SK Year 5 Mathematics DLP

Days and hours


1 The sailing time for an expedition from
location A to location E is shown in the Sailing Expedition
diagram. A 5
1 days
8
a Calculate the total sailing time from
location A to location C.
B
5 1
1 days + 1 days = days
8 4 1
1 days
5 1 5 1 × 2 4
1 days + 1 days = 1 days + 1 days C
8 4 8 4 × 2
5 2 1 day 5 hours
= 1 days + 1 days
8 8
7 E
= 2 days D
8
1
5 1 7 1 days
6
1 days + 1 days = 2 days
8 4 8
7
The total sailing time from location A to location C is 2 days.
8



b What is the total sailing time, in days and hours, from
location C to location E?
1
1 day 5 hours + 1 days = days hours
6

1 1
1 days = 1 day + day
6 6
day hour
1 4
= 1 day + ( × 24) hours 1 5
6
1 + 1 4
= 1 day + 4 hours 2 9
= 1 day 4 hours

1
1 day 5 hours + 1 days = 2 days 9 hours
6
The total sailing time from location C to location E
is 2 days 9 hours.




• Adding fractions of days is similar to adding fractions by getting 143
4.3.1 (ii)
the common denominators first before doing addition.

2 Refer to the following table and Process Duration
calculate the total duration Preparation, 3.5 days
of the two processes for completing
a robotic car. installation, and
3.5 days + 1.5 days = days finishing of
non-metallic
1
3.5 days materials and
+1.5 days metallic materials
5.0 days Installation of the 1.5 days
3.5 days + 1.5 days = 5 days alarm system


The total duration of the two processes is 5 days.


3 4.75 days + 9 days 18 hours = days hours
day hour
4.75 days = 4 days + 0.75 day 1
4 18
= 4 days + (0.75 × 24) hours + 9 18
= 4 days + 18 hours 1 3 36

= 4 days 18 hours + 1 − 24
1 4 12

4.75 days + 9 days 18 hours = 14 days 12 hours



1
4 3 days + 8.125 days = days hours
2
1 1 8.125 days = 8 days + 0.125 day
3 days = 3 days + day = 8 days + (0.125 × 24) hours
2
2
1 12
= 3 days + ( × 24) hours = 8 days + 3 hours
2
1 = 8 days 3 hours
= 3 days + 12 hours
= 3 days 12 hours
day hour
3 1 2
+ 8 3
1 1 1 5
1
3 days + 8.125 days = 11 days 15 hours
2



144 4.3.1 (ii) 1
4.3.2 (ii) • Carry out mental arithmetic activities, such as day is 12 hours,
2
0.5 day is 12 hours, and 0.25 day is 6 hours.

Years and months


1 The duration to complete three phases of
Indah Housing Project is shown below.















1
1
Phase 1 2 years Phase 2 3 years Phase 3 5 years 9 months
2 4

a Calculate the total duration for Phase 1 and Phase 2.
1
1
2 years + 3 years = years
2 4
1
1
1
2 years + 3 years = 2 1 × 2 years + 3 years
2 4 2 × 2 4
1
2
= 2 years + 3 years
4 4
3
= 5 years
4
3
1
1
2 years + 3 years = 5 years
2 4 4
3
The total duration for Phase 1 and Phase 2 is 5 years.
4
b Determine the total duration, in years and months,
for Phase 1 and Phase 3.
Is the
1
2 years + 5 years 9 months = years months calculation
2 correct?
7 years 14 months Discuss.
year month
2 5 = 7 years + 12 months + 2 months
+ 5 9 = 7 years + 1 year + 2 months
7 14 = 8 years 2 months




1 1 145
• Stress that is equal to 0.5 and relate that year is equal to
4.3.1 (iii) 2 2
6 months.

2 a Based on the brochure, total up the
COUR
SE
COMPUTER
duration of the basic and advanced COMPUTER COURSE
levels for a computer course. Basic level 1.25 years
1.25 years + 1.5 years = years Advanced level 1.5 years

1.25 years Professional level 5 year
+1.50 years 6
2.75 years
SPECIAL
1.25 years + 1.5 years = 2.75 years DISCOUNTS
FOR THE
FIRST 50
The total duration of the basic and REGISTRATIONS
advanced levels for a computer course
is 2.75 years.


b What is the duration of the basic and professional levels for the
computer course? State your answer in years and months.
5
1.25 years + year = years month
6

1.25 years = 1 year + 0.25 year

= 1 year + (0.25 × 12) months year month
= 1 year 3 months 1 3
+ 10
5 5 2 1 13
6 year = ( × 12) months + 1 − 12
6
1 2 1
= 10 months

5
1.25 years + year = 2 years 1 month
6
The duration of the basic and professional levels for the
computer course is 2 years 1 month.









3
4 year + year = 1 year
State the value in decimals.


146 4.3.1 (iii)
4.3.2 (iii) • Carry out a quiz where pupils are able to answer spontaneously.

Decades and years

1 The following diagram shows the reign of the Malacca Sultanate.
Sultan Muzaffar Sultan Sultan Alauddin Sultan
Shah Mansur Shah Riayat Shah Mahmud Shah


1 9 1
1 decades 1 decades 1 decades 23 years
5 10 10
Source: https://rb.gy/02uepq
a Calculate the total reign of Sultan Muzaffar Shah and
Sultan Mansur Shah.
1 9
1 decades + 1 decades = decades
5 10
1 9 1 × 2 9
1 decades + 1 decades = 1 decades + 1 decades
5 10 5 × 2 10
2 9
= 1 decades + 1 decades
10 10
11
= 2 decades
10
11
= 2 decades + decades
10
1
= 2 decades + 1 decades
10
1
= 3 decades
10

1 9 1
1 decades + 1 decades = 3 decades
5 10 10
The total reign of Sultan Muzaffar Shah and Sultan Mansur Shah
1
is 3 decades.
10

b Calculate the reign of the last two sultans.
1
1 decades + 23 years = years
10
1 11 1 1 years
1 decades = ( × 10) years
10 10 + 23 years
= 11 years 34 years
1
1 decades + 23 years = 34 years
10
The reign of the last two sultans is 34 years.



• Discuss the history of the Malacca Sultanate in ancient times. 147
4.3.1 (iv)
Instil the moral value of love for the country.

2 Based on the table, calculate Service duration
Encik Mirza’s duration of service, School Duration
in decades, before he retired. SK Sri Intan 2.4 decades
2.4 decades + 0.8 decade = decades SK Melati 0.8 decade
1
2.4 decades
+ 0.8 decade
3.2 decades

2.4 decades + 0.8 decade = 3.2 decades

Encik Mirza’s duration of service before he
retired is 3.2 decades.





3 I was a temporary school How many years has Miss Alice served

1 as a teacher?
teacher for decade. For the
5 1
next 1.3 decades, decade + 1.3 decades = years
I am a permanent teacher. 5
Method 1
Cara 1

1
5 decade = 0.2 decade


0.2 decade 1.5 decades
+ 1.3 decades = (1.5 × 10) years
1.5 decades = 15 years
Method 2
Cara 2

1 1 2
5 decade = ( × 10) years 1.3 decades = (1.3 × 10) years
5
1 = 13 years
= 2 years


2 years + 13 years = 15 years
1
5 decade + 1.3 decades = 15 years
Miss Alice has served as a teacher for 15 years.

Give the answer of 3.9 decades add 51 years, in decades.


148 4.3.1 (iv)
4.3.2 (iv) • Discuss a few calculation strategies to obtain the answer.

Centuries and decades

1
1
1 Cave A is 6 centuries old. 6 centuries + 3 centuries = centuries
1
5 5 2
1
Cave B is 3 centuries older
1
1
2 6 centuries + 3 centuries
than Cave A. 5 2
1 × 2 1 × 5
= 6 centuries + 3 centuries
5 × 2 2 × 5
2 5
The age of = 6 centuries + 3 centuries
10
10
Cave B is ... 7
= 9 centuries
10
1 1 7
6 centuries + 3 centuries = 9 centuries
5 2 10


3
2 century + 29 decades = decades
10
1
3 3 3 decades
10 century = ( 10 × 10) decades + 29 decades
= 3 decades
32 decades

3
10 century + 29 decades = 32 decades



4
3 2 centuries + 8 centuries 7 decades = centuries decades
5

century decade
4 4
2 centuries = 2 centuries + century 2 8
5 5
4 2 + 8 7
= 2 centuries + ( × 10) decades 1 0 1 5
5
1 + 1 − 1 0
= 2 centuries 8 decades 1 1 5
4
2 centuries + 8 centuries 7 decades = 11 centuries 5 decades
5



State 11 centuries 5 decades in decades.



149
4.3.1 (v)

The number of rings on the
4 Estimate the age, in centuries,
cross-section of tree A indicates
of tree B. that tree A is about 0.2 century old.
0.2 century + 0.3 century = century
Cross-section
0.2 century of tree A
+ 0.3 century
0.5 century
Cross-section
0.2 century + 0.3 century = 0.5 century of tree B

The estimated age of tree B is about Tree B is 0.3 century older
0.5 century. than tree A.



5 12.6 centuries + 58 decades = centuries decades
century decade
12.6 centuries = 12 centuries + 0.6 century 1
1 2 6
= 12 centuries + (0.6 × 10) decades
+ 5 8
= 12 centuries 6 decades
1 2 6 4
+ 6 − 6 0
1 8 4


12.6 centuries + 58 decades = 18 centuries 4 decades

9
6 Add 4 centuries and 3.2 centuries. Give the answer in centuries
10
and decades.
9
4 centuries + 3.2 centuries = centuries decade
10
9
9 9 4 centuries = 4 centuries 9 decades.
century = ( × 10) decades 10
10 10 3.2 centuries = 3 centuries 2 decades.
= 9 decades
century decade
4 9
0.2 century = (0.2 × 10) decades
+ 3 2
= 2 decades 7 1 1

+ 1 − 1 0
8 1

9
4 centuries + 3.2 centuries = 8 centuries 1 decade
10


150 4.3.1 (v) • Provide more exercises on constructing number sentences orally
4.3.2 (v) using flash cards.
• Surf https://rb.gy/rfusfb

Centuries and years
Estimate the age of the Alor Setar
1 Estimated age in 2021
Clock Tower.

4 3
The Kuala Kangsar 5 century + 10 century = centuries
Clock Tower
4 3
4 century + century
about century old 5 10
5 4 × 2
= century + 3 century
Source: http://rb.gy/uhx8hq 5 × 2 10
8 3
= century + century
The Alor Setar 10 10
Clock Tower 11
= centuries
3 10
about century older
10 1
than the Kuala Kangsar = 1 centuries
10
Clock Tower 4 3 1
5 century + 10 century = 1 centuries
10
1
The estimated age of the Alor Setar Clock Tower is about 1 centuries.
10


7
2 2 centuries + 60 years = years
10
7 7 1
2 centuries = (2 × 100) years + ( × 100) years 270 years
10 10
= 200 years + 70 years + 60 years
330 years
= 270 years

7
2 centuries + 60 years = 330 years
10

1
3 8 centuries + 1 century 35 years = centuries years
2
1 1
8 centuries = 8 centuries + century
2 2 century year
1 50 8 50
= 8 centuries + ( × 100) years
2 + 1 35
1 9 85
= 8 centuries 50 years


1
8 centuries + 1 century 35 years = 9 centuries 85 years
2

• Carry out mental arithmetic activities to convert centuries to years 151
4.3.1 (vi)
and years to centuries.

4 7.9 centuries + 6 centuries 42 years = centuries years


7.9 centuries = 7 centuries + 0.9 century century year
= 7 centuries + (0.9 × 100) years 7 9 0
+ 6 4 2
= 7 centuries 90 years
1 3 1 3 2
+ 1 − 1 0 0
1 4 3 2

7.9 centuries + 6 centuries 42 years = 14 centuries 32 years


5 0.82 century + 451 years = centuries years

Convert units of time to years,
as well as centuries and years.



century year
0.82 century = (0.82 × 100) years
8 2
= 82 years
+ 4 5 1
4 1 3 3
451 years = 400 years + 51 years + 1 − 1 0 0

= 4 centuries 51 years 5 3 3


0.82 century + 451 years = 5 centuries 33 years


3
6 5 centuries + 1.3 centuries = years
4
First, convert units of time in
fraction to units of time in decimal.
1
3 23 5.75 centuries
5 centuries = centuries
4 4 + 1.30 centuries
= 5.75 centuries 7.05 centuries


7.05 centuries = (7.05 × 100) years
= 705 years
3
5 centuries + 1.3 centuries = 705 years
4
State 705 years in centuries and years.


152 4.3.1 (vi)
4.3.2 (vi) • Encourage pupils to calculate using various methods of calculation.

1 Add.
1 1
a hour + hour = hour b 0.25 hour + 3 hours = hours
2 10
1 1
c 1 days + day = days d 6.5 days + 4.75 days = days
6 8
e 9.25 years + 10.5 years = years
7 2
f decade + decade = decades
10 5
3 1
g 8 centuries + 1 centuries = centuries
5 2
h 8.47 centuries + 52.9 centuries = centuries
2 Calculate.

3
a hour + 40 minutes = minutes
5
5
b 4 days 20 hours + day = days hours
8
c 7.5 days + 19 hours = hours
1
d 1 years + 4 years 10 months = years
6
1
e 17 years + decade = decade years
5
f 4 decades 1 year + 2.3 decades = years

2
g 2 centuries + 1 century 6 decades = decades
5
9
h 66 years +1 centuries = centuries years
10
3 Calculate.

5
a hour + 0.45 hour = minutes
6
1
b 7.625 days + 1 days = days hours
2
3
c 1 years + 0.75 year = years months
4
4
4 Calculate the sum of 2 centuries and 3.8 centuries. State the answer in
5
centuries and decades.
5 Is the statement on the
1
right correct? Prove it. 2.79 centuries + 8 centuries = 11 centuries 4 years
4


4.3.1 153
4.3.2

SUBTRACTION OF TIME
Health Poster Project

Hours and minutes Name Time Taken to Complete
3
Raden hour
1 4
5
Siti 1 hours
6
Divani 12 minutes earlier than Siti



Divani Siti
Raden
a Based on the table above, calculate the HEALTHY MEAL
difference in time taken to complete the
project by Raden and Siti.
5 3
1 hours − hour = hours
6 4
5 3 5 × 2 3 × 3
1 hours − hour = 1 hours − hour
6 4 6 × 2 4 × 3
10 9
= 1 hours − hour
12 12
1
= 1 hours
12
5 3 1
1 hours − hour = 1 hours
6 4 12
1
The difference in time taken by Raden and Siti is 1 hours.
12
b How long did Divani take, in hours and minutes, to complete her project?

5
1 hours – 12 minutes = hour minutes
6
5 5 hour minute
1 hours = 1 hour + hour
6 6 4 10
5 10 1 5 0
= 1 hour + ( × 60) minutes
6 – 1 2
1 1 3 8
= 1 hour 50 minutes
5
1 hours – 12 minutes = 1 hour 38 minutes
6
The time taken by Divani to complete her project is 1 hour 38 minutes.

• Emphasise that before subtracting fractions, get the common
154 denominators first.
4.3.1 (i)
• Guide pupils to understand keywords to determine the operations such
as earlier which means subtraction.

2 Calculate the difference in cooking time, in hours,
between steamed and boiled keropok lekor as
labelled in the pictures.
steamed
1.5 hours – 0.5 hour = hour 1.5 hours


1.5 hours
− 0.5 hour
1.0 hour
boiled
0.5 hour
1.5 hours – 0.5 hour = 1.0 hour


The difference in cooking time between the steamed and the boiled
keropok lekor is 1 hour.



3 3.45 hours − 1 hour 40 minutes = hour minutes

3.45 hours = 3 hours + 0.45 hour hour minute
2 87 60 minutes
= 3 hours + (0.45 × 60) minutes 3 2 7 + 27 minutes
− 1 4 0 87 minutes
= 3 hours 27 minutes 1 4 7


3.45 hours – 1 hour 40 minutes = 1 hour 47 minutes


1
4 1 hours − 0.35 hour = minutes
6
b How long did Divani take, in hours and minutes, to complete her project? 1 7 10 0.35 hour 6 10
1 hours = ( × 60) minutes 70 minutes
5 6 6 = (0.35 × 60) minutes
1 hours – 12 minutes = hour minutes 1 − 2 1 minutes
6
= 70 minutes = 21 minutes 49 minutes

1
1 hours − 0.35 hour = 49 minutes
6




Complete this.

5 3 1
6
6 hour – minutes = hour – hour
4
4.3.1 (i) • Encourage pupils to buy Malaysian products. 155
4.3.2 (i)
• Surf https://rb.gy/wjpftb

Days and hours


1
Pattern A
1
1 days
3 Pattern B
1
2 days
4
Based on the information above, how much more time is needed to
paint batik pattern B compared to pattern A?

1 1
2 days − 1 days = days
4 3
1 1 1 × 3 1 × 4
2 days − 1 days = 2 days − 1 days
4 3 4 × 3 3 × 4
3 4
= 2 days − 1 days
12 12
27 16
= days − days
12 12
11
= day
12

1 1 11
2 days − 1 days = day
4 3 12
11
The time needed to paint batik pattern B is day more than pattern A.
12


7
2 9 days 18 hours – day = days hours
8
day hour • Convert 9 days to
7 7 3 8 42 8 days 24 hours.
8
8 day = ( × 24) hours 9 1 8
1 − 2 1 • Add 24 hours and
= 21 hours 18 hours to make 42 hours.
8 2 1
7
9 days 18 hours – day = 8 days 21 hours
8
5
Find the difference of time between 10 days and
1 6
4 days. State the answer in hours.
2

156 • Drill pupils on subtraction of time using number cards.
4.3.2 (ii)
• Surf https://rb.gy/1wlvbb

3 Camp Duration
Scouts 2.25 days
Prefect Leadership 1.5 days

Based on the table above, how much

longer is the duration of the scouts camp
than the prefect leadership camp?
2.25 days − 1.5 days = day

1 12
2.2 5 days
− 1 .5 0 days
0. 7 5 day

2.25 days − 1.5 days = 0.75 day

The duration of the scouts camp
is 0.75 day more than the prefect
leadership camp.



4 Subtract 3 days 5 hours from 9.75 days. Give the answer in
days and hours.

9.75 days − 3 days 5 hours = days hours

day hour
9.75 days = 9 days + 0.75 day
9 1 8
= 9 days + (0.75 × 24) hours − 3 5
= 9 days 18 hours 6 1 3


9.75 days − 3 days 5 hours = 6 days 13 hours


7
5 6.5 days − day = days hours
12 day hour
2
6.5 days = 6 days + 0.5 day 7 day = ( 7 × 24) hours 5 36
= 6 days + (0.5 × 24) hours 12 12 − 6 1 2
1
1 4
= 6 days 12 hours = 14 hours 5 2 2
7
6.5 days − day = 5 days 22 hours
12

4.3.1 (ii) 157
4.3.2 (ii) • Guide pupils to convert days to hours using various methods.

Years and months

1 a Find the age difference, in years, between the

hamster and the rabbit.
1 1
10 years − 2 years = years
5 2

1 1
10 years − 2 years
5 2 1
1 × 2 1 × 5 hamster’s age: 2 years
2
= 10 years − 2 years
5 × 2 2 × 5
2 5
= 10 years − 2 years
10 10
12 5
= 9 years − 2 years
10 10
7
= 7 years
10
1 1 7 1
10 years − 2 years = 7 years rabbit’s age: 10 years
5
5 2 10
The age difference between the hamster and the rabbit
7
is 7 years.
10
b What is the age difference between the hamster and the goldfish?


1
My goldfish is about 8 years 8 months − 2 years
8 years 8 months old. 2
= years months


year month
1 1 6
2 year = ( × 12) months 8 8
2
1 − 2 6
= 6 months 6 2

1
Therefore, 2 years = 2 years 6 months.
2
1
8 years 8 months − 2 years = 6 years 2 months
2
The age difference between the hamster and the goldfish is 6 years 2 months.



State the above answer in months.




158 • Encourage pupils to use subtraction in vertical form involving
4.3.1 (iii)
unit conversion.

2 Subtract 16.875 years and 5.625 years.
16.875 years − 5.625 years = years

1 6.875 years
− 5.625 years
1 1.250 years

16.875 years − 5.625 years = 11.25 years


3 How many more months is 30.25 years from 29 months?

30.25 years − 29 months = months 5 13
36 3 months
30.25 years = (30.25 × 12) months − 2 9 months

= 363 months 33 4 months

30.25 years − 29 months = 334 months


3
4 14.5 years − 7 years = years months
4
Method 1 14.5 years = 14 years + 0.5 year

= 14 years + (0.5 × 12) months year month
= 14 years 6 months 13 18
14 6
3 3
7 years = 7 years + year − 7 9
4 4 6 9
3 3
= 7 years + ( × 12) months
4
1
= 7 years 9 months

Method 2 3 3
year = 0.75 year 14.5 years − 7 years
4 4
= 14.5 years − 7.75 years
= 6.75 years

6.75 years = 6 years + 0.75 year
= 6 years + (0.75 × 12) months
= 6 years 9 months

3
14.5 years − 7 years = 6 years 9 months
4

4.3.1 (iii) • Explain to pupils the way to convert the unit of time from years 159
4.3.2 (iii)
to months.

I am on my way home to Taman
Decades and years Universiti. I have been staying
4
there for nearly 1 decades.
1 5 Encik Shamel
Encik Siva


I have been
staying there for
1
about 3 decades.
2
Let me help you.
How much longer has Encik Shamel been staying in Taman Universiti
compared to Encik Siva?
1 4
3 decades − 1 decades = decades
2 5
1 4 1 × 5 4 × 2
3 decades − 1 decades = 3 decades − 1 decades
2 5 2 × 5 5 × 2
5 8
= 3 decades − 1 decades
10 10
15 8
= 2 decades − 1 decades
10 10
7
= 1 decades
10

1 4 7
3 decades − 1 decades = 1 decades
2 5 10
7
Encik Shamel has been staying in Taman Universiti 1 decades
10
longer than Encik Siva.


3
2 9 decades – 6 decades = decades years
10

decade year
3 3 8 10
decade = ( × 10) years Convert 9 decades to
10 10 9 0 8 decades 10 years.
= 3 years − 6 3
2 7


3
9 decades – 6 decades = 2 decades 7 years
10



160 • Instil moral values like the spirit of neighbourliness
4.3.1 (iv)
and respect others.

warranty period
0.2 decade
3 Based on the information given, calculate the difference
in warranty period between these two laptops.
0.3 decade − 0.2 decade = decade

0.3 decade warranty period
−0.2 decade 0.3 decade
0.1 decade

0.3 decade − 0.2 decade = 0.1 decade
The difference in warranty period between these two laptops is 0.1 decade.



4 Calculate the balance, in years, when 47 years is subtracted from
8.1 decades.
8.1 decades – 47 years = years 7 11
8 1 years
8.1 decades = (8.1 × 10) years − 4 7 years

= 81 years 3 4 years
8.1 decades – 47 years = 34 years



1
5 9.4 decades – 2 decades = decades years
2
9.4 decades = (9.4 × 10) years
8 14 69 years
= 94 years 9 4 years = 60 years + 9 years

1 5 5 − 2 5 years
2 decades = ( × 10) years 6 9 years = (60 ÷ 10) decades + 9 years
2 2
1 = 6 decades 9 years
= 25 years
1
9.4 decades – 2 decades = 6 decades 9 years
2







1 2 3 4 7

Use the above number cards to complete the
number sentence below.
6. decades − . decades = years


4.3.1 (iv) • Ask pupils to find the difference of expiry dates of food as a wise 161
4.3.2 (iv)
consumer.

Centuries and decades

1
Calculate the age difference between

Age of the two banknotes.
banknotes
in 2021 1 century − 1 century = century
2 10
1 1 1 × 5 1
2 century – 10 century = 2 × 5 century – 10 century
SPECIMEN 5 1


=
10 century – 10 century
4 ÷ 2
= 10 ÷ 2 century
SPECIMEN 2



=
5 century
1 1 2
2 century − 10 century = 5 century


2
The age difference between the two banknotes is century.
5


3
2 7 centuries – 4 centuries 8 decades = centuries decades
5
Convert 1 century to 10 decades.
3 3 2 Then, add 10 decades and 6 decades
5
5 century = ( × 10) decades to make 16 decades.
1
= 6 decades century decade
Therefore, 6 16

Therefore, 3 7 6
7 centuries = 7 centuries 6 decades.
5 − 4 8
2 8

3
7 centuries – 4 centuries 8 decades = 2 centuries 8 decades
5


Complete this.

4
1 centuries – century = 12 decades
5

162 • Carry out subtraction activities involving centuries and decades
4.3.1 (v) using flash cards.
• Discuss the history and changes of banknotes in Malaysia.

3 Calculate the age difference in the production
of Proton Saga and Perodua Myvi models. 1985 to 2008

0.23 century − 0.06 century = century (0.23 century)
1 13
0.2 3 century
− 0.0 6 century
0. 1 7 century


0.23 century − 0.06 century = 0.17 century
The age difference in the production of 2005 to 2011
Proton Saga and Perodua Myvi models (0.06 century)
is 0.17 century.



4 14.2 centuries – 3 centuries 9 decades = centuries decades

14.2 centuries = 14 centuries + 0.2 century century decade
13 12
= 14 centuries + (0.2 × 10) decades
14 2
= 14 centuries 2 decades − 3 9

10 3
14.2 centuries – 3 centuries 9 decades = 10 centuries 3 decades



1
5 6 centuries – 5.7 centuries = decades
10

1 1 5 11
6 centuries = 6 centuries + century
10 10 6. 1 centuries
= 6 centuries + 0.1 century − 5. 7 centuries
= 6.1 centuries 0.4 century


0.4 century = (0.4 × 10) decades
= 4 decades

1
6 centuries – 5.7 centuries = 4 decades
10

How many centuries and decades are there if
1
2 centuries is subtracted from 4.1 centuries?
5


4.3.1 (v) 163
4.3.2 (v) • Instil moral value of patriotism by buying Malaysian products.

Find the age difference between
Centuries and years
these two historical places.

1 Sultan Abdul Samad Building Fort Cornwallis, Pulau Pinang


Age of
Historical
Places in 2021




1 2 centuries 35 years
about 1 centuries
4
1
a 2 centuries 35 years − 1 centuries = century years
4

1 1 25 century year
4 century = ( × 100) years
4
1 2 3 5
= 25 years − 1 2 5
1 1 0
1
Therefore, 1 centuries = 1 century 25 years.
4
1
2 centuries 35 years − 1 centuries = 1 century 10 years
4
The age difference between these two historical places
is 1 century 10 years.

b How much older is the Kuala Lumpur
Railway Station, in years, compared
to the Sultan Abdul Samad Building?

1
1.3 centuries − 1 centuries = years
4 In 2021, the Kuala
Lumpur Railway
1.3 centuries = (1.3 × 100) years Station is about
= 130 years
1.3 centuries old.
2 10
1 5 25 13 0 years
1 centuries = ( × 100) years
4 4 − 12 5 years
1 5 years
= 125 years
1
1.3 centuries − 1 centuries = 5 years
4
The Kuala Lumpur Railway Station is 5 years older than
the Sultan Abdul Samad Building.


164 4.3.1 (vi) • Discuss our national heritage and other historical places in
4.3.2 (vi) Malaysia. Pupils may conduct research on the age of historical
places in Malaysia in centuries and years as group projects.

1 Find the answers.
3 1
a hour – hour = hour b 0.5 hour – 0.45 hour = hour
4 2
5 1
c day – day = day d 0.25 day – 0.125 day = day
8 3
e 7.75 years – 4.5 years = years
2 1
f 1 decades – decade = decades
5 10
g 8.11 centuries – 6.7 centuries = centuries

2 Find the difference of duration.
5
a hour – 13 minutes = minutes
6
b 1 hour 40 minutes – 0.95 hour = minutes
3
c 2 days – 1 day 2 hours = day hours
8
d 1.375 days – 4 hours = day hours
7
e 9 decades – 2 decades 3 years = years
10
f 8.1 decades – 27 years = decades years
1
g 2 centuries 4 decades – 1 centuries = decades
5
3 Solve these.
7
a Deduct 1 century 34 years from 5 centuries.
10
Give the answer in centuries and years.
b Find the difference between 2.1 centuries and 6 centuries 9 years.
State the answer in years.

4 Find the answers.
4 1
a hour – 0.15 hour = minutes b 1 days – 0.875 day = hours
5 5 8 3
c 4.5 years – 1 years d 9.1 decades – 6 decades
12 10

= years month = decades years
5 Complete the bridge map.

decades century decades years
as as
1 1 1
0.9 century – century 3 centuries – 1.7 centuries 1 centuries – 0.9 century
5 2 4


4.3.1 165
4.3.2

SOLVE THE PROBLEMS


1 The diagram shows a packet

of curry paste and a packet of
potato crisps bought by Vimala.
Calculate the shelf life, in days, of
the curry paste.
Date of manufacture:
9.12.2019
Expiry Date:
8.2.2021


Understand the Date of manufacture: 9.12.2019
problem Expiry date: 8.2.2021
Find out the shelf life, in days, of the curry paste.




Plan the date of
strategy manufacture shelf life expiry date


Solve
1 1 1 1
9.12.2019 to 31.12.2019 31 days – 9 days + 1 day = 2 3 days
23 days
Number of days in 2020 = 366 days
3
6 6 days
3 1 days
Number of days in January 2021 = 3 1 days
1.2.2021 to 8.2.2021 8 days – 1 day + 1 day = + 8 days
8 days
2 8 days
Total days = 4 428 days

Check Use a calendar to check your answer.

The shelf life of the curry paste is 428 days.



Date of
This information is found on
the packet of potato crisps above. manufacture:
Calculate the shelf life, in days, 17.02.2020
of the crisps. Expiry date:
17.08.2020



166 • Emphasise that the expiry date on food products indicates
4.4.1
the shelf life as this will help consumers make the right choice.

breakfast

2 The pictures show the duration of 40 minutes
time Zaidi spent on two activities
in the morning. Calculate the
total duration of time, in hours jogging
and minutes, Zaidi spent on 3 hour
both activities. 4

3
Understand the hour spent on jogging. 40 minutes spent on
4
problem breakfast. Find the total duration of time spent on
both activities.
Plan the 3
strategy hour 40 minutes
4



3
Solve hour + 40 minutes = hour minutes
4

3 Total up. Convert 85 minutes to
Convert hour to minutes.
4 hours and minutes.
3 3 15 45 minutes 85minutes
4
4 hour = ( × 60) minutes + 40 minutes − 60minutes 1 hour
1 85 minutes
= 45 minutes 25minutes

Check 85 minutes 45 ÷ 15
− 40 minutes 45 minutes = ( 60 ÷ 15 ) hour
45 minutes 3
= hour
4
3
4 hour + 40 minutes = 1 hour 25 minutes

The total duration of time Zaidi spent on both activities is 1 hour 25 minutes.



Animated Film minutes
Date of Animated Film minutes Zaidi would like to watch
manufacture: an animated film for 1.5 hours to
17.02.2020 Animated Film minutes 2 hours. Which animated film would
he choose? Discuss.
Expiry date:
17.08.2020




• Guide pupils to solve problems using the Polya method based on 167
4.4.1
story cards.

3 The table below shows the age of herbal tea leaves in three packets
given by Encik Tan to his neighbour.

Colour of the packet Age of herbal tea leaves
Green 10.75 years
Red 9 months more than the green packet

Brown 5
6 year less than the green packet

Calculate the age, in years and months, of the herbal tea leaves in the:
a red packet. b brown packet.


Solution Draw a
9 months diagram.
The green packet 10.75 years
a
The red packet

10.75 years + 9 months = years months

3 year month
0.75 year = year
4 1 0 9
3 3 3 + 9
4 year = ( × 12) months 1 0 1 8
4
1 + 1 − 1 2
= 9 months
1 1 6
Therefore, 10.75 years = 10 years 9 months

10.75 years + 9 months = 11 years 6 months

The age of the herbal tea leaves in the red packet is 11 years 6 months.

5
b 10.75 years − year = years months
6
year month Explain how
2
5
5 year = ( × 12) months 9 2 1 you check
6 6 10 9 the answer.
1
= 10 months − 10
9 1 1

5
10.75 years − year = 9 years 11 months
6
The age of the herbal tea leaves in the brown packet is 9 years 11 months.



168 • Provide various problem-solving questions involving daily life situations.
4.4.1 Demonstrate various strategies for the solution.
• Surf https://rb.gy/2rfhuf

4 In 2020, the Intellect Building and Harmony Building are 0.4 decade and
2 decades old, respectively. When would the age of the Harmony Building
be equal to 3 times the age of the Intellect Building?



Solution In 2020, the Intellect Building is 0.4 decade old.
Harmony Building is 2 decades old.
I use the trial and
error method.
Age
The The Check
Intellect Harmony 0.5 decade
Building Building × 3

First Try 2021 0.5 decade 2.1 decades 1.5 decades

0.6 decade
× 3

Second Try 2022 0.6 decade 2.2 decades 1.8 decades
0.7 decade
× 3
Third Try 2023 0.7 decade 2.3 decades 2.1 decades
0.8 decade
× 3
Fourth Try 2024 0.8 decade 2.4 decades 2.4 decades

The fourth try was accurate.



What are the other methods
to check the answer?





The age of the Harmony Building will be 3 times the age of the
Intellect Building in 2024.




The age difference between Aneka Building and
Harmony Building is 0.1 century. What is the age, in decades,
of the Aneka Building in 2020?





• Emphasise to pupils to check the answers using different calculation 169
4.4.1 strategies such as multiplication for repeated addition and division
for repeated subtraction.

5
1.15 centuries old


The total age of the two antique vases shown in the picture above is
318 years. What is the age, in centuries and years, of the blue and
white antique vase?


Solution


I use the working backward method.


+ 1.15 centuries = 318 years


Convert 1.15 centuries to years.
1.15 centuries = (1.15 × 100) years
= 115 years


5 years 10 years 100 years 115 years




208 218 years 318 years
years
203 years
203 years = 200 years + 3 years
= 2 centuries 3 years


I check using this method.



3 18 years 203 years = 200 years + 3 years
− 1 15 years = (200 ÷ 100) centuries + 3 years
203 years = 2 centuries 3 years





2 centuries 3 years + 1.15 centuries = 318 years


The blue and white antique vase is 2 centuries 3 years old.



170 • Discuss various problem-solving strategies such as making tables
4.4.1
and simulations.

Solve the following problems. Soak the red beans Cooking

a The time taken by Puan Aninah to prepare
the ingredients and to cook red bean
porridge is shown in the picture. What is the 2
total duration, in hours and minutes, of the 1 hours
3
time taken to get the meal ready? 50 minutes

:
:
b A filming began at 4 30 p.m. on Tuesday until 5 30 p.m. on Thursday.
Calculate the duration, in days and hours, of the filming.
c A school held an anti-drug campaign

as shown in the picture. Calculate the Anti-Drug
duration, in days, of the campaign. Campaign
3 February 2020
to 6 March 2020

d Historical Building Age in 2020

Masjid Jamek Kuala Lumpur 1.13 centuries
Royal Museum 92 years
Teluk Intan Leaning Tower 1.35 centuries

Based on the table of the age of historical buildings above,:

i calculate the age difference, in centuries, between
Masjid Jamek Kuala Lumpur and the Teluk Intan
Leaning Tower in Perak.
ii how much older, in years, is the oldest building compared

to the newest one?
e The following is a conversation between two friends.
Navin 1
I studied at SK Sentosa for 4 years and was
2
at SK Sepayan for 15 months.

Oh, I studied 0.75 year longer than
you at SK Sentosa! Agus
Based on the above conversation,:

i total up the duration, in years and months, Agus studied in both schools.
ii determine the duration, in months, Navin studied at SK Sentosa.




171
4.4.1

1 Calculate the duration of time for each of the activities.


a Start climbing on 20.5.2021,
:
at 10 00 a.m.
Finish climbing on 23.5.2021
:
at 1 00 p.m.
Give the answer in days and hours.



b c Food Preparation
Disaster Relief Fund Certificate Course
17 October 2021 to
13 January 2021 to 5 March 2021 9 December 2021
Give your answer in days. Give your answer in days.

2 Convert the units of time.
1
a hour = minutes b 1.2 hours = hour minutes
5
5
c day = hours d 7.25 days = hours
6
11
e 2 years = months f 1.5 years = year months
12
9
g 6 decades = decades years h 13.7 decades = years
10
1
i 3 centuries = decades j 24.1 centuries
2
= centuries decade
3
k 5 centuries = centuries years l 8.23 centuries = years
4
3 Calculate.
1 2
a hour + hour = hour b 1.5 days – 0.625 day = day
4 3
5
c year + 33 months d 4 decades 2 years – 1.8 decades
6
= years months = years
1
e 1 decade 9 years + 8 decades f 7.7 centuries – 38 decades
2
= decades years = decades
7
g 3 centuries 12 years + 4 centuries h 320 years – 1.6 centuries
10
= years = century years


4.1.1, 4.2.1,
172 4.2.2, 4.3.1,
4.3.2

4 Complete the bridge map below.

minutes hours years
as as
1 2 1
2
10 hour + 0.6 hour 3 day + 0.625 day 0.7 decade + decade

5 Find the errors in these calculations and correct them.




a century year c century decade
b decade year
4 13 6 7
5 3 15 10 +1 8
+1 6 1 6 8 8 1 5
3 7 − 4 9 +1 − 1 0
1 1 1 9 5




6 Solve these.


a i 4.2 centuries + 18 decades = decades

ii 7.05 centuries − 106 years = centuries years

11
b Add year and 2.5 years. Give the answer in months.
12
c Calculate the time difference, in centuries and years, between
7
6 centuries and 9.8 centuries.
10
7 The following are three cards; P, Q and R.

1
P 5 years Q 1.5 years R 32 months
4

a Convert the time on card R to years and months.

b Subtract the time on card R from the time on card P. Give the
answer in months.

c How much more time, in years and months, of card P compared to
card Q?




4.2.1, 4.2.2, 173
4.3.1, 4.3.2

8 Solve the problems below.

a The diagram below shows the process and time taken by Aley to
bake a cake.











preparation of
the ingredients mixing baking decorating
1
1 10 minutes 0.75 hour 3 hour
2 hour

i Calculate the total time taken, in hours, for preparing the ingredients
and decorating the cake.

ii What is the time difference, in minutes, between mixing and baking
the cake?

iii Calculate the duration, in hours and minutes, for baking and
decorating the cake.
1
b The duration of a television show is 2 hours including
4
advertisements of 20 minutes. Calculate the duration, in hours and
minutes, for the television show only.
c
Historical Building Age in 2020

Atkinson Clock Tower 1.15 centuries
Kundasang War 58 years
Memorial
3
Masjid Jamek Sandakan 1 centuries
10

The table above shows the age of historical buildings in
Sabah in 2020.
i Calculate the difference of age, in years, between the
Atkinson Clock Tower and the Kundasang War Memorial.

ii Masjid Jamek Sandakan is 15 years older Is this statement true?
than the Atkinson Clock Tower. Prove it.



174
4.4.1

d A study tour to Malacca began on Thursday, 9:00 a.m. until
Saturday, 3:00 p.m. in the same week. Calculate the duration of

the tour, in days and hours.


The calendar shows the effective dates of
e START END
Phase 1 of the Movement Control Order
2020 2020 (MCO) in Malaysia to break the chain of
2020
18 31 COVID-19 transmission. How long, in
March March days, was the Phase 1 of the MCO?



f In 2021, Nelly and Sudir are 8.5 years old and 19 years old respectively.
i How much older is Sudir than Nelly? Give the answer in years

and months.
ii In which year the age of Sudir be twice the age of Nelly?

g The age difference between antique cars P and Q is 2 decades 7 years.
Antique car P is 5.8 decades old. How old, in decades and years, is
antique car Q?

h 0.7
century




Q decades R years
1 1
2 P 5
century century century




Marsha is assigned to complete the above diagram. In the diagram,
the values P, Q and R are not given. The value in the box is the sum of
the two units of time in the circles connected to the box.

i Calculate the values of P, Q and R.
ii Is the sum of P and Q equal to 1 century 9 decades?
Show your calculation.





175
4.4.1

GROUP ACTIVITY


A4 papers, manila cards, glue, coloured pencils, pens,
Tools/ Materials
scissors, recycled materials such as reading materials,
Internet
Task 2 years 3 months

1 On A4 paper, write down two units of 3
4 year + 1.5 years
time involving whole numbers, fractions,
or decimals that give the same number 3.5 years – 15 months

of sum and difference.

2 Cut and paste the A4 paper on a picture such
as pictures of animals that were drawn, pictures
from recycled materials, or from the Internet.
2 years 3 months
3 Present the completed work. Accept suggestions 3 year + 1.5 years



4
for improvement from other groups.
3.5 years – 15 months


TIME


Mohan plucked some mangoes near the mansion,
But would not eat them as they were sour;
Let’s try to answer this question,
How many minutes are there in one and three
quarters of an hour?


When I am with my peers,
I am always full of cheers;
Two point two centuries and six years,
What is the difference, in years?

When Zaiton eats cakes and buns,

She is happy as can be;
Total up half a year and two months,
How many months will it be?


176 4.2.1 (i), 4.3.1,
4.3.2, 4.4.1

5 5 LENGTH, MASS, AND
ASS, AND
LENGTH, M
VOLUME OF LIQUID
VOLUME OF LIQ UID



CONVERT UNITS OF LENGTH


Millimetres and centimetres This weighing tool was invented

1
1 using 9.2 cm thread and a 36 cm
2
clothes hanger.

a Convert 9.2 cm to mm.

9.2 cm = mm
9.2 cm = (9.2 × 10) mm

= 92 mm
9.2 cm = 92 mm
1
b Convert 36 cm to mm.
2
1 1 cm = 10 mm
36 cm = mm
2 × 10
1 73 5
36 cm = ( × 10) mm 1
2 2 cm mm
1 7 3
= 365 mm × 5 ÷ 10
1 3 6 5
36 cm = 365 mm
2


2 47 mm = cm 3 20 cm 6 mm = cm

47 mm = (47 ÷ 10) cm 6 ÷ 2
in decimal 20 cm 6 mm = 20 cm + ( 10 ÷ 2 ) cm
= 4.7 cm
3
5
in 47 mm = 47 cm = 20 cm + cm
fraction 10 3
7 = 20 cm
5
= 4 cm
10 3
20 cm 6 mm = 20 cm
7 5
47 mm = 4.7 cm or 4 cm
10
• Carry out simulation activities for measuring length, thickness of objects,
5.1.1 (i) and depths of water in cm and mm. Then, ask pupils to convert the unit 177
5.1.2 (i) to decimals or fractions.
• Recall methods of quick multiplication and division involving any
numbers by 10.

The width of this kite is 1.37 m.
Centimetres and metres

1 Convert 1.37 m to cm.


1.37 m = cm

1.37 m = (1.37 × 100) cm

= 137 cm

1.37 m = 137 cm




1
2 1 m = cm
4
Method 2
Method 1 5
1
1 1 1 m = ( × 100) cm
1 m = 1 m + m 4 4
4 4
1 25 = (5 × ) cm
= (1 × 100) cm + ( × 100) cm
4
1 = cm
= 100 cm + 25 cm

= 125 cm Does method 2 give
1
1 m = 125 cm the same answer?
4


3 39 cm = m 4 5 m 80 cm = m

39 cm = (39 ÷ 100) m 5 m 80 cm = 5 m + (80 ÷ 100) m
= 0.39 m
= 5 m + 0.8 m
39 cm = 0.39 m
= 5.8 m

5 m 80 cm = 5.8 m
1 m = 100 cm
× 100
4
5.8 m is equal to 5 m. Prove it.
m cm 5

÷ 100





• Encourage pupils to appreciate traditional games such as wau, gasing,
178 5.1.1 (ii) and congkak.
5.1.2 (ii) • Use various methods to state the relationships between units involving
fractions and decimals.

Penang Bridge
Metres and kilometres International Marathon
Overall distance 42.195 km
1 Convert 42.195 km to m.
Date: 24 November 2019
42.195 km = m
:
Starting time: 1 30 a.m.
42.195 km = (42.195 × 1 000) m (Men and Women Open, and Veteran)
Qualifying time: 7 hours
= 42 195 m Starting point: Queensbay Mall Parking Lot

42.195 km = 42 195 m



3
2 7 km = m 3 10 300 m = km
8
3 3 10 300 m = (10 300 ÷ 1 000) km
7 km = 7 km + km
8 8
= 10.3 km
= (7 × 1 000) m +
3
3 125 = 10 km
( × 1 000) m 10
8
1 10 300 m = 10.3 km or
= 7 000 m + 375 m
3 3
7 km = 7 375 m 10 km
8 10



4 68 km 4 m = km
4 1 km = 1 000 m
68 km 4 m = 68 km + ( ) km
1 000 × 1 000
= 68 km + 0.004 km
km m
= 68.004 km
÷ 1 000
68 km 4 m = 68.004 km








1 3
2 km 4 km

0 375 m P Q R 1 000 m

State the value of Q in fractions.


179
5.1.1 (iii) • Encourage pupils to use various strategies during multiplication or division
5.1.2 (iii) such as shifting the decimal point or cancellation.

1 Convert the measurements below to the required units.
1
a 3.1 cm = mm b 7 cm = mm c 56 mm = cm
2
3
d 8 cm 4 mm = cm e 0.19 m = cm f 10 m = cm
4
g 37 cm = m h 5 km 2 m = km i 2 043 m = km

2 State the answers in decimals.
a 908 mm = cm b 24 m 6 cm = m c 79 cm = m

d 45 cm 3 mm = cm e 6 005 m = km f 18 km 14 m = km

3 State the answers in fractions.
a 25 mm = cm b 4 cm 1 mm = cm c 920 cm = m

d 6 m 75 cm = m e 1 300 m = km f 50 km 600 m = km








GET TO KNOW ME
Activity card

Height Shoe School Distance
Tools/Materials activity cards, pens, Measurement sole bag from home
measuring tapes, length width to school
rulers, manila mm/cm/m/km
cards, photos fraction or
decimal unit
Participants in pairs
Results



Task Name: Kamini a/p Muthu

1 Carry out measurement activity and Height : 139 cm = 1.39 m
complete the activity card. Shoe sole length: 18.6 cm
2 Copy your friend’s details on the manila School bag width: 20.3 cm

card and paste the photo. 7
3 Compile everything in a scrapbook. Distance from home to school: 3 km
10




• Carry out a quiz to be answered spontaneously. For example, 3.5 cm
180 5.1.1 in fraction is 3 cm.
1
5.1.2 2
• Guide pupils to use Google Maps to find the distance from home to school in
the Smart Trail” activity.

ADDITION OF UNITS OF LENGTH
Uranus
18.4 cm
1 a Calculate the total length of the strings Earth
of the Earth and Uranus replicas. 26.3 cm

26.3 cm + 18.4 cm = cm
Mercury
1 1
26.3 cm 30 cm
2
+ 1 8.4 cm
44.7 cm
26.3 cm + 18.4 cm = 44.7 cm

The total length of the strings of the Earth and
Uranus replicas is 44.7 cm.

b Total up the length, in mm, of the strings of the Earth,
Uranus, and Mercury replicas.

1
26.3 cm + 18.4 cm + 30 cm = mm
2
1 1
1 1
30 cm = 30 cm + cm 2 6.3 cm
2 2 1 8.4 cm
= 30 cm + 0.5 cm + 3 0.5 cm 75.2 cm
= 30.5 cm 7 5.2 cm = (75.2 × 10) mm

1 = 752 mm
26.3 cm + 18.4 cm + 30 cm = 752 mm
2
The total length of the strings of the Earth, Uranus, and Mercury

replicas is 752 mm.

3
2 74 cm + 1.08 m + 2 m = m
4
2 .7 5m
74 cm = (74 ÷ 100) m 3 11
2 m = m 4 1 1.0 0m
= 0.74 m 4 4 − 8
= 2.75 m
3 0
3 −
74 cm + 1.08 m + 2 m 2 8
4
= 0.74 m + 1.08 m + 2.75 m 2 0
− 2 0
= 4.57 m 0
3
74 cm + 1.08 m + 2 m = 4.57 m
4
• Ask pupils to make sure that all the measurements have been
converted to the same unit and same form (fraction or decimal) 181
5.1.3 before performing addition.
• Carry out an activity of adding all the sides of various triangular
shapes involving measurements in fractions and decimals.

3
Hani’s 8 km flower shop
5
3 Calculate the distance, in m, home
from Hani’s home to the bird 3 km 20 m 4.701 km
park through the flower shop
and restaurant. 11 km 65 m bird
park
3 2.9 km
8 km + 3 km 20 m + 2.9 km = m restaurant
5

3 km 20 m = 3 km + 20 m
3 43 200
8 km = ( × 1 000) m = (3 × 1 000) m + 20 m
5 5
1 = 3 000 m + 20 m
= 8 600 m
= 3 020 m

1
2.9 km = (2.9 × 1 000) m State the shortest
8 600 m
= 2 900 m 3 020 m distance to the
bird park from
+ 2 900 m
Hani’s home.
1 4 520 m

3
8 km + 3 km 20 m + 2.9 km = 14 520 m
5
The distance from Hani’s home to the bird park
through the flower shop and restaurant is 14 520 m.







1 Add the measurements below according to the required units.
a 37.9 cm + 4.8 cm = cm b 6.7 cm + 33.9 cm = mm
1
c 20 cm + 7.6 cm = cm d 81.4 cm + 65 cm = mm
5
1 4
e 80 cm + 2.04 m + m = m f 31 m + 103 cm + 18.9 m = cm
2 5
1 3
g 11 km + 45.7 km = km h 50.207 km + 48 km + 30 m = m
8 10
2 Add 78.3 cm and 27 cm. Give your answer in mm.

3 Based on the cards given, find 2
the total distance in: 23 km 4 km 960 m
5
a
km b m 9.012 km



182
5.1.3 • Vary the questions such as calculating the sum of numbers.

SUBTRACTION OF UNITS OF LENGTH



1 a What is the difference in height 62.7 cm 3 cm
between Robot R and Robot S? 54.9 cm 5
shorter
62.7 cm – 54.9 cm = cm
than
11
5 1 17 Robot S
62.7 cm
– 54.9 cm
7.8 cm R S T

62.7 cm – 54.9 cm = 7.8 cm
The difference in height between Robot R and Robot S is 7.8 cm.

b Calculate the height, in mm, of Robot T.
3
54.9 cm – cm = mm
5
3 3 2
54.9 cm – cm = (54.9 × 10) mm – ( × 10) mm
5 5
= 549 mm – 6 mm 1
= 543 mm
3
54.9 cm – cm = 543 mm
5
The height of Robot T is 543 mm.


4
2 2.07 m – 16 cm – m = m
5
First, convert the measurement in
16 cm = (16 ÷ 100) m 0.8 m decimal m. Then, subtract.
5 4.0 m
= 0.16 m
−0 1 10
4 0 2. 0 7 m
−4 0 – 0. 1 6 m
0
1 . 9 1 m
– 0. 8 0 m
4 1 . 1 1 m
2.07 m – 16 cm – m = 1.11 m
5




• Encourage pupils to subtract by finding the balance or difference
of length of an object. 183
5.1.4
• Ask pupils to carry out the required conversion of unit of length
according to the questions.

3 How much longer is the Penang Bridge compared
to the Terengganu Drawbridge?
13.5 km – 638 m = km
14 9
2 41010
638 m = (638 ÷ 1 000) km
1 3 . 5 0 0 km
= 0.638 km – 0 . 6 3 8 km
1 2 . 8 6 2 km
Terengganu Drawbridge
638 m
13.5 km – 638 m = 12.862 km

The length of the Penang Bridge is 12.862 km
longer than the length of the Terengganu
Penang Bridge Drawbridge.
13.5 km

7
4 90 km – 34.3 km – 1 180 m = m
8

7 7 34.3 km = (34.3 × 1 000) m
90 km = 90 km + km
8 8 = 34 300 m
7 125
= (90 × 1 000) m + ( × 1 000) m 8 10 4 17
8
1 90 8 7 5 m 56 5 7 5 m
= 90 000 m + 875 m – 34 3 0 0 m – 1 1 8 0 m
= 90 875 m 56 5 7 5 m 55 3 9 5 m

7
90 km – 34.3 km – 1 180 m = 55 395 m
8

1
Emperor Penguin’s height: 1. m – m = 1.15 m

The number on is the same.
What is the number?




Calculate these.
9
a 53.1 cm – 12.9 cm = cm b 67.8 cm – 2 cm = mm
10
3 3
c 18 km – 6.509 km = km d 4.15 m – 72 cm – 1 m = m
4 5
3
1
e 30 m – 340 cm – 25.7 m = cm f 26 km – 8 km 85 m – 9.27 km = m
2 4

184 • Carry out a quiz in groups involving subtraction up to three
5.1.4
measurements of length.

MULTIPLICATION OF UNITS OF LENGTH



1 a What is the width of
the decorative frame?

6 × 2.8 cm = cm Think
Effort is
4 Stay Positive the Key to width
2.8 cm FOCUSed! Be Success
Positive
× 6
1 6.8 cm
2.8 cm

6 × 2.8 cm = 16.8 cm 1.9 cm

The width of the decorative frame is 16.8 cm.
b Calculate the length, in mm, of the decorative frame.
3
14 × 1.9 cm = mm
1 9 mm Calculate the
1.9 cm = (1.9 × 10) mm × 1 4 length and
= 19 mm 1 7 6 width of each
+ 1 9 0 motivational
14 × 1.9 cm = 266 mm 2 6 6 mm card on the
frame above.
The length of the decorative frame is 266 mm.


3
2 56 × 7 m = cm
4
3
3
Method 1 Method 2 7 m = 7 m + m
4 4 25
3 14 31 3
56 × 7 m = 56 × m = (7 × 100) cm + ( x 100) cm
4 4 4
1 1
= 434 m = 700 cm + 75 cm

= (434 × 100) cm = 775 cm
3 2
= 43 400 cm 4 3
7 7 5 cm
× 5 6
1 1 1
3 4 6 5 0
56 × 7 m = 43 400 cm
4 + 3 8 7 5 0
4 3 4 0 0 cm


• Use various daily life situations involving multiplication such as 185
5.1.5 finding the length of joined benches or tables.
• Instil other moral values such as perseverance and diligence.

3 Calculate the total distance, in m, that Aiman travelled to
school for 5 days on a round-trip.
10 × 2.735 km = m
10 × 2.735 km = 10 × (2.735 × 1 000) m 2.735 km

= 10 × 2 735 m
= 27 350 m

10 × 2.735 km = 27 350 m

The total distance that Aiman travelled to school for
5 days on a round-trip is 27 350 m.


1 4
4 100 × 48 m = km 5
2 1 000 × 19 cm = m
5
1
m = 0.5 m 4 cm = 0.8 cm
2 5
1 4
100 × 48 m = 100 × 48.5 m
2 1 000 × 19 cm = 1 000 × 19.8 cm
5
= 4 850 m = 19 800 cm
= (4 850 ÷ 1 000) km = (19 800 ÷ 100) m
= 4.850 km = 198 m

1
100 × 48 m = 4.85 km 4
2 1 000 × 19 cm = 198 m
5




1 Multiply.
3
a 8 × 4.39 cm = cm b 6 × 9 cm = mm
4
1
c 13 × 7 cm = m d 25 × 7.44 m = km
5
1
e 42 × 18.05 km = km f 70 × 10 m = km
2
2 Complete these.
a b
0.2 km m 8.3 cm mm
1
100 × 1 m = cm 1 000 × 2 m = cm
4 5
1.567 km km 0.046 km m



186 • Drill multiplication of measurements of length using charts or
5.1.5
picture cards.

DIVISION OF UNITS OF LENGTH



1 What is the thickness of a 10 sen coin?
12 mm ÷ 8 = mm


1 . 5 mm
8 1 2 . 0 mm
− 8
4 0
− 4 0 12 mm
0



1.5
12 mm ÷ 8 = mm
The thickness of a 10 sen coin is 1.5 mm.




1
2 45.18 cm ÷ 9 = mm 3 3 m ÷ 16 = cm
5
Step 1 Step 1
5 . 0 2 cm 1 16 20

9 4 5 . 1 8 cm 3 m = ( 5 × 100) cm
5
−4 5 1
0 1 = 320 cm
− 0
1 8
− 1 8 Step 2
0
2 0 cm
Step 2 1 6 3 2 0 cm

– 3 2
5.02 cm = (5.02 × 10) mm 0 0
= 50.2 mm – 0

45.18 cm ÷ 9 = 50.2 mm 0


1
3 m ÷ 16 = 20 cm
Can you convert to mm unit 5
first, then divide? Discuss.




• Carry out simulation activities such as finding the thickness of 187
5.1.6
a book from a stack of similar books.

4 Calculate the distance, in m, of the
resurfaced road in 1 hour. We took 10 hours to resurface
1
1 2 km of road.
2 km ÷ 10 = m 4
4
1 9
2 km ÷ 10 = km ÷ 10
4 4
= (2.25 × 1 000) m ÷ 10

= 2 250 m ÷ 10
= 225 m
1
2 km ÷ 10 = 225 m
4
The distance of the resurfaced road
in 1 hour is 225 m.




5 238.9 km ÷ 100 = m 6 30 m 72 cm ÷ 1 000 = cm
238.9 km ÷ 100 = 2.389 km 30 m 72 cm = (30 × 100) cm + 72 cm

= (2.389 × 1 000) m = 3 000 cm + 72 cm
= 2 389 m = 3 072 cm

238.9 km ÷ 100 = 2 389 m 3 072 cm ÷ 1 000 = 3.072 cm


30 m 72 cm ÷ 1 000 = 3.072 cm





1 Divide.
4
a 0.12 cm ÷ 3 = cm b 83 mm ÷ 10 = mm
5
1
c 56.64 m ÷ 16 = cm d 25 km ÷ 25 = m
8

2 Complete these.
a 48.3 km ÷ 10 = km

b 48.3 km ÷ 100 = m


3 Divide the following. State the answer in m.
a 3.672 km by 18. b 32 m 10 cm by 100.




188 • Drill division of measurements of length using suitable materials
5.1.6
such as pieces of thread, string, and ribbon.

CONVERT UNITS OF GRAM AND KILOGRAM



1 a Convert 1.8 kg to g.


1.8 kg = g
1.8 kg = (1.8 × 1 000) g

= 1 800 g kg
1.8 kg = 1 800 g



3
b 2 kg = g 1.8 kg 3
4 2 kg
4

Method 1 Method 2

3 11 250 3 3
2 kg = ( × 1 000) g 2 kg = 2 kg + kg
4 4 4 4
1 2 5 0 250
3
= 2 750 g × 1 1 = (2 × 1 000) g + ( × 1 000) g
2 5 0 4
1
+2 5 0 0 = 2 000 g + 750 g
2 7 5 0 = 2 750 g
3
2 kg = 2 750 g
4





2 3.07 kg = kg
3.07 kg = 3 kg + 0.07 kg


= 3 kg + kg

1 kg = 1 000 g
= kg
× 1 000

kg g

1
Is 2 kg equal to 2 200 g? Prove it. ÷ 1 000
5


189
• Pupils carry out the activity of converting unit of kg to g or vice versa
5.2.1 based on the printed mass on product packaging.

3 Convert 6 900 g to kg.
6 900 g = kg

6 900
6 900 g = (6 900 ÷ 1 000) kg 6 900 g = ( 1 000 ) kg
in decimal in fraction
= 6.9 kg 69
= kg
10

9
= 6 kg
9 10
6 900 g = 6.9 kg or 6 kg
10


4 Convert 5 kg 800 g to kg.

5 kg 800 g = kg

5 kg 800 g = 5 kg + 800 g
= 5 kg + (800 ÷ 1 000) kg
= 5 kg + 0.8 kg
State the answer
= 5.8 kg in fraction.

5 kg 800 g = 5.8 kg

5. 25 kg = 5 kg
8
Find the possible
value of and .




1 Complete these.
3
a 0.01 kg = g b 6 kg = g c 4 250 g = kg
5
9
d 8 kg 400 g = kg e 3 kg = g f 7 kg 2 g = kg
10
2 State the answers in decimal.

a 5 130 g = kg b 65 g = kg

3 State the answers in fraction.

a 500 g = kg b 7 125 g = kg




190 • Carry out a quiz on converting units of mass involving fractions
5.2.1 and decimals.

ADDITION OF UNITS OF MASS



The mass of a
1 cabin baggage Total up the mass of the
should not bag and the present.
exceed 7 kg.
3.505 kg + 0.48 kg = kg
3.505 kg 3.505 kg
+0.480 kg
3.985 kg

3.505 kg + 0.48 kg = 3.985 kg

1 0.48 kg
3 kg The total mass of the bag and
8 270 g the present is 3.985 kg.


b Calculate the total mass, in kg, of clothes and a pair of sports shoes.


1
3 kg + 270 g = kg
8

1 1 25 270
Convert 3 kg and 3 kg = kg 270 g = kg
8 8 8 1 000
270 g to decimal kg
first. 3 . 1 2 5 kg = 0.27 kg
8 2 5 . 0 0 0 kg 1
−2 4 3 kg + 270 g
8
1 0
− 8 = 3.125 kg + 0.27 kg
2 0 = 3.395 kg
− 1 6
4 0
− 4 0
0

1
3 kg + 270 g = 3.395 kg
8
Cabin baggage is a
The total mass of clothes and a pair of sports clothes bag and other
shoes is 3.395 kg. items that are carried
along or placed in the
State the items that can be put compartment of an
into the bag as cabin baggage. aeroplane.



191
• Carry out simulation activities such as weighing every product or tool using
5.2.2 a digital weighing scale to find the total mass.

9
2 6.73 kg + 1 080 g + 4 kg = kg
10
9 1 080
6.73 kg + 1 080 g + 4 kg = 6.73 kg + kg + 4.9 kg
10 1 000 1 1
= 6.73 kg + 1.08 kg + 4.9 kg 6 . 7 3 kg
1 . 0 8 kg
= 12.71 kg
+ 4 . 9 0 kg
9
6.73 kg + 1 080 g + 4 kg = 12.71 kg 1 2 . 7 1 kg
10


7
3 kg + 4.305 kg + 945 g = g
8
7 7
8
8 kg + 4.305 kg + 945 g = ( × 1 000) g + (4.305 × 1 000) g + 945 g
= g + g + g

= g





1 Calculate.
3
a 7.42 kg + 0.845 kg = kg b kg + 760 g = g
5
1 1
c 12 kg + 4.8 kg + 370 g = kg d 80 g + 6 kg + 9 kg = g
2 4

2





kg
Add the mass, in g, for
pineapple and papaya.



1.608 kg 1.4 kg

3 Calculate the total
mass, in g, for all
three packets of the
wafer as shown in 1 kg 217.5 g 0.25 kg

the pictures. 8



192
5.2.2 • Drill addition of mass using question cards or supermarket pamphlets.