MathematicsDLP Tahun 6

9 Zaidi travelled 196.65 km in 2.3 hours at a constant
speed. Calculate the distance travelled by Zaidi in
3 hours if he continues at the same speed.

196.65 km ÷ 2.3 hours × 3 hours =

196.65 km ÷ 2.3 hours × 3 hours = 196.65 km × 3 hours
2.3 hours

STEP 1 STEP 2 STEP 3

Multiply 2.3 with 10 Divide. Multiply.
so that it becomes 23.
Multiply 196.65 with 85.5 km 11
10 too. 23 1966.5 km
85.5 km
2.3 196.65 km − 184 ×3
× 10 × 10 126
256.5 km
− 115
115
−115
0

196.65 km ÷ 2.3 hours × 3 hours = 256.5 km

The distance travelled by Zaidi in 3 hours is 256.5 km.

10 2.835 ÷ 1.5 × 2.6 =

STEP 1 STEP 2 STEP 3 2 decimal places
1.89 1 decimal place
1.5 2.835 11
× 10 × 10 15 28.35 55 3 decimal places
− 15
Multiply the divisor 1.8 9
and the dividend 13 3
with 10. − 12 0 × 2.6

1 35 1
− 1 35
11 34
0 + 37 8 0

4.9 1 4

2.835 ÷ 1.5 × 2.6 = 4.914 3.1 (i)

Teacher’s Notes
Guide pupils to convert the divisor to a whole number by moving the decimal

44 places when dividing decimal numbers by decimal numbers.

Surf http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_
TEXT_RESOURCE/ U03_1_2_T2_text_final.html

FUN ADVENTURE Template of a Circle Map

Participants 5 pupils in a group 2.08

Task Example of work

1 In groups, prepare a template of the circle Teacher Reference
map. books
2 × 3.12
2 Discuss to form a few number sentences 3 1.3 × 8
which give the same answers as the 5
answer in the centre of the circle.
The number sentences must involve 20 × 0.52 2.08 0.338 × 8
multiplication and division operations or 1.3
vice versa. Write all the number sentences 5
in the blue space.
10.4 × 1.6 6.4 × 1.3
3 The group which forms the most number 84
of number sentences within 15 minutes
wins.

4 Write the source of the answers in the
green space.

5 Display your work at the mathematics
corner.

Friends

SELF-PRACTICE

1 Calculate.

a 9 × 60.9 ℓ ÷ 5 = b 13 × 8.617 km ÷ 7 =
d 50 × 9.042 g ÷ 30 =
c 24 × RM17.25 ÷ 40 = f 34.215 ÷ 1.5 × 11 =
h 712.2 × 2.8 =
e 106.08 ÷ 8 × 6 =
60
g 56 4.7 98 × 10 =
2.6 b 60.38 × (3 ÷ 1.5) =

2 Calculate.
a 701.9 km × (2 ÷ 4) =

3 Solve the following.
a Divide the product of 25 and 14.364 ℓ by 38.
b Divide 150.63 kg by 0.6. Then, multiply the quotient by 7.9.

3.1 (i) Teacher’s Notes 45

Encourage pupils to use a variety of calculation methods such as lattice
multiplication.
Modify the questions according to pupils’ abilities.
Fun Adventure activity can assess pupils’ thinking skills, communication skills,
soft skills, and reasoning skills.

B Solve the Problems

1 Puan Hanim receives an order for 20 pieces
of wedding tray mats. She uses 9 rolls of lace
to sew them. The length of each roll of lace is
3.1 m. Calculate the length, in m, of lace used
for a piece of mat.

Solution

Given 9 rolls of lace for 20 pieces of mats.
Length of each roll is 3.1 m.

Asked for The length of lace for each mat

Operation Multiplication and division

Solve 9 × 3.1 m ÷ 20 =

3.1 m 1.3 95 m Check the answer with a
×9 20 2 7.90 0 m calculator.

2 7.9 m –20 1 . 39 5
79 × 20
÷9
– 60 = 3.1
1 90

– 1 80
100

– 100
0

9 × 3.1 m ÷ 20 = 1.395 m

The length of lace used for a piece of mat is 1.395 m.
BRAIN TEASERS

Puan Hanim wants to divide a roll of lace
into several parts of equal length. She
cuts the lace 5 times. Calculate the length
of 2 parts of the lace.

3.1 m

Teacher’s Notes

Solve problems with various methods such as simulation using concrete
46 materials. 3.2 (i)

Encourage pupils to use estimation to check whether the answer is reasonable.

2 The diagram shows 25 packets of sugar in a container. 0.125 kg
Each packet has equal mass. Calculate the mass,
in kg, of 15 packets of sugar.

Solution Ensure that the information

➙METHOD 1 asked for is on the right.
➙Important
➙information 25 packets — 0.125 kg
1 packet — 0.125 kg ÷ 25 =

15 packets — 15 × =

Solve 0.125 kg ÷ 25 × 15 =

0.0 05 kg 2
25 0.1 2 5 kg
0.0 05 kg
–0 × 15
01
–0 0 025
12 + 00 05 0
–0
0.07 5 kg
125
– 125 0.125 kg ÷ 25 × 15 = 0.075 kg
0

METHOD 2 Draw a diagram. 153= 3_
255 5
The mass of
25 packets = 0.125 kg

Solve 3_ × 0.125 kg = Use a calculator
5 to check the
answer.

_3 × 0.0 2 5 =3× 0.025 kg
5
0.125 kg

1 = 0.075 kg

_3 × 0.125 kg = 0.075 kg
5

3.2 (i) The mass of 15 packets of sugar is 0.075 kg. 47

Teacher’s Notes
Guide pupils to highlight the keywords in the problems given.
Introduce pupils to various problem solving strategies.

3 Punitha spends 15.75 hours on revision for 4.5 days. The number of hours she
allocates per day is the same. Calculate the total time, in hours, that she uses
for revision in 6.5 days.

Solution Important information

➙ ➙
➙

Duration of 4.5 days, The number of hours 6.5 days = ? hours

revision time is 15.75 hours. allocated per day is the

same.

Solve 15.75 hours ÷ 4.5 days × 6.5 days =

15.75 hours ÷ 4.5 days × 6.5 days = 15.75 hours × 6.5 days
4.5 days

Estimate the answer.

3.2 hours 1
5 16.0 hours
−15 3.2 hours

10 × 7
➙ ➙15.75 hours~16 hours
4.5 ~ 5 22.4 hours

6.5 ~ 7

−1 0

0

Calculate the actual answer. ➙ 3
➙ 3.5 hours 2
4.5 15.75 hours 45 157.5 hours
3.5 hours
× 10 × 10 −135 × 6.5

22 5 175
+ 2100
−22 5
2 2.7 5 hours
0

22.75 hours is close to 22.4 hours.
Therefore, 22.75 hours is the reasonable answer.

15.75 hours ÷ 4.5 days × 6.5 days = 22.75 hours
The total time for revision within 6.5 days is 22.75 hours.

Convert 22.4 hours in hours and minutes.

Teacher’s Notes

Guide pupils to find information or keywords and discuss various strategies to
48 achieve Performance Level 5. 3.2 (i)

Surf http://www.mathgoodies.com/lessons/decimals_part2/multiply_decimals.

html

4 The length of the windowpane in Amin’s room is 1.2 m and its width is
1.14 m. The window consists of two windowpanes of the same size. The right
part of the windowpane has broken and needs to be replaced. Calculate
the area, in m2, of the broken windowpane.

Solution

METHOD 1 METHOD 2
The length of the broken
Given The length of the windowpane windowpane: 1.2 m ÷ 2 = 0.6 m
is 1.2 m. The width of the
windowpane is 1.14 m. There 1.2 m
are two parts of windowpanes
with one part broken. 1.14 m

Asked for Area of the broken windowpane.

Solve 1.2 m × 1.14 m ÷ 2 =

1.14m 0.684 m2 0.6 m
× 1.2 m 2 1.368 m2
−0 The area of the broken windowpane:
2 28
+ 11 40 13 2
− 1 2
1.3 6 8 m2 1. 1 4 m
16 × 0.6 m
−16
0.6 8 4 m2
08
−8 Check the
0 answer with a
calculator.

1.2 m × 1.14 m ÷ 2 = 0.684 m2

The area of the broken windowpane is 0.684 m2.

BRAIN TEASERS
The cost of installing tint film on the windows in the living room is RM50 per
square metre. The width of the window in the living room is the same as the
width of the window in Amin’s room. The total cost is RM684. Calculate the
length, in m, of the window in the living room.

3.2 (i) Teacher’s Notes 49

Post more Higher Order Thinking Skills (HOTS) questions involving units of
measurement to enhance pupils' understanding.

SELF-PRACTICE

Solve the following problems.

a A total of 6 pieces of book covers were printed in 0.12 hours. Each piece of
the book cover was printed in equal time. Calculate the time, in hours, to
print 30 book covers.

b The diagram shows the locations of Asyraf’s house, Hui Hui’s house, and
the school.

School

Hui Hui’s house

Asyraf’s house

11.608 km
Hui Hui’s house is located in the middle between Asyraf’s house and the
school. The distance between the school and Asyraf’s house is 11.608 km.
Hui Hui goes to school for 5 days in a week. Calculate the total distance
travelled by Hui Hui to commute from his house to the school for a week.

c Mother bought a box of oat biscuits
weighing 400 g as in the diagram.
Calculate the mass of carbohydrate,
in g, for half of the total weight of the
oat biscuits.

d Alias’ father receives a wage of RM80.75 for working 8.5 hours. Calculate
the total amount of wages that Alias’ father will receive for working 2.5 hours.

e Ai Lee’s mother buys 15 bottles of strawberry juice containing 2.5 ℓ in each
bottle. She pours the juice equally into several glasses. Each glass has
a volume of 0.3 ℓ . Calculate the number of glasses needed.

f Pak Imran’s farm area has a width of 8.4 m and a length of 25.9 m. The
area of Pak Imran’s farm is 3 times the area of Pak Mail’s farm. Calculate
the area, in m2, of Pak Mail’s farm. State the possible length and width,
in m, of Pak Mail’s farm.

Teacher’s Notes

50 Construct problem solving questions which enable pupils to use various strategies. 3.2 (i)

SMART PROJECT

Tools/Materials MS Word, set of numbers to complete the answers,
manila cards, glue, a few pieces of papers/an exercise book

Set of numbers to
complete the answers

4 16 5 2

10 3 8

Participants 2 pupils in a group

Task = 4.096 ×

1 Construct questions involving mixed ÷ 10
operations using MS Word creatively. ÷

2 Print the questions and paste them 1.024 =
on a manila card. ×

3 Get a friend to paste the numbers 8 2.56
from the set of numbers to complete
the answers. Write the calculations × =
on a piece of paper. 1.2

4 Decorate the card and display it at ÷×
the mathematics corner.

= 1.92 ÷

BRAIN TEASERS

÷4×6=

is a decimal number. While calculating, Alia forgot to write the
decimal point and her answer was 103.5.
What is the value of ?

3.2 (i) Teacher’s Notes 51
The Smart Project activity can evaluate pupils’ skills in using technology.

SKILFUL MIND b 10 × 6.012 kg ÷ 9 =

1 Calculate.
a 6 × 15.04 km ÷ 8 =

c 18 × 0.356 ℓ ÷ 12 = d 34 × RM11.80 ÷ 40 =
f 45.87 ÷ 3.3 × 9 =
e 5.6 × 2.7 ÷ 8 =

g 7.04 × 1.2 = h 10.23 × 6.1 =
4.8 6.2

2 Aishah completes the number sentence 37.4 ÷ 4 × 5 =
in the manner shown. Justify the answer.
37.4 37.4
4×5 = 20

=1.87

3 Complete the number sentences below. Show the solution in the vertical form
and one other method.

a 64 × 9.037 ÷ 8 = b 38.34 ÷ 2.7 × 9 =

4 Solve the following problems.
a The length of a stick is shown in the diagram below. The stick is divided
into 5 different colours of equal length.

_2 6.015 m
3
of the white part is used. What is the length, in m, of the part used?

b In a party, 14 bottles of soya milk, as shown in the diagram, 1.25 ℓ
were poured equally into 50 glasses.

i. Calculate the volume, in ℓ, of soya milk in a glass.
ii. At the end of the party, 6 glasses of soya milk were not

consumed. Calculate the volume of soya milk that was 1.25ℓ
consumed.

c The mural of Dewan Bahasa dan Pustaka (DBP)
was produced using about 1.5 million mosaics of
equal size. What is the estimated cost of 0.5 million
mosaics if the total estimated cost is RM0.45 million?

Source: Briefing on the conservation of DBP Mural on 11 March 2015.

Teacher’s Notes 3.1 (i)
Post more HOTS questions to achieve Performance Levels 5 and 6. 3.2 (i)

52

A Solve the Problems 4
Percentage in savings and investments
SMART
1 DICTIONARY

Good morning, madam. Savings Money
I wish to open an account. or valuables saved and
used when in need.
Good morning. You can
choose to do savings or Investment Money
investments. used for specific
business such as buying
Kevin saves RM1 000 in a bank. The bank gives an shares and becoming a
interest rate of 0.5% for the savings. Calculate the member of the school’s
interest for his savings and the total amount of cooperative which will
money that he will have. give profits in the future.

Solution

Given Cash of RM1 000
Savings interest rate 0.5%

Asked for The interest

The total amount of money including the interest

Operation Multiplication Check your answer
with a calculator.

Solve The interest The total amount of money
including the interest
RM1 000 × 0.5% =
RM1 000 + RM5 = RM1 005
RM1 000 × 0.5 = RM5
100

4.1 (i) The interest is RM5 and the total amount 53
of money including the interest is RM1005.

Teacher’s Notes
Surf Bank Negara’s website at http://www.bnm.gov.my/index.php?ch
=en_mal_currency&consulist=1&lang=bm to get information on Awareness
and Financial Education.
Discuss with pupils the benefits of savings and investments.

2 Encik Raihan received a cheque of RM2 500 as
payment for his shop’s rental in January. He
deposited it in his bank account and received

an interest rate of 0.8% per month. Calculate the

amount of money at the end of the month.

Solution

Given Rental payment RM2 500.
The bank paid an interest rate of 0.8% per month.

Asked for Encik Raihan’s total savings at the end of the month

Operation Multiplication and addition

Solve RM2 500 × 0.8% × 1 + RM2 500 =

0.8% × 1 because the

Draw a diagra m. Interest received: interest is for 1 month.

100% 0.8% × 1

RM2 500 ?

RM2 500 × 0.8% × 1 = RM2 500 × 0.8
100

= RM25 × 0.8


= RM20

The total amount of money at the end of the month:
RM2 500 + RM20 = RM2 520

Check 4

RM20 × 100% = 4 × 100%
RM2 500 500
500
= 0.8%

The total money at the end of the month is RM2 520.

Estimate the time taken for Encik Raihan to
raise his savings up to RM5 000.

Teacher’s Notes

54 Discuss the interest given by several banks based on their brochures. 4.1 (i)

Carry out problem-solving activities involving interest in savings and investments

based on the brochures of several financial institutions.

3 Danial won RM4 000 in the 2016 Innovative Designing
competition. His mother invested the money in the
Amanah Saham for his education. He will get a dividend
of 11% per year. Calculate Danial’s total savings after
3 years.

Solution

Impo rta nt The value of investment: RM4 000.
in formation A dividend of 11% per year for 3 years.
Find the total amount of money after 3 years.


Solve 100% 11% 1 11% × RM4 000 = 111 × RM4 000
RM4 000 100
First year
= 1.11 × RM4 000

= RM4 440

100% 11% 1 11% × RM4 440 = 111 × RM4 440
RM4 440 100
Second year
= 1.11 × RM4 440

= RM4 928.40

100% 11% 111% × RM4 928.40 = 111 × RM4 928.40
RM4 928.40 100
Third year
= 1.11 × RM4 928.40

= RM5 470.52

Check Create a table. Calculate the dividend and the balance
at the end of the year with a calculator.

Year Balance at Dividend Value of Balance at the
the beginning rate dividend end of the year

of the year

1 RM4 000 11% RM440 RM4 440

2 RM4 440 11% RM488.40 RM4 928.40

3 RM4 928.40 11% RM542.12 RM5 470.52

Danial’s total savings after 3 years is RM5 470.52.

How long would Danial need to maintain his investment so
that the money will increase to more than RM10 000?

4.1 (i) Teacher’s Notes 55

Use a calculator to check the calculation of interest for each year.
Recall the previous lessons about simple interest and compound interest which
have been learned in Year 5.

4 Puan Balqis’ investment in her bakery has increased by 22%. Her total
investment now is RM1 525. If she wants the value of her investment to be

2 times her total investment, how much initial capital should she have invested?

Solution

Given Puan Balqis’ investment increases by 22%.
Total investment becomes RM1 525.

Asked for Initial capital to get 2 times the investment value of RM1 525

Solve
M ethod 1 Simplifying the problem

Investment increased to: 100% + 22% = 122%

2 times the investment value: 2 × RM 1 525 = RM3 050

122% — RM3 050

1% — ? Find the value for 1% first.

RM3 050 × 1% = RM3 050
122% 122

= RM25

1% — RM25
100% — 100 × RM25 = RM2 500

M ethod 2 Draw a diagram

RM3 050 × 122% = RM3 050

100% 22% × 122 = RM3 050 Explain how you check
100 your answer.
RM ?
× 1.22 = RM3 050

= RM3 050
1.22

= RM2 500

The initial capital that should be
invested by Puan Balqis is RM2 500.

Teacher’s Notes

Guide pupils to understand the problem and draw a diagram to solve the
56 problem. 4.1 (i)

Instil the moral values of long term savings for specific purposes such as in

SSPN-i and Tabung Haji.

Percentage in daily situations

1 Vasanti obtained 85% in a test. There were
60 questions in the test. How many questions
did Vasanti answer wrongly?

Solution

Given Percentage of marks: 85% Asked for The number of questions
Total number of questions: 60 answered wrongly

Operation Multiplication and subtraction 17 3
Solve
The number of questions answered correc tly: 85 × 60 = 51
100
2
1
The number of questions answered wrongly: 60 – 51 = 9

Check Percentage of questions answered wrongly: 100% – 85% = 15%
3
Th e num ber of ques tions a nswered 15 3
wrongly: 15% × 60 = 100 ×
60

5
1

The numb er of q uestio ns an swere d wro ngly was 9. =9

2 A company printed 27 560 magazines in January. The
number of magazines printed increased by 15% in
February. Calculate the number of magazines printed
in February.

Solution 100% 100% 15%

27 560 27 560 ?

Draw a model. January February

The increase in the number of magazines in February: 15 × 27 560 = 4 134
100

The number of magazines printed in February: 27 560 + 4 134 = 31 694

C heck 115 % × 27 560 = 115 × 27 560
100

= 1.15 × 27 560

= 31 694

The number of magazines printed in February is 31 694 copies.

4.1 (i) Teacher’s Notes 57

Discuss other daily situations which involve percentage. For example, nutrient
contents in food, data of disease, and population census.

3 In 2014, the number of tourists who visited Malaysia was 25.6 million.
In 2015, the number of tourists increased by 4%. In 2016, there were
30 million tourists. What was the increase in percentage in 2016
compared to 2015?

Source: http://www.motac.gov.my

Solution The number of tourists in 2015:

25.6 million + 4% × 25.6 million = 25.6 million + 4 × 25.6 million
100

Use a calculator to calculate = 25.6 million + 1.024 million
the increase in percentage. = 26.624 million

The increase in the number of tourists in 2016:

30 million − 26.624 million = 3.376 million

The increase in percentage: 3.376 × 100% = 12.68%
26.624

The increase in percentage of tourists in 2016 was 12.68%.

4 The diagram shows the number of beads in boxes A Box A
and B. Eli takes out a number of beads from Box A and 840 beads
30% of the beads from Box B. The total number of beads
taken is 345. Calculate the percentage of beads taken
from Box A.

Solution Box A Box B Total Box B
450 beads

Number of beads 840 beads 450 beads

Beads taken ? 30% 345 beads Use a calculator
The number of beads taken from Box B:
to check the
answer.

30 × 450 beads = 135 beads
100

The number of beads taken from Box A: 345 − 135 = 210

The percentage of beads taken from Box A:

210 × 100% = 2 100%
840 84

= 25%

The percentage of beads taken from Box A is 25%.

Teacher’s Notes

Guide pupils to understand the problem and draw a diagram to represent
58 the problem. 4.1 (i)

Surf http://www.mathworksheetsland.com/7/grade7-7-5pack.pdf

5 The number of investors in a trust fund scheme with the investments of
RM5 000 and less is 5 million. The number of investors with investments of
RM5 001 to RM10 000 is 0.4 million. A total of 0.7 million investors invested
RM10 001 to RM50 000. After a certain period, there was an increase of 30%
of the total investors. 10% of the increase was from investors who invested
RM5 001 to RM10 000. Calculate the increase in the number of investors who
invested RM5 001 to RM10 000.

Solution

Solve Create a table

No. Inv veasltume ent Ni(nup vmeeobspetolrero)sf An increased of 30% of the
total investor.

Below 30 × 6.1 million = 0.3 × 6.1 million
RM5 000 100
1 5 million = 1.83 million

2 RM5 001 to 0.4 million 10% of the increase was by
RM10 000

3 RM10 001 to investors who invested
RM50 000
0.7 million RM5 001 to RM10 000

Total 6. 1 million 1
10
100 × 1.83 million = 0.1 × 1.83 million

10 = 0.183 million

Check

1 0 ÷ 1 0 0 × 1 . 8 3 = 0.183

The number of investors that had increased is 0.183 million.

BRAIN TEASERS

RM1.2 million was inherited by four siblings. Jason received 40% of
the money. Jerry received 30% of the amount and the remainder
was received equally by Jenifer and Jenny. How much money did
Jenny receive?

4.1 (i) Teacher’s Notes 59

Construct questions on percentage which involve a group or categories in an
event such as a drawing competition.

TEROKFAUNRIAADVENTURE

WHO IS A WISE AND WEALTHY PERSON?

Tools/Materials play money, dice, Participants 3 to 5 pupils in a group
plasticine (including one pupil as a
banker)

Preparation Move Bank Excellent Move forward Your RM1 000 Move
backward miscalculated Community two boxes. share matures. forward two
1 Design play money of RM500, 4 boxes. your money. Services. Each Receive 5% of boxes or pay
RM100, RM50, RM20, RM10, Pay 50% of Receive player pays this money. 10% of your
RM5 and RM1 using MS Word. what is being RM150 from you RM100. total money.
Print an adequate number of charged. the bank.
the play money.
You won a WISE AND WEALTHY PERSON Your RM5 000
2 Create game piece from Designing investment
plasticine or coloured papers. Competition. matures.
Receive RM500 Receive 10%
from the bank. of it.

You are being Pay your
summoned. education
Pay RM200. fees of
RM600 to the
bank.

Game rules LOSE Pay RM100 Receive You donate You START
A TURN for tax. dividend of 6% RM300. contribute
1 Choose one of the players as of your total 1% of your
a banker. money. total money.

2 Each player is given a sum of RM5 000, that is 6 pieces of RM500, 11 pieces of
RM100, 10 pieces of RM50, 10 pieces of RM20, 10 pieces of RM10, 15 pieces of
RM5 and 25 pieces of RM1.

3 Decide the turns.

4 The first player throws the dice and moves his/her game piece on the game
board beginning from’’START’’according to the number on the dice.

5 Follow the instructions stated in the space where the game piece has landed.

6 The following player repeats steps 4 and 5.

7 If the game piece lands on’’LOSE A TURN’’, the player must get 6 on the dice
from his throw to enable him to continue the game or pay RM200 to the bank.

8 The game continues until a player runs out of money. The player who collects
the most money wins the game.

Teacher’s Notes

60 This game can be modified according to pupils’ abilities. Instil moral values such 4.1 (i)
as honesty and cooperation.

SELF-PRACTICE

1 Solve the following problems of savings and investments.

a The profit of Syarikat Inovasi Kreatif in 2015 was RM5 million. The company
invested 40% of its profit in a property trust fund. What was the value of the
investment?

b Mr Gan pays RM2 400 per year for his life insurance. The insurance
company gives an interest rate of 2.6% per year. Total the amount he paid
for the year with the interest he earned.

c Kasturi’s sister won RM12 750 in a short story writing competition. She
saved the money in her savings account and was given an interest rate
of 2.5% per year. How much will she have after 2 years?

d Encik Limat invested RM15 000 for
his child’s education. The bank
gave an interest rate of 3.5% per
year. How much interest will he
receive for 3 years?

e Laili’s father invests RM6 000 in Amanah Saham which gives a dividend
of 4.1% per year. Her father also has a savings of RM5 000 which gives a
simple interest rate of 3.8% per year. Calculate the total amount of money
after a year.

2 Solve the daily problems.

a There are 400 pieces of coloured cards inside a box. 35%
of them are red and the remaining are blue. Calculate the
number of blue cards inside the box.

b In a Mathematics test, Akmal answered 38 out of 50
questions correctly.
i. What is Akmal’s score in percentage?
ii. If Akmal wishes to get 90%, how many more questions must he answer
correctly?

4.1 (i) Teacher’s Notes 6611

Discuss and remind pupils about simple interest, compound interest, and the
ways of calculating.

SKILFUL MIND

1 Solve the following problems of savings and investments.

a Sukdev’s father invests RM8 000 for Sukdev’s education. He receives an
interest rate of 3.2% every year. He does not withdraw the money for a
year. How much does he have after a year?

b
Nabil receives RM4 as pocket money every day. He saves
RM1 daily. How many days does Nabil need to save in
order to get 200% of weekly total pocket money?

c Puan Lily saved RM2 100 in a bank. She kept her savings for 2 years. In
the first year, she received an interest rate of 3%. In the second year, she
received an interest rate of 1.25%. Calculate her total savings after 2 years.

d The investment shares of education for Jothi made by her mother

increased by 14% and is worth RM15 200. If she wants 1 1 times the value
2

of the investment, how much does she need to invest?

e The table shows the savings and yearly Name Savings Yearly
dividend received by Irfan and Li Suan dividend
from different financial agencies. Whose Irfan RM4 800
savings is more after 2 years? Li Suan RM5 000 5%

3.5%

2 Solve the daily problems below. 4.1 (i)

a Puan Nadia receives a monthly salary of RM3 625. She uses
20% of her salary to buy groceries. How much does she
spend to buy her groceries?

b Pak Rahim sold 20% of 250 durians which he had collected
from his orchard. 60% of the unsold durians were sent to
Puan Halimah for her business. How many durians were
left?

Teacher’s Notes
Discuss with pupils about the different types of savings and investments provided

62 by financial institutions particularly for the benefits of education.

5

A Recognise Cost Price, Selling Price, Profit, and Loss

1 Factory Wholesaler Retailer/Dealer Buyer

Why are the prices of goods different at
each level? Discuss.

2 A box of rubber bands costs RM10. We can sell each bracelet at

These rubber bands can be shaped RM2. The selling price for 20

into 20 bracelets. bracelets is RM40.

Yes, that’s right. We can
get a profit of RM30.

Identify the cost price, selling price, and DISCMTIAORNTARY
profit in this situation.
Cost price The price of
Cost price or buying price is RM10 . goods obtained by dealers.
Selling price is RM40 . Selling price The price of
Profit is RM30 . goods sold to the buyers.

5.1 (i) Teacher’s Notes 63

Discuss the various situations to explain the cost price and the selling price.
Instil ethics and moral values when setting the profit/selling price by taking into
consideration the wage, time, and creativity.

3 Model A a The cost price of a Model A camera is RM7 650.
How much is the profit?

Profit = Selling price – Cost price
RSeMlli8ng 2p0ric0e
= RM8 200 – RM7 650

MMooddeell AB = RM550
The profit is RM550.

Selling price b The profit of a Model B camera is RM250.
How much is the cost price?
RM2 130

DISCMTIAORNTARY Profit = Selling price − Cost price
Cost price = Selling price – Profit

= RM2 130 – RM250
thPerosfeitlliinsgobptraicineeids hwihg ehner =

th an the c ost price. The cost price of Model B camera is .

4 The capital spent for selling cendol today was

RM129. The sales for today is only RM85.

My sales are
also less.

Calculate the loss incurred by the cendol hawker. SMART
Loss = Cost price – Selling price DICTIONARY

= RM129 – RM85 Loss occurs when the
= RM44 cost price is higher than

The loss incurred was RM44. the selling price.

Did the kite seller incur a loss?
Discuss.

Teacher’s Notes

Use brochures or real objects in sales and purchases activities to relate to daily
64 situations in terms of profit, loss, selling price, and cost price. 5.1 (i)

Discuss the methods of calculating the selling price either in a profit or loss situation.

Surf http://www.math-only-math.com/worksheet-on-profit-and-loss.html

5 What is the selling price of the I loss RM8 950 when I sold this
car shown? used car which I had bought it for

Loss = Cost price – Selling price RM42 436.

RM8 950 = RM42 436 – Selling price

Selling price = RM42 436 – RM8 950

=

The selling price of the car is .

6 Item Cost Price Selling Price Profit Loss

Tre ad mill RM5 270 ? RM930

? RM5 218 RM220
CLSETAORCAKNCE

Massage
chair

Based on the table above, what is the selling price of the treadmill?

Selling price = Cost price + Profit Calculate the cost price
of the massage chair.
= RM5 270 + RM930

= RM6 200

The selling price of the treadmill is RM6 200.

BRAIN TEASERS

RM186.90 RM125.70

KedaI Sukan KITa KedaI Sukan RIa
Buy ONE and get
Buy ONE, get
ONE FREE. ANOTHER ONE FOR ONLY RM1.

The cost price of the bag at Kedai Sukan Kita is RM90. The cost price of
the bag at Kedai Sukan Ria is RM32 less than the cost price of the bag at
Kedai Sukan Kita. If you are the retailer, which sale of these bags is more
profitable? Compare and discuss.

5.1 (i) Teacher’s Notes 65

Provide more exercises on the cost price, selling price, profit, and loss through
quizzes or conduct simulation activities using picture cards.
Discuss the considerations that should be taken when buying goods during
promotion.

7 Study the table below.

Jersey Selling price Cost price
Short sleeve RM75 RM60
Long sleeve RM108 RM90

a Which jersey sales will get a higher profit?

Remember, subtract the cost price from the selling price to calculate the profit.



Profit of short sleeve jersey: Profit of long sleeve jersey:
RM75 – RM60 = RM15 RM108 – RM90 = RM18

The sale of long sleeve jerseys gets a higher profit.

b Retailers will order more short sleeve jerseys. Explain.

SMART CALCULATION

Percentage = Profit × 100% Percentage = Profit × 100%
profit Cost price profit Cost price

= 1 × 25 Percentage profit:

RM15 100%

RM60 2
4
1 RM 18
RM90 × 100% = 20%
= 25%
1

Retailers will order more short sleeve jerseys because
the percentage profit earned is higher than the long sleeve jerseys.

The stock clearance sale offers RM35 SMART CALCULATION
for short sleeve jerseys and RM65
for long sleeve jerseys. What is your Percentage = Loss × 100%
opinion about the percentage loss loss Cost price
of the sale?

Teacher’s Notes

Create another situation that involves calculating the percentage profit or loss
66 and ask pupils to make conclusions. 5.1 (i)

B Solve the Problems of Cost Price, Selling Price, Profit, and Loss

1 The incomplete table shows the cost Item Cost Selling
price and selling price of two electrical price price
appliances. The profit from the sale of Oven
the cake mixer is RM46 more than the Cake RM1 450 RM1 608
profit from the sale of the oven. What is mixer
the selling price of the cake mixer? RM695

Solution

Given The selling price of the oven is RM1 608.
The profit of the cake mixer is RM46
more than the profit of the oven.

Asked for The selling price of the cake mixer

Operation Subtraction and addition

Solve Profit Profit from Selling price
from oven cake mixer of cake mixer

5 10 11 RM6 9 5
+ RM2 0 4
RM1 6 0 8 RM 1 5 8
+ RM 4 6 RM8 9 9
– RM1 4 5 0
RM 2 0 4
RM 1 5 8

Check Make an estimation Profit from cake mixer:
RM100 + RM50 = RM150
Profit from oven:
RM1 600 – RM1 500 = RM100

Selling price of the cake mixer:
RM700 + RM150 = RM850

RM850 is close to RM899.
Therefore, the answer is reasonable.
The selling price of the cake mixer is RM899.

5.1 (ii) The selling price of a refrigerator is RM2 590 and the profit 67
is equal to the total profit from the sale of an oven and a
cake mixer. Calculate the cost price of the refrigerator.

Teacher’s Notes
Ask questions involving an operation before switching to higher level
questions involving mixed operations.
Surf http://www.kwiznet.com/p/takeQuiz.php?ChapterID=2496&
CurriculumID=22

2 A food seller incurred losses as much as 15% when the food that he prepared
did not sell well on that day. The cost for the food and the workers’ wages is
RM2 560. Calculate his loss and the total sales on that day.

Solution

Cost price: RM2 560 15% Draw a diagram.
Important Percentage loss: 15% Loss ?
information Loss: RM2 560
Selling price
Total sales:

Solve 11050 × R M2 560 = RM3 840
10

= RM384

The loss is RM384.

Total sales = Cost price – Loss

= RM2 560 – RM384

15

4 5 10

RM2 560

– RM 384

RM2 1 7 6

The total sales obtained is RM2 176.

I used the method on the

rig ht to ch eck my answe r. 85 × RM2 560 =
Is yo ur ans wer the same 100

as mine?

If the seller gets a profit of RM1 024 with the
same cost on the following day, calculate his
percentage profit.

Teacher’s Notes

68 Use analogies to solve problems. 5.1 (ii)

Surf http://www.math-only-math.com/calculating-profit-percent-and-loss-

percent.html

3 The picture shows the cost price of two types Cap A
of caps, A and B. Encik Yusof wants to make a RM10
20% profit from each type of cap he sells. How
many caps A and B should he sell to get a profit Cap B
of RM120 on that day? RM15



Solution Important
information

Cap A Cap B
Cost price = RM10 Cost price = RM15
Profit = 20% Profit = 20%

Solve Calculate the profit:

1 2 1 3
20 20
C a p A = 100 × RM10 = RM2 Cap B = 100 × RM15 = RM3

5 5
1 1
Trial and error.

First trial: The number of caps must
be divisible by 2 or 3.

Cap A = 30 × RM2 = RM60 Possibilities
RM120
Number Number Total
Cap B = 20 × RM3 = RM60

Second trial: of Cap A of Cap B Profit

Cap A = 1 5 × RM2 = RM30 30 20 RM120
RM120 15 30 RM120

Cap B = 30 × RM3 = RM90

Encik Yusof should sell either 30 Caps A and 20 Caps B
or 15 Caps A and 30 Caps B.

Try to list other pairs of number for caps A
and B, which may be sold by Encik Yusof
on the same day with the same profit.

5.1 (ii) Teacher’s Notes 69

Use different cost price and percentage profit to discuss with pupils.
Surf http://www.indiabix.com/aptitude/profit-and-loss/formulas

SELF-PRACTICE
Solve the following problems.

a The picture shows the selling price of a table fan. The profit RM69
from the sale of the table fan is RM31. Calculate the cost
price of the fan.

b The pictures show the selling price of two types of seafood. RM25
The cost price of black pomfrets is RM20 per kilogram. RM18
The cost price of prawns is RM15 per kilogram.
Calculate the percentage profit per kilogram
for each of the seafood.

c Item Cost Selling Syarikat Tuah gets equal profit from
price price the sale of furniture and televisions.
Based on the table shown, what is
Television RM 11 600 RM13 900 the selling price of the furniture?

Furniture RM18 500

d The picture shows the selling price of 5 boxes of CHOCBAORLCATOEKLBTACEROKLBTACEROKLBTCAEROKLBTAER
chocolates. Mr Lim buys 100 boxes of the chocolates.
Then, he sells a box of the chocolates at RM16. How 5 boxes — RM60
much is his profit?

e Encik Samad sold 3 old cameras. He incurred a loss of RM128 from the sale
of each camera. The cost price of the camera is RM3 605. Calculate the total
sales of the 3 cameras.

f The table shows the prices of three items Item Price per unit
in shops P and Q. Razak compares the Shop P Shop Q
prices in both shops. He buys each item LED TV RM9 888 RM10 670
from the shop that offers a lower price. Air
Ramu buys each item from Shop Q. RM 1 250 RM999
How much is the difference in expenses Purifier
between them? Hi-fi Set RM4 130 RM3 866

Teacher’s Notes

Carry out group activities to solve problems involving cost price, selling price,
70 profit, and loss. 5.1 (ii)

C Recognise Discount, Bill, Rebate, and Invoice

Discount

1 Sir, can the price of Model A MODEL B

car be reduced by RM1 000? We have
given a good
MODEL A discount, sir.

a Calculate the discount offered for Model A car.

Discount = Original price – Sale price

= RM55 599 – RM49 000 DISCMTIAORNTARY

4 15 Discount
Price reduction from the
RM5 5 5 9 9
– RM4 9 0 0 0 original price.

RM 6 5 9 9

RM55 599 – RM49 000 = RM6 599

The discount offered for Model A car is RM6 599.

b Calculate the discount fo r c Find the price of Model B car

Model B car. after the discount.

D120i0s0c ×o uRnMt: 6 8 00 0 = R M 13 60 0 18000 × 100% – 20% = 80%

RM68 000 = 80 × RM680
= RM54 400

The discount for Model B The price of Model B car after
car is RM13 600. the discount is RM54 400.

Between Model A and Model B, which one
would you choose? Give your reasons.

5.1 (i) Teacher’s Notes 71

Discuss the moral values as a smart buyer.
Ask pupils to give examples of other discounts in their daily situations such as
sales in conjunction with National Day, festive seasons, and New Year.
Surf http://www.math-only-math.com/worksheet-on-discounts.html

Bill and rebate Total cost is All right. Just pay RM204.50,
RM209.50. madam. You will receive more
1 coupons for today’s purchases.
This is your receipt and coupon.

Thank you.

Oh, I got a rebate
coupon for RM5
last week. This is
the coupon.

PRM Pasar Raya Mewah Sdn. Bhd.
(023890 K)
Pasar Raya N0. 23A, Jalan Mustika A21/B, RM5 REBATE
Taman Raya Baru,
Mewah 48050 Rawang, Selangor. for each
Tel. : 03 7956 3201 purchase of RM100.

Cooking oil 2 × RM14.70 RM29.40 How many pieces of
9555216 552634 3 × RM30.50 RM9 1.50 rebate coupons did
Rice 4 × RM22.15 RM88.60 Puan Sunita get? Explain.
9555147 201649
Jug DISCMTIAORNTARY
9555406 889814
Rebate Deduction of a
Quantity: 9 Items: 3 certain amount of payment
or the return of part of the
Total price RM209.50 money after buying an item.
Rebate RM 5.00 Bill A written statement
on the purchase of goods or
Total payment RM204.50 services received.
Cash RM204.50

THANK YOU. PLEASE COME AGAIN.
Friday 30-01-2015 Time 8:20 p.m.

Teacher’s Notes

Show examples of rebates in the form of cash or vouchers, and items discount
72 through search engines. Discuss the differences. 5.1 (i)

Discuss the various types of bills such as utility bills, cash bills, and restaurant bills.

2 Look at the pictures below. What is the difference between a rebate and

a discount? Model Y

Model X RM80 50 × RM80 = RM40
100
RM80 Coupon
50% discount 50% rebate

When I get a discount, I only When I give the rebate
pay RM40 at the counter to coupon to pay for the Model Y
buy the Model X calculator. calculator, I just pay RM40.

If you are a trader, which method would
you choose, rebate or discount?

SMART PROJECT

Tools/Materials manila cards, household goods Participants 2 pupils in
brochures, glue, marker pen a group

You wish to decorate your EXAMPLE
living room with furniture
and electrical appliances.
Get brochures on electrical
appliances and furniture.
Your budget is RM50 000.

Task

1 Cut the pictures from the

brochures and paste them The price of each item after discount:

on a manila card. 1 . L ED TV : 90 × RM15 688 = RM14 119.20
2 Label the selling price together with the price 100

deduction, discount or rebate. Decorate the 2. TV Rack : 80 × RM2 900 = RM2 320
created catalogue so that it is attractive. 100

3 Get a friend to calculate the discount and the price after the discount, price
deduction or rebate.

4 Record the total expenditure of the goods bought from the created catalogue.

5 Display your work at the mathematics corner.

5.1 (i) Teacher’s Notes 77733

This project can assess pupils’ mastery of knowledge, communication skills,
thinking skills, soft skills including attitude, and values.
Teacher can use other situations such as mini library, science garden, and
download brochures from websites.

Invoice

This is the invoice for the All right. Please keep
goods that will be delivered the copy in the file for
to Pustaka Cerah. Please the company’s record.
sign it, sir.

Company’s name
and address
Syarikat ABC INVOICE Based on the invoice,
state the quantity of
Buyer’s name 45, Jalan Indah, items purchased by
and address 52100 Kuala Lumpur. Pustaka Cerah and
the total payment.
To:
Pustaka Cerah, Invoice number Date of invoice
60, Jalan Pasar,
40680 Gombak, Invoice no.: AT1050
Selangor. Date: 8 August 2016

Quantity Details Price per unit Total
(RM) (RM)
50 Calculator 53.00 2 650.00 Explain the steps
(model AA) to calculate the
30 Dictionary 22.40 67 2.00 discounted value.
20 File 6.90 1 38.00
Total 3 460.00 DISCMTIAORNTARY
Details of Payment 692.00
order/goods details Less 20% Invoice A record
purchased trade discount 2 768.00 of goods or
services supplied
Total to customers and
payment amounts to be paid
by them.
(Ringgit Malaysia: Two Thousand Seven Hundred and
Sixty-eight Only)

SYARIKAT ABC Company’s

45, Jalan Indah,

____________52_10_0_K_ua_la_Lu_m_pu_r __ verification

(Signature/Company Stamp)

Teacher’s Notes

74 Guide pupils to identify the information required in an invoice. 5.1 (i)

Discuss the difference between an invoice and a bill through some examples

and their uses in everyday life.

Get pupils to create invoices as the example above.

Surf http://www.sabah.edu.my/csm07003/bab03/nota/ndok02invois.htm

D Solve the Problems of Discount, Bill, Rebate, and Invoice

1 In a watch shop, each customer will enjoy a discount of 20% for Model P
each purchase of a wristwatch. Encik Asyraf wants to buy Model P RM450
wristwatch. Calculate the amount of money that he will save. How
much is the selling price after the discount?

Solution

Given Model P watch is RM450. 20% discount. Model Q
RM800

Asked for The amount saved
The selling price after the discount

Operation Multiplication and subtraction

Solve

Method 1 Draw a diagram Method 2

Discount RM450 Discount:
20% 20% 20%
20% 20% 20% of RM450 = 20 × RM450
4 100
1

55 = RM90

Discounted value: 1 × 90 = RM90 3 15

5 RM450 RM450 Original price

1 – RM 90 Discount
RM360 Selling price after
Selling price after the discount: the discount

4 × 90 = 4 × RM90

51 RM450

= RM360

1 20

Check RM45 0 RM90 × 100% = 20%
– RM36 0 RM450
5
RM 90 1

Encik Asyraf will save RM90.

The selling price of Model P wristwatch after the discount is RM360.

A customer who uses a credit card to pay will get a 5% rebate for
each wristwatch after the discount. Calculate the rebate received
when buying Model Q wristwatch.

5.1 (ii) Teacher’s Notes 75
Modify or clone the questions to enhance pupils’ understanding.
Show various calculation or solution strategies to strengthen the concept.

INVOICE No: 301207
SYARIKAT MURNI
2 Encik Din makes an order 63, Jalan 2/81, Kepong,
from Syarikat Murni as 52100 Kuala Lumpur.
stated in the invoice. If he
orders 2 times the number To: Date: 26 March 2016
of cameras of the similar Encik Din b. Ali
type and 2 similar printers Lot 2, Jalan Mas,
in June, how much is the 40100 Sentul,
total payment for the Kuala Lumpur.
invoice for that month?
No. Item Quantity Price per Total
(Unit) unit (RM) (RM)
1. Camera 2 2 380 4 760.00
2. Printer 3 365 1 095.00
5 855.00
Total amount to be paid

Solution (Ringgit Malaysia: Five Thousand Eight Hundred and
Fifty-five Only)

Given Price of a camera Payment by cheque payable to Syarikat Murni account number
is RM2 380. 13200000563201. Please attach the deposit slip if payment is
made directly into our bank account.
Price of a printer
is RM365. SYARIKAT MURNI
63, Jalan 2/81, Kepong,

52100 Kuala Lumpur.

Company’s Manager/Stamp

Number of orders in June: 2 times the number of cameras in
March and 2 printers.

Asked for The total invoice payment in June

Operation Multiplication and addition

Solve Item Quantity Price per Total (RM)
No. unit (RM)
2×2=4 4 × 2 380 = 9 520
1. Camera 2 2 380 2 × 365 = 730
2. Printer
365

The total payment for the invoice in June = RM9 520 + RM730

= RM10 250
76
The total payment for the invoice in June is RM10 250.

Syarikat Murni offers a rebate of 1% for each item for total
payment that exceeds RM10 000. Calculate the price for
the items ordered in June.

Teacher’s Notes 5.1 (ii)

Surf http://www.hasil.gov.my/pdf/pdfam/BM_PanduanPenyimpanan Rekod.pdf
and http://www.sabah.edu.my/csm07003/bab03/bab3_nota_main.htm

3 The incomplete table below shows the goods bought by Puan Nimas.

Quantity Goods Price per unit Price
RM70
2 Milk powder RM35

2 Butter

Total

a Puan Nimas paid RM100 and received a balance of RM15. How much
is the price of a stick of butter?

b The profit from the sale of 5 tins of milk powder and 2 sticks of butter
is RM51. The profit from selling 2 tins of milk powder and 2 sticks of
butter is RM24. Calculate the profit from selling a tin of milk powder.

Solution

a Working backwards

Milk powder Balance Butter

The price of 2 sticks of butter : RM15
The price of a stick of butter : RM15 ÷ 2 = RM7.50

A stick of butter costs RM7.50.

b Using algebra

Milk Butter Profit Use a calculator
5 2 RM51 to check both
2 RM24 answers.
–2 0 RM27
3

3 tins — RM27
1 tin — RM27 ÷ 3 = RM9

The profit from selling a tin of milk powder is RM9.

5.1 (ii) Calculate the profit from selling a stick of butter. 77

Teacher’s Notes
Discuss various solution strategies such as trial and error, and trying simpler tasks.
Surf http://www.lancaster.k12.oh.us/olc/folder.aspx?id=23539&
c=16875&s=837

SELF-PRACTICE
Solve the following problems.

a Akmal gets a discount of 10% when he buys a goat
that costs RM960. How much money can he save?

b An oil painting that costs RM10 490 was sold at a discount of 20% during a
promotion. Calculate the selling price of the painting after the discount.

c The diagram shows an incomplete bill. MAJU Maju Sendirian Berhad.
N0. 22, Jalan Mustika A21/B,

Taman Raya Baru.

SDN. BHD. 48050 Rawang, Selangor.
Tel. : 03 7956 0123

i. Calculate the total price that Daim has Navy blue paint 4 × RM75 RM
to pay.
Light green paint 2 × RM120 RM
ii. A rebate of RM10 is given for each
purchase that exceeds RM100. How Pink paint 5 × RM138 RM
much rebate is received?
Quantity: 11 Items: 3

Total price RM

THANK YOU. PLEASE COME AGAIN.

Saturday 31-01-2015 Time: 10:10 a.m.

d The picture shows the price of a water RM2 680 RM1 320
filter and a microwave oven. Rekha has
RM3 121. She buys the two items with
a discount of 25%. How much is her
balance?

e The price of a leather wallet in JAYA INVOICE
the invoice is 3 times the price JAYA Enterprise (045678 K) ENTERPRISE
of a necktie.
N0. 8, Jalan Jaya A19/A, Taman Jaya Baru, 68100 Batu Caves, Selangor.
i. What is the total payment
after the discount? Tel. : 03 6865 3412 Faks : 03 6865 3124

ii. The payment is made through PASAR RAYA MEWAH SDN. BHD., Invoice No. : 00143
three cheques of equal value. No. 23A, Jalan Mustika A21/B,
Calculate the value of each Taman Raya Baru, Date : 28-02-2015
piece of cheque. 48050 Rawang, Selangor.
No. P/O : 00234

Quantity Goods Price per unit Price

50 Belt RM49 RM1 520

40 Necktie RM38

30 Leather wallet

Less 10% trade discount

Total amount

Teacher’s Notes 5.1 (ii)
Surf http://www.lancaster.k12.oh.us/userfiles/837/Classes/16875/

78 SalesTaxandDiscountWorksheet-0.doc

E Recognise Asset and Liability, Interest, and Service Tax

Assets and liabilities

1 Puan Seri Hamidah is a wealthy ngs/investm
y Car
woman. She owns assets such as land, Jeweller s
Savi ents
bungalows, and cash.

Assets

Houses Cash

Wow! She has a DISCMTIAORNTARY
lot of assets.

This is my neighbour. He dit card deb Asset What is being
experiences emotional stress. owned such as cash
He has a lot of liabilities. and property.

RM Liability Debts.

Hous ts Taxes
Cret
e instalmen All taxes such as:
• service tax.
Liabilities • income tax.
• assessment tax.

Discuss the types of assets Car instalment
and liabilities. What are the
disadvantages when we
have a lot of liabilities?

5.1 (i) Teacher’s Notes 79

Gather information from Bank Negara such as brochures and discuss with pupils.
Discuss the problems of debts related to credit cards and ways of good financial
management.
Surf http://www.savingtoinvest.com/your-car-asset-or-liability/

2 The table below shows the assets and liabilities of Encik Latif and Encik Fariz.
Their yearly income is the same, that is RM51 000.

Encik Latif’s yearly income
RM51 000

Assets RM Encik Fariz’s yearly income
RM51 000

House 90 000 Assets RM

Fixed deposits 30 000 House 90 000

Car 40 000 Fixed deposits 10 000

Liabilities RM Car 20 000

Housing loan 60 000 Liabilities RM

Car loan 20 000 Housing loan 30 000

Education loan 1 8 000 Car loan 1 0 000

Calculate the total assets and Education loan 1 5 000
liabilities of Encik Latif and
Encik Fariz. Who has more Credit card debts 5 000
assets and liabilities?

Encik Latif’s assets: RM90 000 + RM30 000 + RM40 000 =
Encik Latif’s liabilities: RM60 000 + RM20 000 + RM18 000 =

Encik Fariz’s assets: RM90 000 + RM10 000 + RM20 000 =
Encik Fariz’s liabilities: RM30 000 + RM10 000 + RM15 000 + RM5 000 =

Who is better at How could Encik Fariz
managing his income? reduce his liabilities?
Discuss.

AMAZING FACTS

Assets more than liabilities means good financial management.
Liabilities more than assets means bad financial management.

Teacher’s Notes

Instil moral values such as increase savings, spend wisely, avoid debts, and settle debts.

80 Explain that there are two types of assets: investment assets and non-investment assets. 5.1 (i)

Investment assets give dividends and capital profits. Non-investment assets are assets that do

not generate cash flow. For example, houses and cars.

Surf http://www.hartanahdisini.com/memahami-konsep-aset-liabiliti/

Interest Mum, why is there RM12.90
1 in my account?

Date Debit Interest/ Credit Balance
dividend/

bonus

BBaa3nn0kkMMDeeggeaahhcBBaa2nn0kkMM1ee5ggaahh*BB*aa*nn4kkMM3ee0gg.aa0hhBB0aa nnkkMMeeggaa hhBBaannkkMMee ggaahhBBaannkkMMeeggaahhBBaannkkMMeegg*aa*hh*BB4aann3kk0MM.ee0ggaa0hhBBaa Oh, the bank gave an
BBaa3nnkk1MMDeeggeaahhcBBaa2nn0kkMM1ee6ggaahhIBBaannntkkeMMreeeggaashhtBBaann*kkMM**eegg*aa*hh*BB1aa2nnkk.9MMee0ggaahhBBaannkkMMeeggaahhBBaannkkMMeegg*aa*hh*BB4aann4kkMM2ee.gg9aa0hhBBaa interest rate of 3%.

Calculate the interest received by Rina in a year.

Interest = Savings × Interest × Time DISCMTIAORNTARY
rate (in years)
Interest Money
= RM430 × 3% × 1 earned from the
savings in the bank.
= RM430 × 3 × 1
100

= RM43 × 0.3

= RM12.90

The interest received by Rina in a year is RM12.90.

If the interest offered is AMAZING FACTS
3.5%, calculate the total
savings in the account Bonus or dividend is
after a year. another term for the
interest offered by a
particular financial
institution.

2 Ben gets RM150 000 as an education loan with an interest rate of 1% per year.
How much interest should Ben pay in 5 years?

Interest = RM150 000 × 1% × 5

= RM150 000 × 1 × 5
100

= RM7 500

5.1 (i) Ben should pay an interest of RM7 500 in 5 years. 81

Teacher’s Notes
Discuss examples of interests, dividends, and bonuses received from
financial institutions.
Surf http://www.ptptn.gov.my/web/guest/pinjaman

Service tax The food costs only RM45.80. Time : 03:02:09 p.m.
1 Why is the total payment Cashier : QORIDAH
RM48.55? Receipt No. : C6-647148

ITEM QUANTITY PRICE TOTAL
(RM) (RM)
18.00
CHICKEN SATAY 30 0.60 6.00
2.00
TRIPE SATAY 10 0.60 3.00
KETUPAT 4 0.50 2.60
2.20
ABC 1 3.00 12.00

ICED TEA 2 1.30

Oh, that WATERMELON JUICE 1 2.20
includes the
service tax of CHICKEN RICE 3 4.00
6%, sir.
TOTAL RM 45.80
6% tax RM 2. 75
Discount RM 0.0 0
Round up RM 0.0 0

TOTAL RM 48.55
PAYMENT
CASH RM 48.55
RM 0.00
BALANCE

Calculate the service tax and the total Thank You. Please Come Again.
payment in the situation shown.
DISCMTIAORNTARY
Service tax = 6% of RM45.80
Service tax
= 6 × RM45.80 Tax needed to be paid on
100 the services provided by
certain businesses such
34 as hotels and fast food
RM 45.80 restaurants.

× 6 RM274.80 ÷ 100 = RM2.748

RM274.80 RM2.75

The service tax is RM2.75.

Total payment: RM45.80 + RM2.75 = AMAZING FACTS

1 A 6% GST or Goods
and Services Tax has
RM45.80 been implemented in
+ RM 2.75 Malaysia effective
1 April 2015.
RM48.55

RM45.80 + RM2.75 = RM48.55

The total payment is RM48.55.

Teacher’s Notes

Discuss other taxable services such as transportation and hotels. Discuss the
82 purpose of taxes and their impact on the country’s economy. 5.1 (i)

2 The receipt shows the payment of a car parked for JALAN LABA
4 hours totalling RM3 including service tax. How much CAR PARK
is the parking fee without the service tax?
-REPE-EDSTe-n-anx-e-ucoyt--tirertrt-m-rvayia--ytp-i-lteicd--mtitpn-e-oiaN-m-atnet--tyeod-a-em--.xa -- t-R-ee-T-nE--h--tC --a -E--n-I--Pk-- --T-Y-::-:-:o:7--:00:9-1-u:48666--:R:0-6-/0/%h--M05330--o--0//3au--p22--.rm.--0m0s--1-1.-.--66----
106% = Percentage of parking fee + 6% service tax Please come again
without service tax

Percentage of parking fee = 106% – 6%
without service tax

= 100%


106% — RM3

100% — ?

RM3 × 100% = RM2.83
106%

The parking fee without the service tax is RM2.83.

3 The total for this bill is RM217.30. tv ria
This payment is inclusive of the
service tax of RM12.30.

Calculate the basic payment. 12.30
217.30

Total payment = Basic payment + Service tax payment

RM217.30 = + RM12.30
RM217.30 – RM12.30 =

The basic payment is .

5.1 (i) Teacher’s Notes 83

Use a variety of ways to guide pupils to calculate service tax.
Surf http://www.customs.gov.my/ms/pg/pages/pg_st.aspx

F Solve the Problems of Asset and Liability,
Interest, and Service Tax

1 The table below shows the total assets and liabilities of Mrs Chua and
Mrs Wong. Who is richer?

Ò Name Mrs Chua Mrs Wong

Total RM120 163 RM249 618
RM39 509 RM181 325
Assets

Liabilities

Solution

Mrs Chua Assets RM120 163
Liabilities RM39 509

Assets – Liabilities = RM120 163 – RM39 509 Use addition to
= RM80 654 check the answers.

Mrs Wong Assets RM249 618
Liabilities RM181 325

Assets – Liabilities = RM249 618 – RM181 325
= RM68 293

Mrs Chua is richer than Mrs Wong.

The total assets of Mr John is half the assets of
Mrs Wong but his liabilities are RM15 839 more
than Mrs Chua. Which number sentence below
is correct to determine Mr John’s wealth?

a RM249 618 – (RM39 509 + RM15 839) =
2

b (2 × RM249 618) – (RM39 509 + RM15 839) =
84
Teacher’s Notes 5.1 (ii)

Use other strategies such as drawing diagrams and logical reasoning to solve
daily problems.
Instil moral values such as avoiding debt practices.

2 Haikal’s brother applied for a loan of RM90 000 from Tabung Ekonomi
Kumpulan Usaha Niaga (TEKUN) to start a business. He pays 4% of his loan
per year to TEKUN. How much is his monthly commitment?

Solution Important
information

Loan: Percentage of Monthly
RM90 000 commitment commitment: ?
4% per year

There are 12 months in a year. Draw a diagram
that is divided into 12 equal parts.

RM90 000

?
1 year (4%)

The yearly commitment = RM90 000 × 4%

= RM90 000 × 4 1 year = 12 months
100
RM 300
12 RM3 600
= RM900 × 4
–36
= RM3 600 00

The monthly commitment = RM3 600 ÷ 12 –0
= RM300 00

Use a calculator to check the answer. –0
0

The monthly commitment is RM300.

Bank Q imposes a 3.5% interest rate for the first half of the year
on the same loan, but the interest rate increases by 1.5% for
the second half of the year. Calculate the interest imposed in
that year.

5.1 (ii) Teacher’s Notes 85

Get pupils to bring a few bank brochures. Expose pupils to agencies that
provide financial assistance to small entrepreneurs. Examples: IKS, TEKUN.

3 During the last holidays, Farah and her family stayed W+ i62th%RdoausMyetsrb1v1rie5cnae0ikgtfahaxtst
in a hotel in Pulau Langkawi. A 6% service tax was
imposed. Farah’s mother paid RM477. How many days
and nights did Farah and her family stay in the hotel?

Solution

Payment for 2 days and 1 night including a 6% service
tax:



( )
3 × 3 Solve the
simpler task
RM150 + (6% × RM150) = RM150 + 6 RM150 first.
100
2
1

= RM150 + RM9

= RM159

Payment for 2 days 1 night = RM159

Payment for 3 days 2 nights = RM159 + RM159 Explain how
= RM318 you can check
the answers.
Payment for 4 days 3 nights = RM318 + RM159
= RM477

Farah and her family stayed for 4 days 3 nights.

Farah and 5 of her family members had breakfast
at the hotel restaurant. The hotel charged RM30 per
person for breakfast. A 5% service tax was imposed
for the breakfast. Calculate the cost of breakfast for
the whole family on the first day.

Is this the correct way to calculate? Discuss.

(6 × RM30) + (5% × RM180) =

Teacher’s Notes

Provide a variety of problem-solving questions involving daily situations. Show
86 various strategies to solve the problems. 5.1 (ii)

Discuss other services in the hotel that imposes taxes.

SELF-PRACTICE

Solve the following problems. Name Asset Liability

a The table shows the assets and liabilities Encik Shahril RM408 517 RM21 7 089
of Encik Shahril and Encik Aidil. Encik Aidil RM526 039 RM348 510
Who is richer?

b Puan Suriati invested RM50 000 in a unit trust. After a year, she received a
dividend of 4.5%. Calculate the dividend.

c The price of a meal set as shown in the picture is RM12.90.

The service tax that should be paid is 6%. What is the total

price to be paid? 1 set

RM12.90

TEROFKUA NRIAADVENTURE

Tools/Materials folded papers, score
cards, pens, play
money

Participants 4 pupils in a group
(including a cashier)

Task

1 Prepare materials as shown in the Example: Question 1
pictures. On the outer side of the folded
paper, write the question numbers. Cost price = RM500
On the inside, write questions about
Selling price = RM750

Profit =

cost price, selling price, profit, loss, discount, bill, rebate,

invoice, assets and liabilities, interest, and service tax.

2 A pupil becomes the cashier and 3 other pupils take turns to play against one
another. Each participant is given RM500.

3 The first participant will select one of the eight numbers and answers the
question for the selected number.

4 The cashier will pay the player if the answer is correct.

5 The next player repeats steps 3 and 4. Continue the game for 4 rounds.

6 The player who collects the most play money wins the game.

5.1 (ii) Teacher’s Notes 87

The level of questions in the Fun Adventure activity can be modified according to
pupils’ abilities.

SKILFUL MIND

Solve the following problems.

a In conjunction with Entrepreneurship Day, the pupils of Year 6 Arif sell
ice creams. The cost price of an ice cream is 60 sen and the profit to be
obtained is 30 sen. Calculate the sales for 50 ice creams.

b Puan Salmah sold a house for RM420 000 and earned a profit of 5%. What is

the cost price of the house?

c The incomplete invoice on the right shows SPORTS EQUIPMENT SUPPLIER
the orders made by Encik Firdaus. Calculate INSPIRASI SENDIRIAN BERHAD

No. 3, Jalan Ria, 47300 Petaling Jaya, Selangor Darul Ehsan.

the amount to be paid by him if the supplier To: Encik Firdaus bin Isa Invoice no.: MS6002
Kedai Sukan Gaya, Date: 10 April 2016
gives him a 10% discount. Lot 6A, Jalan 5, Cheras,

54062 Kuala Lumpur.

d Kalai reloaded his prepaid card for RM50. No. Quantity Item Price Total (RM)
A 6% service tax was charged. What is (Unit) per unit (RM)
the total cost of the prepaid card?
1. 20 Sports shoes RM80.00

2. 30 Set of sports wear RM120.00

e A factory owner took a loan for RM1 million from a bank to expand his business.

An interest rate of 8% per year was imposed. Calculate the total amount to be

paid for 2 years.

f The diagram shows the selling price of a 10% rebate RM4 500

set of kitchen cabinet and a dryer. Puan

Rohana paid RM14 742 for the purchase of

the two goods. What is the percentage of RM12 380

discount for the dryer? Discount ?

g The incomplete bill shows the record Quantity Goods Price per unit Price
of several groceries. The price of a Rice RM2.90 RM14.50
packet of milk powder is 2 times the 5 kg
Biscuits
price of a tin of biscuits. Calculate the 12 tins
price of a tin of biscuits and a packet 4 packets Milk powder

of milk powder. Total RM206.50

h The assets of Encik Hamid and Puan Shanti are RM0.8 million and RM1 million
respectively. Encik Hamid’s liabilities are RM234 618 which is half of Puan
Shanti’s liabilities. Who is richer?

Teacher’s Notes 5.1
Surf http://www.primaryresources.co.uk/maths/pdfs/money3.pdf

88 http://www.primaryresources.co.uk/maths/pdfs/10money.pdf

6

A 24-Hour System
Recognise the 24-hour system

Our flight time is displayed TIME FLIGHT DESTINATION GATE
in the 24-hour system.
Therefore, we will depart 16:00 MH 1138 Penang A7
at sixteen fifteen hours.
16:15 MH 2612 K. Kinabalu A5

16:25 CX 0720 Hong Kong C32

16:25 MH 0611 Singapore H4

1166::3300 Wt hahta,tmtimumeMM?iHHs 0376 Guangz C24
0724 Phom P H6
H10
16:30 MH 0786 Phuke

16:45 MH 1560 Chennai C38

16:55 MH 0000 Oamen C37

17:00 MH 0000 Perth C12
17:00 MH 0000 Pen1615 hours is equal to
4:15 p.m. in the 12-hour

system.

a 4sTyhdse itg etiimmts.ei sin wthrite te2n4 -uhs oinugr 241-h6o1u5 r system sixteen fifteen The first 2 digits
hours hours represent hours
and the last 2
digits represent

minutes.

12-hour system

4:15 p.m. four fifteen p.m.

b The clock below shows the time the zero seven zero nine hours
family will arrive in Kota Kinabalu. 709 hours 0709 hours



Which answer card is
correct? Why?

eighteen forty hours

6.1 (i) Teacher’s Notes 89

Discuss situations which use the 24-hour system in daily routines. For example,
the train and commuter schedules.
Use flash cards to carry out activities of reading aloud and writing time in the
24-hour system in words and numerals.

The relationship between the 24-hour system and the 12-hour system

1 a The yellow loop indicates the time in the The time in the 12-hour
24-hour system. The blue loop indicates the system is differentiated
time in the 12-hour system. by writing a.m. or p.m..

Time Loop

4:00 a.m.5:00 6:00 a.m.7:00 a.m.8:00 a.m.
a.m.

3:00 a.m. 9:00 a.m.

2:00 a.m. 03000400 0500 0600 0700 0800 10:00 a.m.
1:00 a.m. 0900 11:00 a.m.
0200 1000

0100 1100

12:01 a.m. 0001 midnight midday 1159 11:59 a.m.
12:00 0000 1200 12:00
11:59 p.m. 2359 1201
12:01 p.m.

2300 1300

11:00 p.m. 2200 1400 1:00 p.m.
10:00 p.m. 21002000 1900 1800 1700 1600 1500 2:00 p.m.

9:00 p.m. 3:00 p.m.
8:00 p.m. 7:00 p.m.
6:00 p.m.5:00 p.m4. :00 p.m. DISCMTIAORNTARY

In the 24-hour system, the time in a.m. ante meridian refers to the
a day is stated from 0000 hours until time after midnight until before
2359 hours. midday.

Four digits are used in this system. p.m. post meridian refers to the
The first two digits represent hours time after midday until before
in a day and the last two digits midnight.

represent minutes.

This system avoids confusion of the BOOST
same time. YOUR KNOWLEDGE

Convert the time from

b State 0800 hours in the 12-hour system. 0100 hours until 1159 hours

0800 hours = 8:00 a.m. to 12-hour system
 The hour and minute

The dividing point between Refers to before digits do not change.
hours and minutes. midday.  Ignore the first digit

0800 hours in the 12-hour system is 8:00 a.m.. when it is 0.
 Write a.m..

Teacher’s Notes

Relate to the routine of saying time in the 12-hour system. For example, 9:00 a.m.
90 can also be said as 9 o’clock in the morning. 6.1 (i)

Create a class timetable or a schedule of activities in school using the 24-hour

system.

2 My mother fetches my younger sister from BOOST
school at 1245 hours. What is the time in the YOUR KNOWLEDGE
12-hour system?
Convert the time from
1245 hours =
1200 hours until 1259 hours
1200 hours 1230 hours1245 hours1300 hours
to the 12-hour system
12:45 p.m.  The hour and minute digits

12:00 noon 12:30 p.m. 1:00 p.m. do not change.
 Write p.m..
1245 hours = 12:45 p.m.

3 If Mr Lim’s return flight is at 2230 hours, what is the
time in the 12-hour system?

2230 hours = In the time loop of the 12-hour
system, the corresponding time to
2230 hours is in the middle between
10:00 p.m. and 11:00 p.m..

Method 1 BOOST
YOUR KNOWLEDGE
2200 hours 2300 hours Method 2
2230 hours Convert the time from
hours minutes
10:30 p.m. 22 30 1300 hours until 2359 hours

10:00 p.m. 11:00 p.m. – 12 00 to the 12-hour system.
10 30  Subtract 12 hours from the

2230 hours = 10:30 p.m. hour digits.
 The minute digits do not

change.
 Write p.m..

4 0045 hours = Why is 12 hours added BOOST
to the time? Discuss. YOUR KNOWLEDGE

0045 hours = 0045 + 1200 hours Convert the time from
= 1245 0000 hours until 0059 hours
to the 12-hour system
12:45 a.m.  Add 12 hours to the hour

0045 hours = 12:45 a.m. digits.
 The minute digits do not
State 0425 hours, 1209 hours, and
1750 hours in the 12-hour system. change.
 Write a.m..

6.1 (i) Teacher’s Notes 91

Use a timeline, an actual clock face or a clock model to convert time from the
24-hour system to the 12-hour system and vice versa.
Remind pupils to write the correct period of the day (a.m. or p.m.).

5 Raihana and her mother wanted to go back to their
village by train. Raihana checked the train schedule
online as shown.

Train no. 9047 9411 9410
9:00 a.m. 12:20 p.m. 10:45 p.m.
Departure
time

a What is the corresponding time to 9:00 a.m. in the 24-hour system?

9:00 a.m. =

Method 1 I use the Method 2
time loop.
9:00 a.m. = 0900 hours
9:00 a.m. 10:00 a.m.
Remember! Write zero
9:30 a.m. as the first digit.

0930 hours

0900 hours 1000 hours

9:00 a.m. = 0900 hours

b State the train departure time, 12:20 p.m. in the 24-hour system.

12:20 p.m. = For the time between 12:00 noon
until 12:59 p.m., you do not need to
add 12 hours.

12:00 noon 12:30 p.m. 1:00 p.m.
1200 hours 12:20 p.m. 1300 hours

1220 hours
1230 hours

12:20 p.m. = 1220 hours

Teacher’s Notes

92 Emphasise the conversion of time from the 12-hour system to the 24-hour system 6.1 (i)

is the reverse of the conversion of time from the 24-hour system to the 12-hour

system.

c Raihana wants to book a train ticket at 10:45 p.m.. Convert the time to the

24-hour system.

10:45 p.m. = Add 12 hours to the time
between 1:00 p.m. until

10:45 p.m. = 1 045 + 1200 hours 11:59 p.m. to convert it to
= 2245 the 24-hour system.

10:45 p.m. = 2245 hours

d 12:15 a.m. =

hours minutes BOOST
12 15 YOUR KNOWLEDGE

– 1 2 00 While converting the time
00 1 5 from 12:00 midnight until
12:59 a.m. to the 24-hour
12:15 a.m. = 0015 hours system, subtract 12 hours
from the original time.
SELF-PRACTICE

1 Read aloud the following times.

a 0009 hours b 0206 hours c 1431 hours d 1500 hours e 2355 hours

2 Write the following times in numerals.

a zero ten hours. b zero five forty-five hours.

c thirteen zero two hours. d nineteen hundred hours.

e zero four twenty hours. f zero six zero three hours.

3 Read aloud the two corresponding times. 4 Complete the following table.

11:10 p.m. 10:02 a.m. 1710 hours 12-hour system 24-hour system
1:25 a.m. 5:10 p.m. 6:00 p.m. 12:05 a.m.
1002 hours 2310 hours 1:40 p.m. 2 125 hours
1340 hours 1800 hours 0125 hours 0050 hours
7:00 p.m.
9:40 p.m.
1 435 hours

6.1 (i) Teacher’s Notes 93

Give more exercises to convert time from the 12-hour system to the 24-hour
system and vice versa to enhance pupils’ understanding.
Surf http://www.helpingwithmath.com/resources/wor_time.htm