Maths Form 1 Chapter 1 Whole Numbers
WHOLE NUMBERS
1. Whole numbers are 0,1,2,3,4,5,6,7,8,9,10,11,12,....
2. (Zero) is the first whole number.
3. Whole numbers can be written in words or figures.
4. Each whole number is made up of the digits from 0 to 9.
For example:-
(a) 304 is made up of the digits 3,0 and 4.
It is read as 'three hundred and four'.
(b) 4263 is made up of the digits 4, 2, 6 and 3.
It is read as 'four thousand two hundred
and sixty-three'
A) Place Value and Value of Each Digit in Whole Numbers.
1. Each digit in a whole number has its own place value.
2. The place values for whole numbers include units (ones),
tens, hundred, thousand, hundred, thousand, ten thousand,
millions and so on.
3. The value of a digit in a whole number depends on its place value.
5 972 436 is read as 'five million nine hundred and seventy-four
thousand two hundred and thirty -six.
Worked Example
Write the following in words.
(a) 530 274
Solution
(a) five hundred and thirty thousand two hundred and seventy-four.
Worked Example
Write the following in figures.
(a) five thousand six hundred and twenty-four.
Solution
(a) 5 624
Worked Example
State the place value of digit 7 in each of the following numbers.
(a) 573 (c) 307 842
(b) 9 704 (d) 7 951 650
Solution
(a) ten (c) thousand
(b) hundred (d) millions
Worked Example
State the value of digit 9 in each of the following numbers.
(a) 391 (c) 29 710
(b) 9 004 (d) 4 951 650
Solution
(a) 90 (c) 9 000
(b) 9 000 (d) 900 000
B) Rounding off Numbers
A number can be rounded off to a certain place value by following the
rules below. Look at the digit on the right next to the place value involved.
(a) If the digit is 5 more, add 1 to the digit at the place value involved and
replace all the other digits on its right with zeros.
(b) If the digit is less than 5, retain the digit as it is at the place value
involved and replace the other digits on its right with zeros.
c) Estimation
1.In our daily life, we use estimation when an accurate answer is unnecessary.
2. We often use rounding off to give an estimation to the actual value.
ADDITION AND SUBTRACTION
OF WHOLE NUMBERS.
A) Addition
1. Addition is a process of finding the total of two or more numbers.
2. The total is also known as the sum.
For example:-
The sum of 300 and 5 000 is 5 300.
3. The order of addition of numbers does not change sum.
4.The sum of any number and 0 is the number itself.
For example:-
(a) 12 + 0 = 12
(b) 0 + 6 = 6
5. Follow the steps below when carrying out addition.
Step 1:- Arrange the numbers according to their place values.
Step 2:- Add from right to left.
B) Problem Solving involving Addition
Worked Example
There are 25 apples, 3 760 durians and 948 oranges in Mr Tan's stall.
Find the total number of fruits in his stall.
Solution
1. Understand the problem
Given information:-
Number of apples = 25
Number of durian = 3 760
Number of oranges = 9 48
Find:- Total number of fruits
2. Devise a plan
Use addition.
3. Carry out the plan
4. Check
Add again to see if the answer is the same.
c) Subtraction
1. Subtraction is a process of finding the difference between two numbers.
For example:-
65 - 20 = 45 (Difference or remainder)
2. The difference between two same numbers is 0.
For example:-
19 - 19 = 0
3. When we subtract 0 from a number, the number remains the same.
For example:-
75 - 0 = 75
4. Follow the steps below when carrying out subtraction.
Step 1:- Arrange the numbers according to their place values.
Step 2:- Subtract or minus from right to left.
5. Addition is the inverse of subtraction.
For example:-
76 - 15 = 61
62 - 15 = 47
D) Problem Solving Involving Subtraction.
Worked Example
There are 1 244 male students in a college.If the number female students
is 327 less than the number of male students, how many female students
are there?
Solution
1. Understand the problem
Given information:-
Number of male students = 1 244
The number of female students is 327 less
than the number of male students.
2. Devise a plan
Use subtraction.
3. Carry out the plan
4. Check
Use addition to check.
MULTIPLICATION AND DIVISION
OF WHOLE NUMBERS
A) Multiplication
1. Multiplication is a process of repeated addition.
not affect the product.
For example:- 6 × 3 = 18
3 × 6 = 18
3 × 6 = 18
3. The product of any number and 0 is 0.
For example:- 10 × 0 = 0
0 × 10 = 0
0 × 10 = 0
4. A number multiplied by 1 is the number itself.
For example:- 36 × 1 = 36
Worked example
Find the product of 42 and 426.
Solution
B)Problem Solving involving Multiplication
Worked example
Marrion can sew 45 handkerchiefs in one day.
How many can she sew in a week?
Solution
1.Understand the problem
Given information:-
Number of handkerchiefs sewn in one day
= 45
Find: Total number of handkerchiefs sewn
in a week.
2. Devise a plan
Use multiplication.
3.Carry out the plan
4. Check
Multiply again to see if you gate the same answer.
C) DIVISION
1. Division is equal gathering or equal sharing.
2. When a number is divided by 0, it cannot be defined.
For example:-
8 ÷ 0 cannot be defined.
3. When a number is divided by 1, the quotient is the
number itself.
For example:-
5 ÷ 1 = 5
4. When 0 is divided by any number, the quotient is 0.
For example:-
0 ÷ 58 = 0
5. Changing the order of numbers in division will affect
the answer.
For example:-
Worked Example
(a)Divide 1 694 by 14
(b) Find the value 925 ÷ 4
Solution
D) Problem Solving involving Division
Worked Example
160 table are arranged equally in 10 rows.
How many table are there in each row?
Solution
1. Understand the problem
160 table are arranged equally in 10 rows.
2. Devise a plan
Use division.
3. Carry out the plan
Therefore, there are 16 table in a row.
4. Check
Check by multiplication.
10 x 16 = 160
COMBINED OPERATIONS OF
WHOLE NUMBERS
A) Combined Operations involving
Addition and Subtraction
For combined operations involving addition and subtraction,
calculate from left to right.
Worked Example
Find the value of each of the following.
(a) 22 + 18 - 24
(b) 230 - 165 + 8
Solution
B) Problem Solving involving
Addition and Subtraction
Worked Example
A basket contains 32 fruits. 11 are taken out and then 21
are added in. How many fruits are there in the basket now?
Solution
1. Understand the problemGiven information:-
Number of fruits in the basket = 32
Number of fruits taken out = 11
Number of fruits added in = 21
2. Devise a plan
Perform subtraction followed by addition.
3. Carry out the plan
32 - 11 + 21
= 21 + 21
= 42
Therefore, 42 fruits are in the basket now.
4. Check
C) Combined Operations involving
Multiplication and Division
For combined operations involving multiplication
and division, calculate also from left to right.
Worked Example
Find the value of each of the following.
(a) 18 x 7 ÷ 3
(b) 600 ÷ 8 x 5
Solution
D) Problem Solving involving
Multiplication and Division
Worked Example
Sasha, Hanim and Akma bought 20 novels
costing RM16 each. They shared the cost
equally. Find the amount paid by each of them.
Solution
1. Understand the problem
Given information:-
Number of novels bought by Sasha, Hanim
and Akma = 20
Cost of each novels = RM 16
Find: Amount paid by each of them
2. Devise a plan
Perform multiplication followed by division.
3. Carry out the plan
21 x RM16 ÷ 3
= RM 336 ÷ 3
= RM 112
The amount paid by each of them was
RM 112.
4. Check
21 x RM16 = 336
3 x RM 112 = 336
E) Combined Operation involving +, -, x and ÷
For combined operations where addition, subtraction,
multiplication, and division are involved, perform multiplication
and divition before addition and subtraction.
Worked Example
Simplify
(a) 7 x 40 - 10 x 11
(b) 48 + 32 x 24 ÷ 6 -2
Solution
F) Combined Operations involving Brackets
1. For combined operations involving brackets,
work the calculation within the brackets first.
Worked Example
1. Solve each of the following.
(a) 6 x ( 6 - 2 ) ÷ ( 9 - 6 )
(b) 20 x (2 + 28 ÷ 4 ) - 95
Solution
(a) 6 ( 6 - 2 ) ÷ ( 8 - 2 )
= 6 x 4 ÷ 6
= 24 ÷ 6
= 4
(b) 20 x ( 2 + 28 ÷ 4 ) - 95
= 20 x ( 2 + 7 ) - 95
= 20 x 9 - 95
= 180 - 95
= 85
2. Brackets are also operative symbol for multiplication.
For example:-
( 8 - 3 ) ( 9 - 5 ) -10
= ( 5 ) ( 4 ) - 10
= 20 - 10
= 10
G) Problem Solving involving +, -, x, ÷ and Brackets
Worked Example
Azan and Amir have 7 and 15 bottles of marble.
If each bottle has 55 marble in it, Find the total
number of marbles.
Solution
1. Understand the problem
Given information:
Number of bottles bought by Azan = 7
Number of bottles bought by Amir = 15
Number of marbles in each bottles = 55
Find: Total number of marbles
2. Devise a plan
Perform addition within the brackets and followed
by multiplication.
3. Carry out the plan
( 7 + 15 ) x 55 = 22 x 55
= 1 210
Therefore, the total number of marbles is 1 210.
4. Check
22 - 15 = 7
1 210 ÷ 55 = 22
Worked Example
Mr Lee bought 8 Dozens exercise books. He give
26 of them to his daughter. He then distributed the
rest evenly to his 3 sons. How many exercise books
were given to each of his sons?
Solution
( 8 x 12 - 21) ÷ 3
= ( 96 - 21 ) ÷ 3
= 75 ÷ 3
= 25
25 exercise books were given to each of his sons.
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