Recap:
1. Positive number are numbers greater than 0
2. Negative numbers are less than 0
3. Zero 0 is neither positive or negative
Also,
1. When there is no sign ’attach’ to a number => the number is positive
2 + 3 = 5;
2, 3 and 5 are all positive numbers
2. The sign + , - ‘belongs’ to the number on the right
Example:
-2 (negative 2),
5 + (-3) is 5 (positive 5) + (add) (-3) negative 3
Number Operations
The four number operations are
Symbol. Some Words/phrases
+ add, sum, plus, total, more than, increased by
- subtract, difference, minus, r less than, decreased
x multiply, product, times
/, ÷ divide, quotient
* Negative number is NOT – MINUS a number
5 + (-3) = 2 is positive 5 add negative 3
5 – 3 = 2 is positive 5 minus positive 3
5 + (-3) = 5 - 3
Explanation for positive and negative numbers multiplications
a x -b = -ab
5 x -2 = -2 + (-2) + (-2) + (-2) + (-2)
= -10
=> + x - = -
Negative number and negative number multiplications
-5(0) = 0
-5 [ 3 + (-3) ] = 0
-5 x 3 + -5 x -3 = 0
-15 + (-5)x(-3) = 0
(-5) x (-3) must be equal to 15 for -15 + (-5) x (-3) = 0
=> -5 x -3 = 15
=> - x - = +
Order Of Operations
First Order : ( ) e Bracket Exponential BE / BO (e.O – Order)
Second Order : ÷ X Multiplication And Division DM
Third Order : + - Addition And Subtraction AS
[ B E D M A S] / [B O D M A S]
Do the question by: (1) completing all FIRST order,
(2) follow by all SECOND order,
(3) and then the THIRD order.
Step 1: Write BODMAS and Underline by the ORDER
Step 2: Do calculation using order
Step 3: Repeat step 1-2 until question is solved.
** Order within bracket -> must follow order as well
Example
Find the value of:
9 + 3 x 4 – (3 + 5) ÷ 2
BODMAS (Step1 : Write BODMAS)
9 + 3 x 4 – (3 + 5) ÷ 2 (Underline by Order)
= 9 + 3 x 4 – (8) ÷ 2 (Step 2 : Do calculation)
= 9 + 3 x 4 – 8 ÷ 2 (Step 3 : <<do ÷ and x>, repeat step 1-2> )
= 9 +12 – 4 (Step 3 : <do + and - > )
= 21 – 4 = 17
Example:
Calculate 24 ÷ 4 x 5 ÷ 6
[For computation with only the same order, working from left to right]
BODMAS (Step 1)
24 ÷ 4 x 5 ÷ 6 [ all are 2nd order - Do from left to right ]
= 6 24 x 5 (Step 2)
4 6 [ Write ÷ as a denominator]
= 5
Example:
Calculate 25 + 144 – 2 x 5 x 12 [15/1/5a/1]
(BEDMAS)
25 + 144 – 2 x 5 x 12 (Step 1)
= 25 + 144 – 120 (Step 2)
= 25 + 144 – 120 (Step 3)
= 169 – 120 (Step 3)
= 49
Example
Estimate the value of 39.68 x 21.8 / (4.003)2
39.68 x 21.8 / (4.003)2. (Step 1 : Round Each Number)
~ 40 x 24/ 42
= 40 x 24 / 16 (Step 2 : Do x / + -)
= 10 x 6
= 60
Time Zone Variation (NT - for -ve no. problems)
There are 24 time zones from UTC -11 to UTC + 12.
[UTC=Coordinated Universal Time]
Example
United Kingdom is at UTC 0, Singapore is at UTC 8 and New York is at UTC -5
There are two types of notation for time:
- 12-hour notation using a.m. and p.m
- 24-hour notation using 0000 to 2359
Example:
Singapore is at UTC +8, Paris is at UTC +1 and San Francisco is at UTC -7
(a) It is 2p.m at Paris, what is the time in Singapore?
(b) What is the time difference between Singapore and San Francisco?
(a)
Step1: Find the difference between Paris and Singapore
UTC 8 - UTC 2 = 6
Step2: Add 6 to Paris time
2 + 6 = 8pm
Step3: Answer
Singapore time is 8 p.m
(b)
UTC 8 - (-7) = 8 + 15 (Step 1)
The time difference is 15 hours (Step 2)
