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Introduction:

Addition is a fundamental mathematical operation that is used to find the total value or sum of two or more numbers. It is one of the four basic operations of arithmetic, along with subtraction, multiplication, and division. Addition is a crucial skill that is taught to students from an early age and is used in everyday life, from calculating a restaurant bill to determining the total amount of money in a savings account.

Definitions:

• Number: A number is a mathematical object used to count, label, and measure. There are several types of numbers, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
• Addend: An addend is a number that is added to another number in an addition problem. For example, in the problem 2 + 3, the numbers 2 and 3 are the addends.
• Sum: The sum is the result of an addition problem. In the problem 2 + 3, the sum is 5.
• Plus sign: The plus sign (+) is used to indicate that two or more numbers should be added together.
• Equal sign: The equal sign (=) is used to show that the value on the left side of the sign is equal to the value on the right side.

Examples:

1. Two-digit addition: In this example, we will add two two-digit numbers using the traditional method of carrying and borrowing.

Problem: 37 + 28

Solution:

First, we add the ones digit of the two numbers: 7 + 8 = 15. Since 15 is greater than 9, we carry the 1 to the tens place.

Next, we add the tens digit of the two numbers along with the carried 1: 3 + 2 + 1 = 6.

Finally, we write down the sum of 6 in the tens place and the remainder of 5 in the ones place.

The final answer is 65.

2. Three-digit addition: In this example, we will add three three-digit numbers using the traditional method of carrying and borrowing.

Problem: 123 + 456 + 789

Solution:

First, we add the ones digit of the three numbers: 3 + 6 + 9 = 18. Since 18 is greater than 9, we carry the 1 to the tens place.

Next, we add the tens digit of the three numbers along with the carried 1: 2 + 5 + 8 + 1 = 16. Since 16 is greater than 9, we carry the 1 to the hundreds place.

Finally, we add the hundreds digit of the three numbers along with the carried 1: 1 + 4 + 7 + 1 = 13.

The final answer is 1368.

3. Decimal addition: In this example, we will add two decimal numbers using the traditional method of aligning the decimal points and carrying.

Problem: 3.14 + 2.7

Solution:

First, we align the decimal points and add the numbers: 3.14 + 2.7

Next, we add the numbers in the ones place: 4 + 7 = 11. Since 11 is greater than 9, we carry the 1 to the tens place.

Finally, we add the numbers in the tens place along with the carried 1: 1 + 3 + 2 + 1 = 7.

The final answer is 6.84.