Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:54 minutes

Problem 18

Textbook Question

State the name of the property illustrated: (3 • 7) + (4 • 7) = (4 • 7) + (3 •7)

Verified step by step guidance

Identify the operation being used in the expression: addition.

Notice that the order of the terms being added is changed: (3 \cdot 7) + (4 \cdot 7) becomes (4 \cdot 7) + (3 \cdot 7).

Recognize that the property allowing the change in order of addition is the Commutative Property of Addition.

The Commutative Property of Addition states that changing the order of addends does not change the sum.

Therefore, the property illustrated in the given expression is the Commutative Property of Addition.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Commutative Property of Addition

The Commutative Property of Addition states that the order in which two numbers are added does not affect the sum. In the context of the given equation, it illustrates that (3 • 7) + (4 • 7) can be rearranged to (4 • 7) + (3 • 7) without changing the result, emphasizing the flexibility of addition.

Associative Property of Addition

The Associative Property of Addition indicates that when adding three or more numbers, the way in which the numbers are grouped does not change the sum. Although not directly illustrated in the question, understanding this property helps in recognizing how addition can be manipulated in expressions involving multiple terms.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac, allowing for the multiplication of a single term across a sum or difference. In the equation provided, the expression (3 + 4) • 7 can be simplified using this property, demonstrating how multiplication interacts with addition in algebraic expressions.