Answer the following with the Interesting Integers Presentation:
Section 1
1. 8 + 13 =
2. –22 + 11 = 3. 55 + 17 = 4. –14 + 35 = 
Section 2
1. –12 + 22 =
2. –20 + 5 = 3. 14 + (7) = 4. –70 + 15 = 
Section 3
1. 8 – (12) = 8 + 12 = 20
2. 22 – (30) = 22 + 30 = 52 3. – 17 – (3) = 17 + 3 = 14 4. –52 – 5 = 52 + (5) = 57 
Final Section
3 – 10 =
17 – (12) = 20 – ( 5) = 7 – (2) 


Additive IdentityFind the definition of this term somewhere in the following lesson.

Multiplicative IdentityFind the definition of this term somewhere in the following lesson.

Adding Signed Numbers
In this section we will study how to add positive and negative numbers. The next few sections will introduce the subtraction, multiplication and division of positive and negative numbers. These are probably the MOST IMPORTANT sections of this class. Understanding how to add, subtract, multiply and divide signed numbers will be utilized in every section of this course. Many times when students have trouble with problems in later sections, it is really a problem with working with signed numbers. Make sure you make every effort to understand these next few sections. We will start with an explanation of absolute value.
Absolute Value
The absolute value of a number is the distance between that number and zero on the number line with no regard for direction. The symbol for the absolute value of a real number x is x.
Find the following absolute values:
a.  3  b.  3  c.  0  d.  5  e.  5  f.   5  
a. 3 b. 3 c. 0 d. 5 e. 5 f. 5 
Notice that the absolute value of a number can not be a negative number. Notice in this case, there is a negative outside the absolute value symbol! 
Adding Integers and Other Signed Numbers
Many times people say that algebra doesn't make sense. When adding signed numbers, it appears that sometimes we actually add the numbers but in other cases it appears we really subtract. Remembering that mathematics was created to help us wrok with real life situations should help us understand the rules associated with the adding of signed numbers. This section will take an everyday life and everyday language approach to the understanding of the addition of signed numbers and will then generalize to some traditional mathematical properties. Some of the best examples of positive numbers and negative numbers being combined in real life are associated with our personal finances. We will therefore take this as our approach in presenting the operations involving signed numbers.
The answer to an addition problem is called the sum.
The numbers being added together are called the 'addends' or 'terms'.
Add 5 and 3.
The answer to the proposed problem is obviously 8. Think about if this a little more in order to understand what would happen if these two numbers weren't both positive numbers. Again, we realize we really are familiar with positive and negative numbers when we think about the concept of money. We can think about positive as deposits in a new checking account. We can think about negatives as checks we have written from our checking account.
Thinking this way 5 + 3 would represent a 5 dollar deposit combined with a 3 dollar deposit in a new checking account for a balance of 8 dollars.
Add 5 and 7.
In this case we can think of the 5 as owing 5 dollars and the 7 as having 7 dollars. This would mean that we would be left with 2 dollars, since we have more than we owe. Therefore, the sum of  5 + 7 is 2.
We can also think about the situation as having a new checking account where we in one month have written a check for 5 dollars (  5 ) and make a deposit of 7 dollars. This would equate to find a final balance of 2 dollars. Therefore 5 + 7 = 2
Add 5 and 7
In this case we can think of 5 as having 5 dollars in our pocket and the 7 as owing 7 dollars to a friend. This means we can give our friend the 5 we have but we still owe him 2 dollars. The result is negative since we owe more than we have. In other words, the result of combining of a 5 and 7 is 2.
We can also think of this situation as having a new checking account where we in one month have deposited 5 dollars but have written a check for 7 dollars. This would not be good since we would be overdrawn 2 dollars. Our ending balance would be overdrawn by 2 dollars. 5 + 7 = 2.
Add 5 and 3
In this case we can think of owing two different friends money. We owe one friend 5 dollars (5) and another 3 dollars (3). This means we owe a total of 8 dollars. In other words, combining 5 and 3 gives us 8. Some students will say 'but I thought two negatives make a positive!' You will find later that two negatives make a positive for multiplication and division but not for addition. It would be great if saying we owed one friend 5 dollars (5) and another 3 dollars (3) meant we had 8 dollars but this would not make sense.
Therefore, 5 + 3 = 8.
Add 3 and 0.
For many, the answer is obviously 3 since any real number plus zero equals itself. Let's show that this same answer is achieved with the personal finance approach. In this case, we can think of owing a friend 3 dollars (3) but having no money in our pocket. This means we are left owing our friend 3 dollars (3).
We can also think again of a new checking account. In this case, we write a check for 3 dollars (3). The only problem is we never made a deposit. The bank would not like us very much since we would be overdrawn 3 dollars (3). Therefore, 3 + 0 = 3.
ADDITIVE IDENTITY: Zero is referred to as the ADDITIVE Identity since a + 0 = a for all real numbers a. We say that 3 + 1 = 3 by the 'additive identity property (or the additive property of zero).
MULTIPLICATIVE IDENTITY: One is referred to as the multiplicative identity since a * 1 = a for all real numbers a. We say that 3 * 1 = 3 by the multiplicative identity property.
The answer to an addition problem is called the sum.
The numbers being added together are called the 'addends' or 'terms'.
Add 5 and 3.
The answer to the proposed problem is obviously 8. Think about if this a little more in order to understand what would happen if these two numbers weren't both positive numbers. Again, we realize we really are familiar with positive and negative numbers when we think about the concept of money. We can think about positive as deposits in a new checking account. We can think about negatives as checks we have written from our checking account.
Thinking this way 5 + 3 would represent a 5 dollar deposit combined with a 3 dollar deposit in a new checking account for a balance of 8 dollars.
Add 5 and 7.
In this case we can think of the 5 as owing 5 dollars and the 7 as having 7 dollars. This would mean that we would be left with 2 dollars, since we have more than we owe. Therefore, the sum of  5 + 7 is 2.
We can also think about the situation as having a new checking account where we in one month have written a check for 5 dollars (  5 ) and make a deposit of 7 dollars. This would equate to find a final balance of 2 dollars. Therefore 5 + 7 = 2
Add 5 and 7
In this case we can think of 5 as having 5 dollars in our pocket and the 7 as owing 7 dollars to a friend. This means we can give our friend the 5 we have but we still owe him 2 dollars. The result is negative since we owe more than we have. In other words, the result of combining of a 5 and 7 is 2.
We can also think of this situation as having a new checking account where we in one month have deposited 5 dollars but have written a check for 7 dollars. This would not be good since we would be overdrawn 2 dollars. Our ending balance would be overdrawn by 2 dollars. 5 + 7 = 2.
Add 5 and 3
In this case we can think of owing two different friends money. We owe one friend 5 dollars (5) and another 3 dollars (3). This means we owe a total of 8 dollars. In other words, combining 5 and 3 gives us 8. Some students will say 'but I thought two negatives make a positive!' You will find later that two negatives make a positive for multiplication and division but not for addition. It would be great if saying we owed one friend 5 dollars (5) and another 3 dollars (3) meant we had 8 dollars but this would not make sense.
Therefore, 5 + 3 = 8.
Add 3 and 0.
For many, the answer is obviously 3 since any real number plus zero equals itself. Let's show that this same answer is achieved with the personal finance approach. In this case, we can think of owing a friend 3 dollars (3) but having no money in our pocket. This means we are left owing our friend 3 dollars (3).
We can also think again of a new checking account. In this case, we write a check for 3 dollars (3). The only problem is we never made a deposit. The bank would not like us very much since we would be overdrawn 3 dollars (3). Therefore, 3 + 0 = 3.
ADDITIVE IDENTITY: Zero is referred to as the ADDITIVE Identity since a + 0 = a for all real numbers a. We say that 3 + 1 = 3 by the 'additive identity property (or the additive property of zero).
MULTIPLICATIVE IDENTITY: One is referred to as the multiplicative identity since a * 1 = a for all real numbers a. We say that 3 * 1 = 3 by the multiplicative identity property.
Write the following definitions in your math journal.
IntegersPositive or negative numbers
Positive NumberA number to the right of the 0 (zero) on the number line.
Negative NumberA number to the left of the 0 (zero) on the number line.
Rules for Adding IntegersIf the addends have the same sign, add and keep.
Remember: Same sign, add and keep. (+62) + (+14) = 76 (29) + (13) =  42 If the addends have different signs, find the difference between the two numbers and keep the sign of the largest number. Remember: Different signs, subtract. Keep the sign of the highest numbers. Then you will be exact. Integers Practice

Rules for subtracting integersBecause every subtraction problem can be rewritten as a corresponding addition problem you should be able to add its opposite.
Let's take a look at the following problem: (8)  (+9) = Change the sign to the opposite: (8) + (9) = The answer is 17. Let's look at some examples. (+7)  (+4) = (+7) + (4) = The answer is +3 Try these two on your own. (+5)  (6) = (3)  (+8) = Another way to subtract signed numbersChange double negatives to a positive.
Get a sum of terms with the like signs and keep the given sign, using the sign in front of the number as the sign of the number. Find the difference when terms have different signs and use the sign of the larger numeral. Here are some examples. 7  (5) = 7 + 5 = 12 We changed the double negatives to positive and used the integer addition rules. (5)  9 = 14 We used the signs in front of the numbers and used only addition rules: Same Signs Add and Keep. 6  7 = 1 We used the signs in front of the numbers. Use the addition rules when signs are different. Different Signs, Subtract 6  7 + 3  4  2 = Get the sume of the like terms and use the addition rules. 6 + 3 = 9 7 + ( 4) + (2) = 13 9 + (13) = 4 