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Chapter 5: Problem 85

State the distributive property of multiplication over addition and give an example.

Short Answer

Expert verified
The distributive property of multiplication over addition states that, for any real numbers \( a \), \( b \), and \( c \), \( a \cdot (b + c) = a \cdot b + a \cdot c \). An example is: \( 3 \cdot (4 + 5) = 3 \cdot 4 + 3 \cdot 5 \) or \( 27 = 27 \).

Step by step solution

01

State the Distributive Property

The distributive property of multiplication over addition is a fundamental property of numbers which states that the sum of two numbers times a third number is equal to the sum of each addend times the third number. It can be expressed algebraically as:For any real numbers \( a \), \( b \), and \( c \), \( a \cdot (b + c) = a \cdot b + a \cdot c.\)
02

Illustrate with an Example

To illustrate the distributive property, consider \( a = 3 \), \( b = 4 \), and \( c = 5 \):Applying the distributive property, we have: \( 3 \cdot (4 + 5) = 3 \cdot 4 + 3 \cdot 5 = 12 + 15 = 27\). When checking the left side of the equation, we find that: \( 3 \cdot (4 + 5) = 3 \cdot 9 = 27\).Both sides of the equation match, confirming the distributive property.

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