \( x \), we get \( x = 20 \), meaning there are 20 girls.
Converting a Ratio to a Fraction	Expressing a ratio as a fraction.	Write the ratio as a fraction with the first term as the numerator and the second term as the denominator. Simplify if necessary.	The ratio \( 5:8 \) can be written as the fraction \( \frac{5}{8} \).
Real-life Applications	Using ratios to solve practical problems.	To mix ingredients in a recipe based on proportions. To compare distances, prices, or quantities.	If a recipe requires a \( 2:3 \) ratio of sugar to flour and you have 4 cups of sugar, solve \( \frac{2}{3} = \frac{4}{x} \) to find \( x = 6 \), meaning you need 6 cups of flour.