This document defines integers and integer operations. It discusses:
- Integers are positive or negative whole numbers including 0.
- The four integer operations are addition, subtraction, multiplication, and division.
- Rules for adding, subtracting, multiplying and dividing integers determine whether the result is positive or negative based on the signs of the integers.
10. Rule #1 for
Adding Integers (+)
• The sum of two positive integers is
always positive.
5 + 1 = 6
11. Rule #2 for
Adding Integers (+)
• The sum of two negative integers is
always negative.
-5 + (-1) = -6
12. Rule #3 for
Adding Integers (+)
• The sum of a positive and a negative
integer could be positive, negative, or
zero.
13. Rule #3 for
Adding Integers Continued
• When you add a positive and negative
integer, you are really subtracting. Then,
you give the answer the sign of the
greater absolute value.
5 + (-1) = -4
-5 + 1 = 4
-5 + (-5) = 0
16. Rules for
Subtracting Integers (-)
• To subtract an integer, add its
opposite.
• You will need to correctly change all
subtraction problems into addition
problems!
18. There are three steps:
1. Keep the first integer the same.
(Same)
2. Change the subtraction sign into an
addition sign. (Change)
3. Take the opposite of the number that
immediately follows the newly placed
addition sign. (Change)
25. Rules for
Multiplying Integers (x)
• The product of two integers with the
same signs is POSITIVE.
• The product of two integers with
different signs is NEGATIVE.
26. Rules Summary for
Multiplication
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative= Negative
• Negative x Positive = Negative
31. • The rules for division are exactly
the same as those for multiplication.
• If we were to take the rules for
multiplication and change the
multiplication signs to division signs,
we would have an accurate set of
rules for division.
32. Rules for
Dividing Integers (÷)
• The quotient of two integers with
the same signs is POSITIVE.
• The quotient of two integers with
different signs is NEGATIVE.
44. ANSWER
• The sum of two positive integers is always
positive.
• The sum of two negative integers is always
negative.
• When you add a positive and negative
integer, you are really subtracting. Then, you
give the answer the sign of the greater
absolute value.
50. ANSWER
• If the signs are the same, your answer is
always positive.
• If the signs are different, your answer is
always negative.
*Multiplication and Division Rules are the
same!