Addition is a fundamental operation in mathematics, which involves combining two or more numbers to get a sum. In this lesson, we will explore the basic concepts of addition, the notation used, and the properties of addition.
Basic Concepts of Addition
The basic concept of addition involves combining two or more numbers to get a sum. For example, 2 + 3 = 5, where 2 and 3 are the addends and 5 is the sum. Addition can also be thought of as counting on, where you start with the first addend and count up by the value of the second addend.
Notation Used in Addition
Addition is represented using the plus sign (+).
For example, 2 + 3 = 5. The numbers being added are called addends, and the result of the addition is called the sum.
Properties of Addition
Addition has several properties that make it a useful operation in mathematics:
Commutative Property: The order of the addends does not affect the sum.
For example, 2 + 3 = 3 + 2 = 5.
Associative Property: The grouping of the addends does not affect the sum.
For example, (2 + 3) + 4 = 2 + (3 + 4) = 9.
Identity Property: The sum of any number and 0 is the number itself.
For example, 5 + 0 = 5.
Inverse Property: The sum of a number and its additive inverse (the negative of the number) is 0. For example, 5 + (-5) = 0.
Now that you have learned about the basic concepts and properties of addition, let’s try a practice exercise.
Calculate the sum of the following:
a. 7 + 8 = ?
b. 15 + 22 = ?
c. 3 + 0 = ?
d. 10 + (-3) = ?
Identify which property of addition is illustrated in the following: a. 2 + 5 = 5 + 2 b. (4 + 6) + 3 = 4 + (6 + 3) c. 5 + 0 = 5 d. 7 + (-7) = 0
a. Commutative Property
b. Associative Property
c. Identity Property
d. Inverse Property
Addition is a foundational concept in mathematics and is used in various fields such as physics, engineering, and finance. By understanding the basic concepts and properties of addition, you can perform calculations with ease and accuracy. Remember to use the correct notation, apply the properties of addition, and check your work to ensure that your calculations are correct.