I. Intro
One of the four elementary mathematical operations, addition is the process of combining two or more numbers to find their total.The symbol for addition is +.
The numbers being added are called addends and the answer is called the sum.
Horizontal vs Vertical Form
When adding with whole numbers we can write the problem horizontally or vertically.
Horizontal Form
4 + 3 = 7
Vertical Form
4
+3
7
Verbally Expressing Addition Problems
There are many ways to say addition problems. Here are a few common ways of saying 4 + 3:
- Four plus three
- Four added to three
- Add three to four
- Four and three
- The sum of four and three
The standard algorithm for addition has three simple rules.
1) line up the numbers being added vertically by their place value.
2) From right to left, add the digits in each corresponding column.
3) If the total of the digits in any place value column produces a sum greater than 9, carry to the next place value (now known as regrouping).
Carrying (Regrouping)
Regrouping is essentially the rearranging of a number into different groups to make them easier to work with. Regrouping when doing addition used to be referred to as carrying.
For instance, add together the numbers 45 and 17.
45
+17
First we add the numbers in the ones place: 5+7=12. As only one number can go into each place column, we regroup the 12 into one 10 and two 1's. We then put the two 1's (the number 2) in the ones place and carry the one 10 to the tens place. This is represented by writing a small 1 over the tens place column.
1
45
+17
2
Finally, we add the numbers in the tens place: 1+4+1=6
1
45
+17
62
Carrying (Regrouping)
Regrouping is essentially the rearranging of a number into different groups to make them easier to work with. Regrouping when doing addition used to be referred to as carrying.
For instance, add together the numbers 45 and 17.
45
+17
First we add the numbers in the ones place: 5+7=12. As only one number can go into each place column, we regroup the 12 into one 10 and two 1's. We then put the two 1's (the number 2) in the ones place and carry the one 10 to the tens place. This is represented by writing a small 1 over the tens place column.
1
45
+17
2
Finally, we add the numbers in the tens place: 1+4+1=6
1
45
+17
62
III. Conceptual Understanding
Addition can be illustrated with use of a number line. To calculate 4 + 3, we begin at 0 then move 4 units to the right. This represents 4. To add in the number 3, from where we left off, we move 3 more units to the right. This leaves us at seven on the number line, the total of 4 + 3.
IV. Properties of Addition
The operation of addition has several important properties.
Commutative Property
Addition (as well as multiplication) is commutative, meaning the order of the numbers being added doesn't affect the sum. For instance,
3 + 6 = 9 is the same as 6 + 3 = 9.
Associative Property
Addition (and multiplication) is associative, meaning that when adding more than two numbers, the order in which addition is performed does not matter. For example:
(3 + 6) + 2 = 9 + 2 = 11 is the same as 3 + (6 + 2) = 3 + 8 = 11
Additive Identity Property
Additive identity property states that adding 0 to any number results in the number itself.
5 + 0 = 5
V. Inverse Operation
Inverse operations are opposite operations that undo each other. Addition and subtraction are inverse operations. For example:
7 + 3 = 10 then subtract to get back to where we started 10 - 3 = 7
VI. Miscellaneous
V. Inverse Operation
Inverse operations are opposite operations that undo each other. Addition and subtraction are inverse operations. For example:
7 + 3 = 10 then subtract to get back to where we started 10 - 3 = 7
VI. Miscellaneous
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