Demography and Ratios

Grade 10 Math - Demography and Ratios

Lesson Objectives

Understand what population data is and how it is collected.
Interpret demographic data presented in tables and charts.
Calculate and interpret ratios related to population data.
Solve real-life problems involving ratios and population statistics.

Lesson Introduction

Demography is the study of human population data, including birth rates, death rates, age distribution, and population growth. Ratios help us compare different aspects of the population, such as male to female ratios or urban to rural populations. In this lesson, we explore how to analyze and compute such ratios in real-life situations.

Core Lesson Content

Understanding Population Data

Population data is usually collected through censuses and surveys. It can be grouped by age, gender, location, occupation, and other factors.

What is a Ratio?

A ratio is a comparison between two quantities. For example, if a town has 2,000 males and 2,500 females, the ratio of males to females is:

$\frac{2000}{2500} = \frac{4}{5}$

Worked Example

Example 1: In a school with 480 students, 180 are boys. Find the ratio of boys to girls.
Girls = 480 - 180 = 300
Ratio =

\frac{180}{300} = \frac{3}{5}

Example 2: A town has 12,000 people. 7,200 live in urban areas, and the rest live in rural areas. What is the urban to rural ratio?
Rural = 12,000 - 7,200 = 4,800
Ratio =

\frac{7200}{4800} = \frac{3}{2}

Example 3: If there are 75 males and 100 females in a company, find the male to total staff ratio.
Total staff = 75 + 100 = 175
Ratio =

\frac{75}{175} = \frac{3}{7}

Example 4: In a survey, 45% of people preferred product A, 30% product B, and 25% product C. What is the ratio of product A to product B preference?
Ratio =

\frac{45}{30} = \frac{3}{2}

Example 5: A population of 8,000 consists of 3,200 children. Find the ratio of children to adults.
Adults = 8,000 - 3,200 = 4,800
Ratio =

\frac{3200}{4800} = \frac{2}{3}

Example 6: A census shows a state with 5 million males and 6.5 million females. What is the male to female ratio?
Ratio =

\frac{5}{6.5} = \frac{10}{13}

Example 7: A university has 1,800 science students and 2,400 arts students. Find the ratio of science to total students.
Total = 1,800 + 2,400 = 4,200
Ratio =

\frac{1800}{4200} = \frac{3}{7}

Example 8: The birth ratio in a city is 105 males to 100 females. Express this as a simplified ratio.
Ratio =

\frac{105}{100} = \frac{21}{20}

Example 9: A classroom has 16 students from urban areas and 24 from rural areas. What is the ratio of rural to total students?
Total = 40
Ratio =

\frac{24}{40} = \frac{3}{5}

Example 10: [WAEC] A city’s population increased from 120,000 to 150,000. What is the ratio of the old to new population?
Ratio =

\frac{120000}{150000} = \frac{4}{5}

Exercises

A town has 18,000 males and 22,000 females. What is the ratio of males to females?
In a population of 60,000, 15,000 are children. Find the ratio of children to adults.
A school has 400 students, with 240 in junior classes. Find the junior to senior ratio.
[NECO] A company has 45 technicians and 75 office staff. What is the ratio of technicians to all workers? (Past Question)
From a population of 500 people, 300 are employed. Find the ratio of unemployed to employed people.
[WAEC] In a state, 60% are literate and 40% are not. What is the ratio of literate to non-literate citizens? (Past Question)
A town has 1,200 youths and 1,600 adults. What is the youth to total population ratio?
[JAMB] If a country's population is 80 million and 20 million are students, what is the student to total population ratio? (Past Question)
In a company of 120 workers, 72 are men. Find the ratio of women to men.
[WAEC] A school has 75% boys and 25% girls. What is the simplified boy-to-girl ratio? (Past Question)

Conclusion/Recap

In this lesson, we studied how population data is presented and interpreted using ratios. We learned how to simplify and apply ratios in real-world demographic contexts, including interpreting data from surveys, censuses, and population charts.