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Chapter 5: Problem 81

State the commutative property of addition and give an example.

Short Answer

Expert verified
The commutative property of addition states that we can change the order of the numbers we are adding and still get the same sum. An example is: 2 + 3 = 5 and 3 + 2 = 5.

Step by step solution

01

Statement of the Commutative Property of Addition

The commutative property of addition states that changing the order of addends does not change the sum. It is expressed as: if \( a \) and \( b \) are any numbers, then \( a + b = b + a \).
02

Provide an Example

An example of the commutative property of addition using real numbers is: Let \( a = 2 \) and \( b = 3 \). Then \( a + b = 2 + 3 = 5 \), and \( b + a = 3 + 2 = 5 \). Therefore, \( a + b = b + a \) is verified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition
Addition is one of the fundamental operations in basic arithmetic. It is a process where two or more numbers, called addends, are combined to form a sum. This operation is symbolized by the plus sign "+". In simpler terms, addition means putting things together:

* When you add 3 apples to 2 apples, you end up with 5 apples.
* It doesn't matter which number you start adding from, the result will remain the same, thanks to the commutative property.

Addition forms the base for learning other arithmetic operations like subtraction, multiplication, and division. Understanding how addition works helps in solving more complex math problems efficiently.
Mathematical Properties
Mathematical properties are rules or laws that describe numbers and their relationships in mathematics. These properties ensure predictable and reliable results in calculations.

One of the well-known mathematical properties is the commutative property, applied to addition and multiplication. This property allows you to rearrange numbers in an equation without changing the outcome.

For example, with addition, the commutative property states:
\[ a + b = b + a \]
This means if you add 5 and 7, you get the same result as adding 7 and 5; both will yield 12.
Basic Arithmetic
Basic arithmetic is the foundation of all mathematics. It involves four primary operations: addition, subtraction, multiplication, and division. Each operation has properties that make calculations simpler and more flexible.

These operations are used in everyday activities such as counting, shopping, and measuring objects. Understanding basic arithmetic helps in developing problem-solving skills and logical thinking.
  • Without a solid understanding of arithmetic, advancing to more complex math topics would be challenging.
  • Learning arithmetic properties, like the commutative property, aids in faster computation and accuracy.
Real Numbers
Real numbers include all the numbers you interact with daily on a number line. These numbers consist of both rational numbers (like fractions and integers) and irrational numbers (like 鈭�2 and 蟺).

Real numbers have several properties that ensure consistent behavior in mathematical operations:
  • They can be positive, negative, or zero.
  • You can add, subtract, multiply, and divide them all while maintaining their inherent properties.
The commutative property of addition applies to real numbers, confirming that changing the order of addition does not affect the sum, making calculations flexible and intuitive.

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Most popular questions from this chapter

What is a sequence? Give an example with your description.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-9,-5,-1,3, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=1,000,000, r=0.1\).

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{100}\), when \(a_{1}=50, r=1\).
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