Addition

Addition 

Addition is a fundamental arithmetic operation used to combine two or more numbers to find their total or sum. In simple terms, when you add two numbers, you are putting them together to get a single value that represents their combined quantity.

The symbol used for addition is “+”, and the numbers being added are called addends. The result of the addition is called the sum.

For example: 1 + 2 = 3 In this case, 1 and 2 are the addends, and their sum is 3.

Here’s a step-by-step explanation of addition:

Addends: The numbers you want to add together are called addends. For example, let’s consider two addends, A and B.

Plus Sign (+): The plus sign “+” indicates that you are performing the addition operation. It shows that the numbers on its left and right sides will be added together.

Sum: The result of the addition is called the sum. This is the total value obtained after adding the addends.

The addition process: To add two numbers A and B:

♦. Write the numbers A and B next to each other, separated by the “+” sign. For example:  + B.

♦. Starting from the rightmost digits of both numbers, add the digits in the same column. If the sum of the digits is 10 or greater, you write down only the rightmost digit of the result and carry over the leftmost digit to the next column.

♦. Move to the next column to the left and repeat the addition process for the digits in that column, including any carried-over values.

♦. Continue this process until you have added all the columns.

♦. The final result is the sum of the addends.

Example 1: Adding two-digit numbers

   34
+ 25
——-
   59

Example 2: Adding larger numbers

Properties of Addition:

♦. Commutative Property: Changing the order of the addends does not affect the sum. A + B = B + A

♦. Associative Property: Grouping the addends differently does not affect the sum. (A + B) + C = A + (B + C)

♦. Identity Property: Adding zero to any number leaves the number unchanged. A + 0 = A

♦. Inverse Property: Every number has an additive inverse (or opposite), such that adding the inverse to the number results in zero. A + (-A) = 0

Addition is a foundational concept in mathematics and is widely used in various fields, from simple daily calculations to advanced mathematical problems and real-world applications.

 

Addition Table

+	0	1	2	3	4	5	6	7	8	9
0	0	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9	10
2	2	3	4	5	6	7	8	9	10	11
3	3	4	5	6	7	8	9	10	11	12
4	4	5	6	7	8	9	10	11	12	13
5	5	6	7	8	9	10	11	12	13	14
6	6	7	8	9	10	11	12	13	14	15
7	7	8	9	10	11	12	13	14	15	16
8	8	9	10	11	12	13	14	15	16	17
9	9	10	11	12	13	14	15	16	17	18

Addition without regrouping:

Addition without regrouping, also known as carrying, is the process of adding two or more numbers without requiring any adjustments or carrying over to the next place value. Let’s look at an example:

Example: 24 + 15

Step 1: Start by aligning the numbers vertically with the units (ones) placed lined up.

   24
+ 15
 —–

Step 2: Add the digits in the unit place (4 + 5)

   24
+ 15
 —–
    9

Step 3: Now, move to the tens place and add the digits (2 + 1)

   24
+ 15
 —–
   39

Step 2: Add the digits in the unit place (8 + 9):

   68
+ 29
 —–
   17        (write 7, carry over 1 to the tens place)

So, 68 + 29 = 97 without regrouping in this example either.

In both examples, we didn’t need to regroup or carry over any digits because the sum of each place value didn’t exceed 9.

Addition with regrouping:

Addition with regrouping, also known as carrying, is the process of adding two or more numbers where the sum of any place value exceeds 9. When this happens, you carry the value over to the next place value before calculating the next digit. Let’s go through an example:

Example: 57 + 49

Step 1: Align the numbers vertically with the units (ones) placed lined up.

    57
+ 49
——-

Step 2: Add the digits in the unit place (7 + 9):

   57
+ 49
——-
   16      (write 6, carry over 1 to the tens place)

Step 3: Move to the tens place and add the digits, including the carried-over 1 (1 + 5 + 4):

                                                                                                                                                                                                         

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