MATHEMATICS - FORM 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.

    

2.Changing the order of numbers in multiplication does

   not affect the product.

   For example:-    6 × 3 = 18
                               3 × 6 = 18 

3. The product of any number and 0 is 0.

    For example:-    10 × 0 = 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 problem

    Given 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.