Ratio

Ratio - Grade 7

Lesson Objectives

Understand the concept of ratio and its notation.
Simplify ratios to their lowest terms.
Solve problems involving equivalent ratios.
Use ratios to compare quantities in real-life situations.

Lesson Introduction

Ratios help us compare two or more quantities. You see them every day—whether you are mixing drinks, comparing prices in the market, or reading a recipe. This lesson will teach you how to work with ratios and solve real-world problems using them.

Core Lesson Content

Definition: A ratio compares two quantities of the same kind by division. It is usually written with a colon, such as 3:2, or as a fraction $\frac{3}{2}$ .

Worked Example

Example 1: Write the ratio of 4 apples to 6 oranges.

\frac{4}{6} = \frac{2}{3}

The simplified ratio is 2:3.

Example 2: Express 15:25 in its simplest form.
Find the HCF of 15 and 25, which is 5.

\frac{15}{25} = \frac{15 \div 5}{25 \div 5} = \frac{3}{5}

The simplified ratio is 3:5.

Example 3: A class has 12 boys and 18 girls. What is the ratio of boys to girls?

\frac{12}{18} = \frac{2}{3}

The ratio is 2:3.

Example 4: If a bag contains red, blue, and green balls in the ratio 2:3:5 and there are 40 balls, how many of each color are there?
Total parts = 2 + 3 + 5 = 10
Value of 1 part =

\frac{40}{10} = 4

Red =

2 \times 4 = 8

Blue =

3 \times 4 = 12

Green =

5 \times 4 = 20

Example 5: In a recipe, the ratio of sugar to flour is 1:3. If 2 cups of sugar are used, how much flour is needed?

1 : 3 = 2 : x

Cross-multiplying:

1 \times x = 3 \times 2

x = 6

6 cups of flour are needed.

Exercises

Simplify the ratio $16 : 24$
A box contains 12 pencils and 8 erasers. Find the ratio of pencils to erasers.
[NABTEC] Express the ratio 30:45 in its simplest form. [Past Question]
If the ratio of boys to girls in a class is 4:5, and there are 36 students, how many are boys?
Divide $60$ in the ratio 2:3.
[WAEC] A student scored 18 out of 30 in Math and 24 out of 40 in English. What is the ratio of his Math score to English score? [Past Question]
Find x if $3 : x = 6 : 10$
[NECO] Simplify $100 : 250$ [Past Question]
The angle in a triangle are in the ratio 2:3:4. Find the three angles.
[JAMB] If a sum of $1500$ is divided among three people in the ratio 1:2:3, how much does the second person get? [Past Question]

Conclusion/Recap

Ratios help us compare and divide quantities effectively. We’ve learned how to simplify, compare, and apply ratios in real-life contexts. In the next lesson, we’ll explore percentages and how they relate to fractions and ratios.