Topic 3: Fractions, Percentages and Decimals

Every time you cut an orange, an apple, or any kind of fruit, you are taking a part of the whole. You can represent a fractions as a percentage, or as a decimal.

By the end of this topic, you will be able to:

describe different types of fractions

convert improper fractions to mixed numbers and vice versa work out problems from real-life situations involving fractions

add, subtract, divide and multiply decimals

convert fractions to decimals and vice versa

identify and classify decimals into terminating, non-terminating and recurring decimals

convert fractions and decimals into percentages and vice versa

convert recurring decimals into fractions

calculate a percentage of a given quantity

work out real life problems involving percentages

Keywords

1. decimal
2. denominator
3. divisor
4. fraction
5. improper fraction
6. mixed fraction
7. non-terminating
8. decimals
9. numerator
10. percentage
11. proper fraction
12. recurring decimal
13. terminating decimal

Introduction

Every time you cut an orange, an apple, or any kind of fruit, you are taking a part of the whole. You can represent a fractions as a percentage, or as a decimal.

Figure 3.1: Fractions, decimals and percentages represent parts of the whole

When you are given a discount of 10% on sugar that costs UGX 4,000, how much do you pay? In this topic you will learn about fractions, decimals, and percentages and how they will help you solve related problems in everyday life.

Fractions

Describing Different Types of Fractions

When you go to buy sugar or maize flour, you can buy half a kilogram, a kilogram, or even 1 kg and a half. How do you write these quantities as fractions What type of fractions are these?

In the following activity, you will describe the different types of fractions.

Proper and Equivalent Fractions

Activity 3.1 Identifying proper and equivalent fractions (work in groups)

What you need: a piece of paper, notebook, ruler and pen.

What to do:

1. Get equal pieces of paper and fold them into 3 equal parts.

2. Unfold it and shade 2 parts out of three.

3. Write the fraction of the shaded part and name the type of fraction it created.

4. Fold the paper again horizontally and state:

a) the fraction of the shaded part.

b) the relationship between your answers in step 2 and 4a).

Exercise 3.1

Improper Fractions and Mixed Numbers

Activity 3.2 Identifying improper fractions and mixed numbers (work in groups)

What you need: 3 circular cut-out shapes, a pair of scissors.

What to do:

You are required to share the 3 shapes with your friend equally;

1. Place the shapes on a clean surface.

2. Let each of you get one shape. Cut the remaining shape into two equal parts.

3. State your share?

4. State your friend’s share?

Therefore, 1 1/2 is read as ‘one whole number and a half?

11/2 is a mixed number because it is partly a fraction and partly a whole number.

Therefore, 3/2 = 11/2

Give any other examples of mixed and improper fractions.

Exercise 3.2

1. Mulawo bought 5 kg of sugar for his three children. a) Find the fraction each got. b) Which type of fraction is that?

2. A teacher shared 13 oranges between 2 learners equally. Write each one’s share as; a) An improper fraction. b) Mixed number.

3. Use improper or mixed to identify the fractions below.

a) 2 2/7 is……………………………fraction

b) 8/5 …………………………………….is. fraction.

c) 3 2/3 is …………………………………….is fraction.

d) 19/10…………………………………..is fraction.

Solving Problems in Real Life using Fractions

Activity 3.3 Fractions in daily life (work in groups)

What you need: calculator, pen, notebook

What to do:

1. Count the number of students in your class.

2. Express the following as a fraction of the class a) Number of boys b) Number of girls

3. Count the number of members in your group.

If you were given items to distribute to your classmates, copy and complete the table below to show how many students would receive the items.

Example

If you were travelling from Mbale to Kampala, and after covering 1/2 of the distance, you rest in Jinja, after an extra distance, you rest in Jinja, after an extra 1/4 of the distance you rest in Lugazi

a) What is the total fraction of the distance from Mbale to Lugazi?

b) What is the fraction of the remaining distance?

Exercise 3.3 2

1. A village has a population of 8000 people, 2/5 are males and the rest are females. 3/4 of the males are men and the rest are boys. If 4/5 of the females are girls;

a) What fraction of the village are females?

b) How many more females than males are in the village?

c) Find the number of:

i) boys.

ii) girls in the village.

2. Tom, Amina and Willy contributed a certain amount of money to start up a business. Tom contributed 1, Amina contributed 1 and Willy contributed the rest. 3

a) Find the fraction contributed by Willy. 4

b) If Tom contributed UGX 200,000, how much did:

i) they contribute altogether?

ii) willy contribute?

3. A car broke down after covering 3/8 of a journey.

Find the fraction of the remaining part of the journey?

If there were 40 km left to complete the journey, how long was the journey? 1

4. A trader bought 1/2 kg packet of sugar and packed it into small packets of 1/8 kg each.

a) How many small packets of kg did the trader get?

b) If the trader sold each small packet at UGX 500,

i) How much money did the trader get?

ii) What is the cost of 1 Kg of sugar?

Decimals

Adding, Subtracting, Dividing and Multiplying Decimals

Supposing you cut a sugarcane into 10 equal parts, what fractions would represent one piece, three pieces and 7 pieces? The fractions you have just obtained have 10 as their denominators. They are decimal fractions.

A decimal fraction is one whose denominator is 10 or a multiple of 10, such as 67/100, 483/100, 1458/0,000 .

You can also represent these fractions as 0.67, 0.483 and 0.1458

Addition and Subtraction of Decimals

If Jane covers 0.4 km to school and Ben covers 0.7 km, what is their total distance? What is the difference in the distance they cover? In this section, you will add and subtract decimal fractions.

Activity 3.4 Adding and subtracting decimals (work in groups of 3)

What you need: a sugarcane or any other fruit, knife

What to do:

1. Cut the sugarcane into 10 equal pieces.

2. You are to share the 10 pieces among the three of you.

3. Let the first member take two pieces, the second take 5 pieces and then you take the remainder.

4. Name the fraction that each of you took.

5. Name the fraction your friends took in total.

6. State the difference between your share and that of the first member.

7. Present your work to the whole class.

Example 1

If a baby’s birth mass was 2.45 kg and after two years, its mass increased by 1.71 kg. What is the baby’s current weight?

1.71 kg +2.45 kg = 4.16 kg

Example 2 Mukonge had 3.45 m of wire and used 2.9 m to make a toy car.

Find the length of the wire left.

3.45 m – 2.90 m = 0.55 m

Exercise 3.4

1. Munyereza was pushing 28.43 kg of potatoes on a wheel barrow and his sister adds him 34.3441 kg of maize flour. What was the total mass on the wheel barrow?

2. A tailor needs 5.32 m to make a dress, 3.456 m to make a skirt and 17.7 m to make a suit, if he had 30 metres of cloth, how many metres of cloth did he remain with after making the 3 items?

3. Workout: 151.743 d-283.22 d+ 349.496 d.

4. Add: 24.46 litres plus 38.3839 litres of milk.

5. A cook needs 56.47 litres of milk and 42.678 Litres of water to prepare tea for visitors. What is the minimum capacity of the container she can use to prepare the tea?

Division and Multiplication of Decimals

Activity 3.5 Multiplying and dividing decimals (work in groups)

What you need: pens, pencils, ruler, calculator and notebook.

What to do:

1. Copy and complete the tables below.

2. Observe the answers you get when you divide or multiply a decimal by a multiple of 10.

3. Place your work in a corner and move around the class comparing with the other groups.

Exercise 3.5

1. Without using calculators, workout the following:

a) 7.6 x 1.2 b) 3.44 x 5.6 c) 0.625 0.25

2. How many 5.6 m of rope can be cut out of a roll measuring 151.2 m long?

3. A 20.44m wire was cut into 4 equal pieces, how long was each piece of wire?

4. A welder had 16 pieces of metal bars of length 1.327 m each. He welded them to form one long metal bar. What is the length of the long metal bar formed?

Mixed Operations on Decimals

You can also be given decimals with different operations. It is easier to first convert them to fractions then follow BODMAS.

Example (Discuss in groups)

Converting Fractions to Decimals and Vice Versa

Terminating and Non-Terminating Decimals

Activity 3.6 Identifying terminating and non-terminating decimals (work in groups)

What you need: Pen, pencil, ruler, calculator and a note book.

What to do:

1. Copy and complete the table below using a calculator.

2. Identify the terminating and non terminating decimals from the table.

Some non-terminating decimals have repeating digits. These are referred to as recurring decimals.

Converting Terminating Decimals to Fractions and Vice Versa

The knowledge of place values of decimals will help you. You have already covered this in your previous classes. Review the following questions to remind yourself.

Review Exercise 3.1

1. Convert the following decimals to fractions in their simplest form.

a) 0.08 d) 1.375 b) 3.88 e) 2.44 c) 0.375 f) 0.000625

2. Convert to decimals.

a) 3/4 b) 1/8 c) 5 d)18/5

3. Ali was given sugar of mass 3/8 kg. What is its corresponding mass in decimals?

Converting Fractions to Non-terminating Decimals

Example

Exercise 3.7

Convert the following fractions to non-terminating decimals.

a) 2/3 b) 3/11 c) 5/18 d) /18 d) 11/33

Converting recurring decimals to fractions You need to identify:

i) The repeating digits.

ii) The place value of the last repeating digit.

Example 1

Percentages

Converting Fractions and Decimals into Percentages and Vice Versa

If you attempted a test marked out of 50 and you scored 32, what would your percentage score be? In this section, you will learn to convert fractions and decimals into percentages and vice versa.

Activity 3.7 Converting fractions and decimals into percentages and vice versa (work in groups)

What you need: pen, paper, ruler.

What to do: Draw 10 x 10 grid like the one below and shade some parts of it.

a) What fraction have you shaded?

b) What decimal has been shaded?

c) What percentage has been shaded?

3. Convert the percentages below to fractions in their simplest form.

a) 35% b) 60% c) 90% d) 20% c) 55%

Calculating Percentage of a given Quantity

Just like fractions, percentages are also used to represent part of the whole

Exercise 3.10 1

1. You were given UGX 650,000 while going back to school and you used UGX 5,000 as transport to school. Of the remainder you spent 25% on shopping and 60% on school fees.

a) What percentage was spent on transport?

b) What percentage did you remain with after all the expenditure?

2. Express 300 grams as a percentage of 1 kg.

3. What is 40 minutes as a percentage of 2 hours?

Real-life Problems involving Percentages

When you buy an item from a market or shop, with a discount due to some reasons, how will the seller calculate the discount? What about profit or loss on any product, interest on loans, increase or decrease in production and sales? Al these are in daily life and need an idea of percentages. In which other ways are percentages used in our daily life?

Working-out Real-life Problems Involving Percentages

Example

If 20% of students in a school are male and there are 720 students altogether,

a) what is the percentage of females in the school?

b) how many more females than males are in the school?

c) if 25% of the female students are day scholars, how many female students are in boarding?

d) if all male students are in boarding and 3 students share a decker, how many deckers are needed to accommodate all the male students?

e) if 10% of the females are expected to attend a party of entry fee UGX 50,000, how much money is expected to be collected from the members?

Solution

a)

Exercise 3.11

1. The table below shows how Mangeric spends his monthly income.

a) What percentage of his salary is spent on savings?

b) If he spends UGX 560,000 on rent, how much does he earn a year?

c) If Mangeric wants to buy a car from his 3 years savings, what is the cost of the car?

d) How much more money does he spend on food than on rent per month?

2. The table below shows a student’s marks in Beginning of Term Exams. Study it carefully and answer the questions that follow.

a) What was the student’s best subject?

b) In which two subjects did the student score the same marks?

3. Mulwana, Akello and Byaruhanga contributed UGX 250,000,000, UGX 300,000,000 and UGX 450,000,000 respectively to construct a building, what percentage did Akello contribute?