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Chapter 15: Problem 26

Simplify. $$ (-87)(0) $$

Short Answer

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Step by step solution

01

Understand the Multiplication Property of Zero

Any number multiplied by zero equals zero. This is known as the Multiplication Property of Zero.
02

Apply the Multiplication Property of Zero

In this exercise, the given expression is \((-87)(0)\). Applying the Multiplication Property of Zero gives us \((-87)(0) = 0\).

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Key Concepts

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

Simplification
Simplification generally means making an equation or expression easier to handle. When faced with an arithmetic expression, like \((-87)(0)\), we aim to simplify by applying known mathematical properties. Knowing the relevant properties and rules, like the Multiplication Property of Zero, helps achieve the simplest form quickly.
For example:
  • Combining like terms in algebraic expressions
  • Using basic arithmetic properties such as distribution, commutativity, and associativity

In this case, because we know the Multiplication Property of Zero, we can simplify \((-87)(0)\) directly to zero without further steps.
Multiplication
Multiplication is one of the fundamental arithmetic operations. It involves taking two numbers and finding their product. Here are some basic properties of multiplication:
  • Commutative Property: \(a * b = b * a\)
  • Associative Property: \( (a * b) * c = a * (b * c) \)
  • Identity Property: \( a * 1 = a \)

When multiplying, consider:
  • Each number's sign - multiplying two negatives makes a positive
  • Repetition - multiplication is repeated addition

In our example, even though \(((a)(b)]\)\
Zero Property of Multiplication
The Zero Property of Multiplication is a simple yet powerful rule. It states that any number multiplied by zero is zero. This property is universally accepted and can simplify problems immediately.
  • For example: \((-87)(0) = 0\)
  • Regardless of how large or small the number is, the result remains zero.
  • This highlights the unique nature of zero in multiplication.
The Zero Property makes solving algebraic expressions easier, as seen in our exercise. Without extra calculations, \((-87)(0)\) resolves to zero instantly.

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