Date: 0206/2020
Class: #1
Syllabus Topic: Computation and Numeration
Title: BODMAS, Operators, Directed Numbers
Directed Numbers
“numbers with a direction”
1. Directed Numbers:
2. Numbers can be Positive as well as Negative
We must now consider the number line and notice that there are numbers that exist before
Zero!
-3
-2
-1
4. 0
6. 1 8. 2
3
Pay attention to how the numbers are arranged before the zero.
Do not confuse it with this:
-1
-2
-3
0
1
2
3
THIS IS WRONG
But it is a very
common mistake
Think of negative numbers as being “owed”
For example, if you put $10 into the bank but borrowed $15 from the bank you now owe
the bank. It can be said that you have −𝟓 dollars in the bank!
If you borrowed even more... let’s say you borrowed $20 now you will have −25 in the
bank. You owe the bank 25 dollars!
The Basic Operators are Addition, Subtraction Multiplication and Division
+
−
×
÷
We can use the number line to examine what happens when we add and subtract numbers.
1+2=
1+2=3
Start on 1 (the first number)
-3
-2
-1
0
1
2
3
When we add, we move to the right!
2−5=
2 − 5 = −3
Start on 2 (the first number)
-3
-2
-1
0
1
2
3
When we subtract, we move to the left!
To Do
On your own find the answer to the following using number lines
1) 2 − 4
2) −3 + 5
3) −1 − 3
Using a number line is impractical for operations with large numbers.
Let us examine two sets of rules that we apply to find the answers for Problems with
Directed Numbers
The Rules
For Multiplication, Division or if two Signs are next to each other
1st Sign
2nd Sign
Result
+
+
+
−
−
+
+
−
−
−
+
−
For Addition and Subtraction
•
Check to see if signs are next to each other. (If so, change to one sign)
•
Same signs? →
add the numbers (without the signs) → put back the sign
•
Different signs? →
subtract the numbers (without the signs) → put back sign of
larger number
Examples
1) −(−1) = 1
2) −3 × −3 = +9 (or we can just write 9)
3) 4 × −6 = −24
1
5
4) 5 × −2 = − 2
BODMAS
This is an acronym used to help understand the order in which operations take place
when finding the solution to a question.
Brackets Of Division Multiplication Addition Subtraction
To Do
Solve the following
1) 5(1 − 5) × 1 + 2
2) 6 − 5 ÷ 5
3) 17 − (7 − 4)
Solutions
1) 5(1 − 5) × 1 + 2
= 5(−4) × 1 + 2
= −20 × 1 + 2
= −18
2) 6 − 5 ÷ 5
=6−1
=5
3) 17 − (7 − 4)
= 17 − 3
= 14
Summary
•
Directed Numbers deal with negative and positive numbers
•
It introduces the idea of numbers having a “direction”
•
A number line can be used to solve simple questions with directed numbers
•
For more complex questions we must understand the rules governing
o ×,÷ and when signs are next to each other
o +, −
•
Note what are the basic operators in mathematics
•
BODMAS