# Ordering of Fractions Percentages and Decimals

**Subject : **

Mathematics

**Term :**

First Term

**Week:**

Week 6

**Class :**

Jss 1

**Previous lesson : **

The pupils have previous knowledge of **Fractions continued: Equivalent Fractions ( Identify and apply equivalent fractions in showing commodities and problems solving in quantitative aptitude)**

**Topic : **

Ordering of Fractions

Percentages – Conversion

Conversion of Fractions to Decimals and Vice–versa.

**Behavioural objectives :**

At the end of the lesson, the pupils should be able to

- Mention ways of converting equivalent fractions to lowest term .
- order fraction based on their real values either in ascending order or descending order
- convert from percentages to decimals
- convert decimals to percentages and vice versa
- explain the steps that are involved in using equivalent fractions in sharing commodities

**Instructional Materials :**

- Wall charts
- Pictures
- Related Online Video
- Flash Cards

**Methods of Teaching :**

- Class Discussion
- Group Discussion
- Asking Questions
- Explanation
- Role Modelling
- Role Delegation

**Reference Materials :**

- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- 9 Year Basic Education Curriculum
- Workbooks

**Content :**

**WEEK SIX**

**TOPIC: FRACTIONS**

**CONTENT**

Ordering of Fractions

Percentages – Conversion

Conversion of Fractions to Decimals and Vice–versa.

**Ordering of Fractions**

It is much easier to compare the size of fractions, when they have the same denominator.

Example 1

Which is the larger fraction: ^{5}/_{7} or ^{6}/_{8}?

Solution

= ^{5}/_{7} or^{6}/_{8}

to have a common denominator

= ^{5}/_{7} x ^{8}/_{8} or^{6}/_{8} x ^{7}/_{7}

= ^{40}/_{56} or ^{42}/_{56}

hence 6/_{8} is larger than ^{5}/_{7},

Examples

Which has the greater mass: 3054g or 3.56kg

Solution

= 3054g or 3.56kg

= 3054kg or 3.56kg

1000

= 3.054kg or 3.56kg

therefore, 3.56kg is greater than 3054kg

Examples

Which is the larger fraction in this pairs?

a. 3 ^{21}/_{50} or 3 ^{31}/_{60} b. ^{37}/_{45} or^{19}/_{24}

Solution

a. 3 ^{21}/_{50} or 3 ^{31}/_{60}

The whole number “3” can be ignored in the working . Consider the fractional part of the mixed fraction.

= ^{21}/_{50} or ^{31}/_{60}

= ^{21}/_{50} x^{ 6}/_{6} or ^{31}/_{60} x^{ 5}/_{5}

= ^{126}/ _{300} or ^{155}/_{300}.

Considering the values of the numerator 155 > 126

Therefore, 3 ^{31}/_{60} is larger than 3 ^{21}/_{50}.

(b) ^{37}/_{45} or^{19}/_{24}

= ^{37}/_{45} x^{8}/_{8} or ^{19}/_{24} x ^{15}/_{15}

= ^{296}/_{360} or^{285}/_{360}

Considering the values of their numerators,

296 > 285.

:. The fraction ^{37}/_{45} is larger than ^{19}/_{24}.

Example

Arrange the following fractions in ascending order

^{1}/_{3},^{1}/_{9},^{5}/1_{8}^{2}/_{3},^{ 5}/_{6},^{7}/_{12}, ¾

Solution

a. ^{1}/_{3}, ^{ 1}/_{9}, ^{5}/_{18}

= ^{1}/_{3} x ^{6}/_{6} =^{6}/ _{18}

= 1/_{9} x^{2}/_{2} = ^{2}/ _{18}

= ^{15}/_{18 }x ^{1}/_{1} =^{5}/ _{18}.

Comparing their numerator, 2,5,6,

:. The fractions are

^{1}/_{9}, ^{5}/_{18}, ^{1}/_{3}.

(b) ^{2}/_{3}, ^{5}/_{6}, ^{7}/_{12}, ^{3}/_{4}/

= ^{2}/_{3} =^{2}/_{3} x ^{4}/_{4} =^{8}/ _{12}

= ^{5}/_{6} =5/_{6} x^{2}/_{2} = ^{10}/_{12}

= ^{7}/_{12} =^{7}/_{12} x ^{1}/1 =^{7}/ _{12}

¾ =^{3}/_{4}x ^{3}/_{3 } =^{9}/_{12}.

Comparing their numerators, 7,8,9 10.

The fractions are

^{7}/_{12}, ^{2}/_{3}, ^{3}/_{6}, ^{5}/_{6}.

**READING ASSIGNMENT**

Essential Mathematics for JSS 1 by AJS Oluwasanmipg 51

New General Mathematics for JSS 1 by MF.Macraepg 31-32.

**EVALUATION**

1. Which of the following fractions is larger?

a.^{ 2}/_{5} or ^{5}/_{7} b.^{ 5}/_{6} or^{4}/_{9}

2. Arrange the following fractions in ascending order

^{3}/_{5}, ^{8}/_{15}, ^{17}/_{30 } (b) ^{3}/_{5}, ^{5}/_{8}, ^{7}/_{10}, ^{13}/_{20}.

**PERCENTAGES**

“Per cent’ means per hundred or ‘out of ‘hundred’ or ‘in every hundred’. For example, when we say a student obtained 63 percent in a test, what we mean is that he or she had 63 marks out of 100 marks this is usually written as 63%. Where the symbol % means per cent.

**a. Converting From percentage to fraction.**

Here, the given value in percentage is divided by 100.

A% = in fraction or A ÷ 100, A x 1/_{100.}

Express the following as a fraction in its simplest form

i. 30% ii. 75% iii.7 ½ % iv. 13 ¾ %

Solution.

i. 30% = 30 = 3

100 10

ii. 75% = = ¾

iii. 7 ½ % = 15 = 3

100 x 2 40

iv. 13 ¾ % = 55 x 1 = 11

4 x 100 80

**b. Converting a percentage into a decimal **

To convert a percentage to a fraction divide the percentage by 100.

Examples

Change these to decimals

I 45% ii. 34 ¾ % iii. 5.8%

Solution

i.45% = 45/100 = 0.45

ii.34 ¾ %= 34.75/100 = 0.3475

iii.5.8% = 5.8/100 = 0.0058.

**c. Converting a fraction into percentage**

To convert a fraction into a percentage, multiply it by 100.

Examples

Express these fractions as percentages

i. ¼ ii.25/400 iii. 5/8

Solution

¼ = ¼ x 100% = 25%

ii. 125/400 = 125 x 100

400 = 125/4 = 31.25%

iii. 5/8 = 5/8 x 100 % =500/6 = 62.5%.

**d. Converting a decimal into a percentage.**

To change a decimal to a percentage multiply it by 100

Example.

Express the following as a percentage

a.0.75 b.0.045

Solution

a.0.75 =0.75 x 100 = 75

b. 0.048 =0.048 x 100 = 4.8%.

**e.Finding the percentage of a quantity **

To find the percentage of a quantity, express the percentage as a fraction, then multiply by the quantity.

Examples

i. 4.5% of N 248 ii. 205 of N250

Solution

i. 4.5% of N 248

= 4.5 x 248

100

=N1116/100 =N11.16.

ii. 20% of N250

= 20/100 x 250

=N50.

**Expressing one quantity as a percentage of another .**

To express one quantity as percentage of another write, the first quantity as fraction of the second and then multiply by 100.

Examples

i.8 students did not do their assignments in a class of 40.

a. What is this as a percentage?

b. What percentage of the class did their assignment?

Solution

a. Writing the first quantity as a fraction of the second gives 8/40.

Multiply the fraction by 100

Therefore, 8/40 x 100= 2 x 10 = 20%

20% of the student did not do their assignment .

c.Those who did their assignment were:

40 -8 = 32 students 32/40 x 100 = 32/ 4 x10 =80

80% did their assignments.

2.What percentage of N5 is 150 kobo?

Solution

Convert N5 to kobo first.

N5 = 5 x 100 = 500kobo

Expressing as a fraction , we have 150/500

Therefore, 150 x 100

501

the percentage is 30%

3.What percentage of 15km is 20,000cm?

Solution

Convert both quanities to same unit first

1 km = 100,000cm

15km = 100000 x 15 =1500 000cm

Expressing as a fraction 20000/1500 000

Then multiply by 100

20 000/1500 000 x 100 = 20/15 = 1.33%

**EVALUATION**

1. Calculate the following :

(a) 5% of N500 (b) 18% of 144km.

2. Convert the following fraction into decimal:

(a) 4/5 (b) 1 2/5

**READING ASSIGNMENT**

- Essential Mathematics for JSS1 by AJS Oluwasanmipg 53-56
- New General Mathematics for JSS I by MF. Macraepg 36-38.

III.**Converting Fractions to Decimal**

To convert a fraction into decimal first re-write the number as a decimal then divide it by the denominator

Terminating decimal

When the denominator divides exactly into numerator a terminating decimal is obtained.

Example

Change ¾ into a terminating decimal number

Solution

0.75

4 30

25

20

20

¾ = 0.75.

Recurring or Repeating Decimals

Sometimes when changing fractions to decimal gives the same figure or group figures repeating themselves on and on. These types of fraction are called non-terminating decimals or recurring decimals.

Examples

Change the following into decimals :

(a) 4/9 (b) 6/11

Solution

a. 4/9 = 0.444

9 40

36

40

36

4

Therefore 4/9 = 0.444

= 0.4.

b. 6/11 0.545454

11 60

55

50

44

60

55

50

44

60

55

50

44

6

Therefore, 6/11 = 0.545454…..= 0.54.

Converting the following into fractions

i. 0.4 ii.0.067

Solution

i. 0.4 = 4/10 = 2/5

ii. 0.067 = 67/1000

(d) Addition and subtraction in decimal

Simplify the following :

i. 0.6 + 1. 7 ii. 0.59 – 0.55 iii. 7.5 + 1.8 iv.9.3 – 6.2

Solution

i.0.6 + 1.7

0.6

+1.7

2.3

ii. 0.59

– 0.55

0.44

iii. 7.5

+ 1.8

9.3

iv.9.3

– 6.2

3.1

**e. Multiplication and Division of Decimals**

examples

Simplify the following :

i. 0.08 x 0.7 ii. 0.5 x 7 iii. 0.18 ÷ 1.2

Solution

i. 0.08

x0.7

0.056

i. 0. 5

x 7

3.5

iii. 0.18 ÷ 6 = 0.03

iv. 1.56 ÷ 1.2

1.3

12 15.6

12

36

therefore, 1.56 ÷ 1.2 = 1.3

**EVALUATION**

Simplify the following :

i. 14.5 – 2.5 x 3.14

ii. 0.6 x 0.08

0.8

**READING ASSIGNMENT**

1. Essential Mathematics for JSS1 by AJS Oluwasanmi.

2. New General Mathematics for JSS1 by M.F Macrae et al.

**Presentation**

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

**Conclusion**

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.