Ratio: Meaning, Formulas, How to Solve, Types, Examples

A Ratio is a mathematical expression used to compare two or more quantities. It shows how many times one number contains another and is written in the form of "a:b" or as a fraction "a/b."

What is a Ratio?

Also Check: Pythagoras Theorem

Ratio Formula

1. Step 1 : Identify the two quantities (a and b).
2. Step 2 : Divide both 'a' and 'b' by their greatest common divisor (GCD).
3. Step 3 : Write the simplified ratio as a:b.

How to Solve Ratios?

Step 1: Understand the Ratio

• Identify the Ratio : Look at the ratio you are given. For example, if you have a ratio of 3:4, this means for every 3 parts of one quantity, there are 4 parts of another quantity.
• Know What You Are Comparing : Determine what the two quantities represent. For example, if the ratio is of boys to girls in a class, you need to know how many boys and girls there are.

Step 2: Set Up the Equation

• Use Variables : If you need to find the actual quantities, you can use variables. For example, if the ratio of boys to girls is 3:4, you can let the number of boys be 3x and the number of girls be 4x, where x is a common multiplier.

Step 3: Write the Ratio as a Fraction

• Convert to Fraction : You can express the ratio as a fraction. For the ratio 3:4, you can write it as 3/4 This can help you when you need to solve for unknowns.

Step 4: Cross-Multiply (if necessary)

• Cross-Multiplication : If you are solving a proportion (where two ratios are equal), you can use cross-multiplication. For example, if you have 4:3​=12:x, you can cross-multiply:
  • ( 3times 12 = 4times x )
  • This gives you (36 = 4x).

Step 5: Solve for the Unknown

• Isolate the Variable : If you have an equation like ( 36 = 4x ), divide both sides by 4 to find x: (x = 36/{4} = 9).
• Find the Quantities : If you use variables in Step 2, substitute back to find the actual quantities. For example, if (x = 9), then:
  • Number of boys = ( 3x = 3 \times 9 = 27 )
  • Number of girls = ( 4x = 4 \times 9 = 36 )

Also Check: Area of Square

Types of Ratios in Maths

1. Simple Ratios : These are the most straightforward type of ratio, comparing two quantities directly. For example, if you have 4 apples and 2 oranges, the ratio of apples to oranges is 4:2, which can be simplified to 2:1. This means for every 2 apples, there is 1 orange.
2. Compound Ratios : When you compare more than two quantities, you create a compound ratio. For instance, if a recipe calls for 2 cups of flour, 1 cup of sugar, and 3 eggs, the compound ratio is 2:1:3. This helps you understand the relationship between all the ingredients.
3. Proportional Ratios : These ratios show that two ratios are equal. For example, if the ratio of boys to girls in one class is 3:4 and in another class is 6:8, these ratios are proportional because they simplify to the same value (3:4). This means the relationship between boys and girls is the same in both classes.
4. Part-to-Whole Ratios : This type of ratio compares a part of a quantity to the whole. For example, if there are 20 students in a class and 8 of them are girls, the part-to-whole ratio of girls to the total number of students is 8:20, which simplifies to 2:5. This means that for every 5 students, 2 are girls.
5. Rate Ratios : These compare two quantities with different units. For example, if a car travels 120 miles in 2 hours, the rate ratio is 120 miles/2 hours, which simplifies to 60 miles per hour. This tells you how fast the car is going.

Examples

Step 1: Understand the Ratio

Step 2: Set Up the Ratio

• The number of boys = ( 4x )
• The number of girls = ( 5x )

Step 3: Use the Known Quantity

Step 4: Solve for ( x )

Step 5: Find the Number of Girls

Step 6: Check the Ratio

• Number of boys = 20
• Number of girls = 25