CHAPTER THREE

Chapter 3: FRACTIONS, PERCENTAGES AND DECIMALS.

Learning objectives

By the end of this topic, the learner should be able to

• Describe different types of fractions.

• Convert improper fractions to mixed numbers and vice versa.

• Work out problems from real-life situations.

• Add, subtract, divide and multiply decimals.

• Convert fractions to decimals and vice versa.

• Identify and classify decimals as terminating, non-terminating and recurring decimals.

• Convert recurring decimals into fractions.

• Convert fractions and decimals into percentages and vice versa.

• Finding the Percentage Increase and Decrease

• Work out real-life problems involving percentages.

Introduction

In this topic, you will use knowledge of place values to manipulate fractions, decimals and percentages. You will convert fractions to decimals, decimals to percentages and vice versa.

1. A fraction is a number in the form a/b where a and b are whole numbers and b is not zero.

2. In a fraction the top number is called the numerator(a) and the bottom number is called the denominator(b)

3. A fraction is in simplest form (lowest terms) when the top and bottom cannot be any smaller

3.1 Types of fraction

• Proper fraction

In a proper fraction the numerator is less than the denominator. Thus 3/4 and 7/9 are both proper fractions.

1. Shade 3/4

• Equivalent fractions

Equivalent fractions have the same value. In an equivalent fraction both the numerator and denominator are multiplied or divided by the same number. Thus 5 8 and 10 16 are equivalent fractions

NOTE

In a mixed number a whole number is followed by a proper fraction. Thus 1¾  and 3⅝ are both mixed numbers. A mixed number can be converted into an improper fraction and vice versa

3.1 Exercise Set

1. Roberta shades 3/7 of a shape. What fraction of the shape is left unshaded?

2. A cake is divided into 12 equal parts. Hannah eats 3/12 of the cake and Priscilla eats another

1/12. What fraction of the cake is left?

3.2. CONVERTING IMPROPER FRACTIONS TO MIXED NUMBERS AND VICE VERSA

3. A car park contains 20 spaces. There are 17 cars parked in the car park.

(a) What fraction of the car park is full?

(b) What fraction of the car park is empty?

4. Benjamin eats 3/10 of the sweets in a packet. Shakur eats another 4/10 of the sweets.

(a) What fraction of the sweets has been eaten?

(b) What fraction of the sweets is left?

5. Draw diagrams to show these improper fractions:

(a) 7/2

(b) 8/3

6. Draw a square with its four lines of symmetry.

(a) Shade 3/8 of the shape.

(b) Shade another 2/8 of the shape.

(c) What is the total fraction now shaded?

(d) How much is left unshaded?

7. Shade the following fractions

(a) 3/10

(b) 10/3

(c) 1/2

(d) 4/3

(e) 14/10

(f) 5/6

(g) 9/8

(h) 8/9

3.2 Converting Improper Fractions to Mixed Numbers and Vice Versa

Summary

3.2 Exercise Set

1. Convert these mixed numbers to improper fractions.

(a) 13/5

(b) 71/3

(c) 34/5

(d) 64/9

(e) 103/7

(f) 92/3

(g) 53/5

(h) 712/8

2. Write these fractions in order of increasing size. 61/2; 18/5 ; 31/4; 51/3; 17/3

3. Arrange the fractions 56; 4 9; 78 and 12 in descending order of magnitude

4. A young child is 44 months old. Find the age of the baby in years as a mixed number in the simplest form.

5. In an office there are 31/2 reams of paper. There are 500 sheets of paper in each full ream.

How many sheets of paper are there in the office?

6. Express the following improper fractions as a mixed number.

(a) 7/2

(b) 22/3

(c) 54/7

(d) 27/13

(e) 10/3

(f) 4/3

(g) 14/10

(h) 9/8

7. Change these mixed numbers to vulgar fractions

(a) 63/5

(b) 317/2

8. Express the following improper fractions as a mixed number.

(a) 38/9 (b) 231/15 (c) 54/7 (d) 29/13

3.3 Operations on Fractions

• For fractions with plus (+) and minus (-) signs only, nd the LCM and workout

• For fractions with combined operations, the BODMAS rule must be observed.

Activity: Work out problems from real-life situations

EXAMPLES

1. Find 1/10 of Ug shs 10000

SOLUTION

3.3 Exercise Set

1. Find:

(a) 1/2 of UGX. 16,000

(b) 1/3 of 15

(c) 6/7 of 49

(d) 4/8 of 800

(e) 3/4 of UGX. 2,500,000

2. In a test, there are 40 marks. Mimmi gets 3/4 of the marks. How many marks does she get?

3. At Taibah international school school there are 850 pupils. If 3/50 of the pupils are lefthanded, how many left-handed pupils are there in the school?

4. There are 600 pupils in a school. How many school lunches must be prepared if:

(a) 3/4 of the pupils have school lunches

(b) 2/3 of the pupils have school lunches

5. A school has 800 pupils. The Headteacher decides to send a questionnaire to 2/5 of the pupils. How many pupils receive a questionnaire?

3.3.1 Addition of Fractions with the Same Denominators

To add fractions with like or the same denominator, simply add the numerators then copy the common denominator. Always reduce your final answer to its lowest term.

3.4 Exercise Set