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Chapter 1: Problem 765

Simplify. $$ 0 \cdot \frac{8}{15} $$

Short Answer

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Step by step solution

01

Identify the Multiplication Property of Zero

In mathematics, any number multiplied by zero is always zero. This is known as the Multiplication Property of Zero.
02

Apply the Property to the Expression

Here, the expression is \(0 \times \frac{8}{15}\). According to the Multiplication Property of Zero, multiplying zero by any number will result in zero.
03

Simplify the Expression

Applying the property, \(0 \times \frac{8}{15} = 0\)

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Key Concepts

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

simplifying expressions
When simplifying expressions, we break them down to their simplest form. This helps in solving math problems more easily and accurately. Consider the expression given in the exercise:

\(0 \times \frac{8}{15}\)

To simplify this expression, we need to apply the rules and properties of arithmetic operations.
basic algebra
Basic algebra involves learning and applying rules that help us solve equations and simplify expressions. In our case, we need to use the Multiplication Property of Zero, which is a fundamental algebraic rule.

This property states that any number multiplied by zero equals zero. It doesn鈥檛 matter what the other number is, be it a fraction, a large integer, or even another algebraic expression.

Knowing and using properties like this simplifies our work in many areas of math.
multiplication rules
Multiplication rules in mathematics guide us on how to carry out multiplication effectively. The rule relevant to this exercise is the Multiplication Property of Zero:

\begin{itemize}
  • Multiplication Property of Zero: For any number a, \(a \times 0 = 0\).


    • This rule is incredibly powerful for simplifying expressions. In our provided expression \(0 \times \frac{8}{15}\), zero multiplied by any fraction or number will always result in zero. Therefore, \(0 \times \frac{8}{15} = 0\).

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