Fractions, Decimals and Percentages – JSS2 Mathematics Lesson Note (First Term)

A fraction is a small part or item forming a piece of a whole. It is the quotient of two rational numbers. A ratio compares the relative sizes of two quantities. A fraction or decimal is changed to a percentage by multiplying by 100. This note covers types of fractions, ratios and conversion to percentages.

Behavioural objectives

By the end of the lesson, students should be able to:

• give examples of equivalent, improper and mixed fractions;
• write a ratio of two quantities as fractions of the total;
• express percentages as a ratio and use the ratio to share a total;
• express fractions and decimals as percentages.

What are the types of fractions?

Equivalent fractions

Examples are 2/5 = 4/10 = 8/20 = 16/40.

Improper fractions

Examples are 13/2, 100/7, 67/5 and 102/5.

Mixed fractions

Examples are 72/3, 91/8, 1421/2 etc.

What is a ratio?

A ratio is the relative magnitude of two quantities (usually expressed as a quotient).

Example 1: ratio as fractions of a total

In a bus station, the ratio of men to women is 2:5. (a) What fraction of the people are men? (b) What fraction of the people are women?

Solution

Total parts = 2 + 5 = 7

The fraction of men = 2/7 (i.e. the men’s share over the total).

The fraction of women = 5/7 (i.e. the women’s share over the total).

Example 2: percentages as a ratio

The population of a country is estimated to be 12 million people. The last survey reveals that 40% were boys, 30% were girls, 10% were men and 20% were women. Express the composition as a ratio and evaluate the estimated number of people in each category.

Solution

1. Remove the % signs: boys 40, girls 30, women 20, men 10.
2. Divide through by 10 to reduce the values: 4, 3, 2, 1. The ratio of boys to girls to women to men is 4:3:2:1, and 4 + 3 + 2 + 1 = 10.
3. Find the number of people in each category:

• Men = 1/10 × 12 000 000 = 1 200 000 (cancel one zero from each)
• Women = 2/10 × 12 000 000 = 2 400 000 (cancel one zero from each)
• Girls = 3/10 × 12 000 000 = 3 600 000 (cancel one zero from each)
• Boys = 4/10 × 12 000 000 = 4 800 000 (cancel one zero from each)

Check: 4 800 000 + 3 600 000 + 2 400 000 + 1 200 000 = 12 000 000.

How do you express fractions and decimals as percentages?

Multiply the fraction or decimal by 100 and write the % sign.

Example: Express the following as percentages: (a) 5/12 (b) 120/500 (c) 0.009

Solution

• (a) 5/12 × 100 = 500/12 = 41 2/3%
• (b) 120/500 × 100 = 24%
• (c) 0.009 = 9/1000 × 100 = 0.9%

Evaluation

1. Write down two equivalent fractions of 2/5.
2. Give two examples of improper fractions.
3. At a motor park, the ratio of men to women is 3:4. What fraction of the people are men, and what fraction are women?
4. Express 3/8 as a percentage.
5. Express 0.007 as a percentage.

Assignment

1. In a school, the ratio of boys to girls is 3:2. What fraction of the students are girls?
2. Express 60/400 as a percentage.
3. Express 0.05 as a percentage.