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

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)

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

Directed numbers on a number line How do we write & say this? – + -6 -2 4 7 < say “minus six is less than four” -6 4 < say “minus two is less than zero” -2 0

Directed numbers on a number line How do we write & say this? – + -6 -2 4 7 > say “seven is greater than minus two” 7 -2 > say “four is greater than zero” 4 0

Directed numbers on a number line How do we write & say this? + – -6 -2 4 7 7 0 -2 -6 > > > This called “Descending Order” -2 0 4 7 < < < This called “Ascending Order”

Why do we learn Directed Numbers? In primary school, you learned: Example 1: 3 + 7 = 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!

The Four Basic Operations Addition: 3 + 7 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”

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

The meaning of “+” and “—” In primary school you learned: Example 1: 3 + 7 = 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

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

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

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

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

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

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

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

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

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

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