Download Adding and Subtracting Integers

Objective 2
Add and subtract integers
© 2002 by R. Villar
All Rights Reserved
Add and subtract integers
How do you add using a number line?
When you add a positive number…
move to the right.
When you add a negative number…
move to the left.
Example:
3 + (–5)
1. Start at the first number.
Example:
3 + (–5)
1. Start at the first number.
3
Example:
3 + (–5)
1. Start at the first number.
3
2. Move the number of spaces
and the direction of the
second number.
Example:
3 + (–5)
1. Start at the first number.
3
2. Move the number of spaces 5 left
and the direction of the
second number.
Example:
3 + (–5)
1. Start at the first number.
3
2. Move the number of spaces 5 left
and the direction of the
second number.
3. The sum is the number
you end at.
Example:
3 + (–5)
1. Start at the first number.
3
2. Move the number of spaces 5 left
and the direction of the
second number.
3. The sum is the number
–2
you end at.
Example:
–2 + 6
1. Start at the first number.
Example:
–2 + 6
1. Start at the first number.
–2
Example:
–2 + 6
1. Start at the first number.
–2
2. Move the number of spaces
and the direction of the
second number.
Example:
–2 + 6
1. Start at the first number.
–2
2. Move the number of spaces 6 right
and the direction of the
second number.
Example:
–2 + 6
1. Start at the first number.
–2
2. Move the number of spaces 6 right
and the direction of the
second number.
3. The sum is the number
you end at.
Example:
–2 + 6
1. Start at the first number.
–2
2. Move the number of spaces 6 right
and the direction of the
second number.
3. The sum is the number
4
you end at.
Rules of Addition
Sometimes, it’s not practical to use a number
line to add. Here are some to add without a
number line.
Example –28 + (–22)
Adding with the same sign:
1. add up the numbers (absolute value)
2. keep the sign
–50
Ex. a. –10 + (–33)
b. –6 + (–12)
–43
–18
Example: 28 + (–22)
Adding different signs:
1. Subtract the numbers.
2. Keep the dominant sign.
6
Ex. a. 24 + (–40)
b. –12.1 + 3.8
–16
–8.3
Example: 8.1 + (–2.3) + (–1.5) + 4
Get all the positives together, get all the
negatives together, then add.
12.1 + (–3.8)
8.3
Is this statement true?
(1 + 2) + 3 = 1 + (2 + 3)
Yes, changing the grouping (parentheses)
does not change the sum. The property
that allows this is called the...
Associative Properties for addition:
(a + b) + c = a + (b + c)
Subtraction of Real Numbers
Adding the opposite of a number is the same as
subtracting the number.
Definition of subtraction:
a – b = a + (–b)
Example: 25 – 47
=
25 + (–47) add the opposite
Now, use the rules for addition
=
–22
Example: 7 – (–2)
=
7 + 2 add the opposite
=
9
Hint: When you have 2 negatives in a row,
cross them both.
Example: 2 – (–5) – 5 + 3
2 + 5 + (–5) + 3 add the opposite
7 + (–5) + 3
2 +3
5