1. Form 1 Mathematics Chapter 1
Directed Numbers
Form 1 Mathematics
Chapter 1

2. Introduction to Directed Numbers
Numbers have two parts:
Size or Magnitude
Sign or Direction
The sign of a number has two possibilities (they are always opposites)

3. Examples of Directed Numbers
What does the negative mean?
Money in bank:
+$1,100 – $950
Students in class (32 students in class)
Mon: – 2; Tue: – 1; Wed: 0; Thu: – 3; Fri:0
World time:
Sydney: +2; Rome: – 6; London: – 8; New York: – 13
Stairs in the building (up is “+”):
Go up 3 steps: +3; Go down 4 steps: – 4

4. Directed numbers on a number line
How do we write & say this? – + -6 -2 4 7
< say “minus six is less than four”
< say “minus two is less than zero”

5. Directed numbers on a number line
How do we write & say this? – + -6 -2 4 7
> say “seven is greater than minus two”
> say “four is greater than zero”

6. Directed numbers on a number line
How do we write & say this? + – -6 -2 4 7
> > >
This called “Descending Order”
< < <
This called “Ascending Order”

7. Why do we learn Directed Numbers?
In primary school, you learned:
Example 1: = 10
“3 apples plus 7 apples is 10 apples”
Example 2: 3 – 7 = – 4
Are “3 apples minus 7 apples negative 4 apples”?
With Directed Numbers, the “–” now has meaning!

8. The Four Basic Operations
Addition:
Say “3 plus 7” or “The sum of 3 and 7” or “Add 3 to 7”
Subtraction: 3 – 7
Say “3 minus 7” or “The difference of 3 and 7” or “Subtract 7 from 3”
Multiplication: 3 × 7
Say “3 times 7” or “The product of 3 and 7” or “Multiply 3 and 7”
Division: 3 ÷ 7
Say “3 divided by 7” or “The quotient of 3 and 7” or “Divide 3 by 7”

9. The Four Basic Operations
Addition: “+” or “sum”
Subtraction: “–” or “difference”
Multiplication: “×” or “product”
Division: “÷” or “quotient”

10. The meaning of “+” and “—”
In primary school you learned:
Example 1: = 10
In high school, you learn Directed Numbers:
Example 1a: (+3) + (+7) = (+10)
Direction or sign
Magnitude or size
What is this?
The Operation
What sort of operation?
Addition or Sum

11. The meaning of “+” and “—”
“+” has two meanings:
Direction of directed number
Operation between two directed numbers

12. The meaning of “+” and “—”
Primary school:
Example 2: 3 – 7 = –4
Directed Numbers:
Example 2a: (+3) – (+7) = (–4)
Direction or sign
What is this?
An Operation
What sort of operation?
Subtraction or Difference

13. The meaning of “+” and “—”
“–” has two meanings:
Direction of directed number
Operation between two directed numbers

14. Rules to Remember (p.1.39) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )

15. Rules to Remember (p.1.39) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
正正得正 負負得正
正負得負 負正得負

16. Adding directed numbers+ – + – -6 -2 3 7 10 + –
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
(+7) + (+3)
= (+10)

17. Adding directed numbers+ – + – -6 -3 3 7 10 + –
(+7) – (+3)
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
(+7) + (–3)
7 – 3
= 4

18. Examples +3 + (+9) = +3 + 9 = +12 –7 + (+12) = –7 + 12 = +5=
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
= +12
–7 + (+12)
= –7 + 12
= +5

19. Time for Practice Page 1.24 of Textbook 1A Page 1.25 of Textbook 1A
Class Practice 1.2
Page 1.25 of Textbook 1A
Questions 1 – 14

20. Enjoy the world of Mathematics!
Good Luck!
Enjoy the world of Mathematics!
Ronald HUI