Class 7 - Ratio: Meaning, Simplification, Steps and Solved Examples

Ratio is a fundamental concept in Class 7 Maths that helps compare two or more quantities in a simple and meaningful way. It shows how much one quantity is related to another and is widely used in daily life situations like sharing money, mixing ingredients, comparing distances, etc. In this guide, you will learn the meaning of ratio, how to simplify it into the lowest form, and how to solve different types of questions step by step with clear explanations and solved examples.

Table of Contents

• What is Ratio?
• Properties of Ratio
• Simplifying Ratios
• Equivalent Ratios
• Comparing Ratios
• How to Divide a Number into a Ratio
• Converting Ratio to Percentage
• Solved Examples on Ratio
• Practice Questions on Ratio

What is Ratio?

A ratio is a way of comparing two quantities or numbers of the same kind by division.The two numbers or quantities are called the terms of the ratio.

It tells you how much of one thing there is compared to another. The ratio does not tell you the exact numbers, but it tells you the relationship between them.

A ratio can be written as a fraction, in words or by using a colon (:).

Consider two quantities, x and y. The ratio of x to y can be written in the following forms.

Fraction: xy
Words: x is to y

Using a colon: x:y

For example: 

• A recipe uses 2 cups of rice and 4 cups of water . The ratio of rice to water = 2 : 4 = 1 : 2

• A bag has 5 red marbles and 7 blue marbles , ratio of red to blue = 5 : 7

Properties of Ratio

Here are few important properties of ratios and how they help in simplifying and comparing quantities.

• Same kind only: You can only compare two quantities that are of the same kind and in the same unit. For example, 5 kg : 10 kg   = 1 : 2 is correct. But we cannot compare 5 kg : 10 metres as they are of different units.

• No units in a ratio: Once the units match and you divide, the result is a pure number with no unit.

• Multiplying or dividing both terms by the same number does not change the ratio. For example, 2 : 3 = 4 : 6 (multiplied both by 2 ) = 6 : 9 (multiplied both by3); 10 : 15 = 2 : 3 (divided both by 5)

• A ratio must always be expressed in simplest form.

• Ratios are always positive numbers. We do not use negative numbers in a ratio.

• The ratio of a to b is a:b and the ratio of b to a is b:a. Both the ratios are different.

• Let a and b be two numbers in ratio. 

• If 'a' and 'b' are equal in the ratio a: b, then a: b = 1.

• If a > b in the ratio a : b, then a : b > 1.

• If a < b in the ratio a : b, then a : b < 1.

Simplifying Ratios

Simplifying a ratio means writing it in its lowest terms similar to simplifying a fraction.

How to simplify a ratio:

Step 1: Find the HCF (Highest Common Factor) of both terms.

Step 2: Divide both terms by the HCF.

Example 1: Simplify 18 : 24

HCF of 18 and 24 = 6

18 ÷ 6 = 3

24 ÷ 6 = 4

Simplified ratio = 3 : 4

Example 2:Simplify 2:20. 

2:20=220=110

Dividing both the terms by 2 gives the ratio 1:10.

Equivalent Ratios

Ratios are said to be equivalent, if they have the same value. Two ratios are equivalent ratios if they simplify to the same ratio in lowest terms just like equivalent fractions.

You can find equivalent ratios by multiplying or dividing both terms of a ratio by the same non-zero number.

Example 1: Find three equivalent ratios of 2 : 3

To find equivalent ratios of 2 : 3, multiply both terms by the same number.

Multiply by 2 ⇒ 4 : 6

Multiply by 3 ⇒ 6 : 9

Multiply by 4 ⇒ 8 : 12

So, three equivalent ratios are 4:6, 6:9, and 8:12.

Example 2: Find the two equivalent ratios of 3:5.

3:5=35=3×55×5=1525=15:25

3:5=35=3×25×2=610=6:10

Comparing Ratios

To compare two or more ratios, convert them to fractions and find a common denominator.

Example 1: Which is greater 3 : 4 or 5 : 7?

Convert to fractions:

3/4 = 0.75

5/7 ≈ 0.714

Since 0.75 > 0.714, 3 : 4 is greater than 5 : 7.

Example 2: Compare 5:6 and 4:7

 5:6=56 and  4:7=47

Cross multiply: 5×7 = 35, 4×6 = 24

Since 35 > 24, 5/6 > 4/7

5:6 is greater than 4:7

How to Divide a Number into a Ratio

If a quantity Q is to be divided in the ratio a : b, then:

First part = a/(a + b) × Q

Second part = b/(a + b) × Q

Example 1: Divide ₹1200 in the ratio 3 : 5.

Total parts = 3 + 5 = 8

First part = 3/8 × 1200 = ₹450

Second part = 5/8 × 1200 = ₹750

Example 2: Divide 90 cm in the ratio 4 : 5.

Total parts = 4 + 5 = 9

First part = 4/9 × 90 = 40 cm

Second part = 5/9 × 90 = 50 cm

Converting Ratio to Percentage

A percentage is simply a ratio out of 100. To convert a ratio to a percentage, follow these steps:

Step 1: Write the ratio as a fraction.

Step 2: Multiply the fraction by 100.

Step 3: Add the % sign.

Example 1: Convert 7 : 20 to a percentage.

 7 : 20 = 720× 100 = 35

7 : 20 in percentage is 35% 

Example 2: Convert 3 : 4 to a percentage. 

3 : 4 =  34× 100 = 75

3 : 4 in percentage is 75% 

Solved Examples on Ratio

Example 1: Express the ratio in their simplest forms:25:50

Solution:  25:50=2550

HCF of 25 and 50 is 25. Dividing each term in the ratio by 25

Therefore,  2550=12

The simplest form is 1:2.

Example 2: The sum of two numbers is 52. If the numbers are in the ratio 4:9, find the two numbers.

Solution: The sum of two numbers is 52.

ratio of the two numbers = 4:9 

Let the numbers be 4x and 9x. Let the common multiple of ratio be 'x'.

4x + 9x = 52

13x = 52

x = 4

4x = 4 × 4 = 16 and 9x = 9 × 4 = 36

Therefore, the two numbers are 16 and 36.

Example 3: Divide 360° in the ratio 2 : 3 : 4.

Solution: Total parts = 2 + 3 + 4 = 9

First part = 2/9 × 360 = 80°

Second part = 3/9 × 360 = 120°

Third part = 4/9 × 360 = 160°

Example 4: A total of 78 litres of water needs to be poured in two pots in the ratio of 6 : 7. Find the volume of water in the two pots.

Solution: Given total liters of water = 78liters

Total parts = 6 + 7 = 13

Value of 1 part = 78 ÷ 13 = 6 litres

Water in first pot = 6 × 6 = 36 litres

Water in second pot = 7 × 6 = 42 litres 

The two pots contain 36 litres and 42 litres of water respectively.

Example 5: The sides of a triangle are in the ratio 3:5:4. If the perimeter of the triangle is 24 cm, find the length of each side.

Solution: Given ratio of sides = 3 : 5 : 4

Perimeter = 24 cm 

Total parts = 3 + 5 + 4 = 12

First side = 3 × (24/12) = 3 × 2 = 6 cm

Second side = 5 × (24/12) = 5 × 2 = 10 cm

Third side = 4 × (24/12) = 4 × 2 = 8 cm

The sides of the triangle are 6 cm, 10 cm, and 8 cm in length.

Practice Questions on Ratio

1. Divide 8 litres in the ratio of 1:2.

2. Divide 40 chocolates between Nisha and Shyam in the ratio 2:3.

3. The ratio of trucks to cars is 7:8. If there are a total of 45 trucks and cars, find the number of trucks and cars.

4. Are 4 : 6 and 10 : 15 equivalent ratios? Verify.

5. A bag has 6 red, 4 blue, and 10 green balls. Find the ratio of red to green balls.

6. Simplify the ratio 48 : 72.

7. Find two equivalent ratios of 5 : 8.

8. Divide ₹2,100 in the ratio 2 : 5.

9. Convert the ratio 3 : 5 to a percentage.

10. There are 90 women and 120 men in an office. Find the ratio of women to men in the office.