Section 1:
1. Opposite Numbers (additive inverse): is a number that when added to a given number yields 0. The opposite number for any number x is -x. Note that x may be positive or negative.
(-5) + 5 = 0
x + (-x) = 0
On the number line, the numbers 5 and -5 are located at the same distance from zero. We say that the numbers 5 and -5 are opposites. We can also say that -5 is opposite to 5, and 5 is opposite to -5 on the number line.
2. Addition of integers:
- Addition of a positive number is taken as a movement to the RIGHT of the number line
- Addition of a negative number is taken as a movement to the LEFT of the number line
(-3) + 4
2 + 3
(-1) + (-3)
2 + (-5)
0 + (-4)
3. Rule for addition:
- If the signs of the integers being added are the same, the sum has the same sign as the integers and we add the absolute values of the integers
For any a > 0, and b > 0,
a + b = a + b; 3 + 5 = 8
(-a) + (-b) = -(a+b); (-3) + (-5) = – (3 + 5) = -8
- If the signs of the integers being added are different,, the sum takes the sign of the integer with the greater absolute value and we find the difference of the absolute values of the integers.
For any a > 0, and b > 0,
a + (-b) = +(a – b) if a >=b; 9 + (-6) = +(9 – 6) = +3 = 3
a + (-b) = – (b -a) if b > a; 15 + (-20) = -(20 -15) = -5
-a + b = -(a – b) if a >= b; -18 + 12 = -(18 -12) = -6
-a + b = +(b -a) if b > a; -23 + 27 = +(27 – 23) = +4 = 4
4. Home Work:
- Handout: one page
- Workbook: page 7: 4
Section 2:
1. (Not today) Quiz on negative number and addition of integers
2. Subtraction of integers:.subtraction is the reverse process of addition. Using a number line:
- Subtraction of a positive number is taken as a movement to the LEFT of the number line
- Subtraction of a negative number is taken as a movement to the RIGHT of the number line
(-3) – 4
2 – 3
(-1) – (-3)
2 – (-5)
0 – (-4)
3. Rule for subtraction: to subtract integers, we change the sign of the integer being subtracted and add them together according to the rule for addition of integers.
For any integers a, and,b,
a – b = a + (-b)
4. Absolute value of the difference:
For any integers a, and,b,
|a – b| = |b – a|
5. Home Work:
- Handout: two pages
- Workbook:
- page 8: 7
- page 9: 17
- page 10: 20
