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Chapter 7: Problem 182

Simplify using the properties of zero. 0\(\cdot \frac{8}{15}\)

Short Answer

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Step by step solution

01

Understand the Zero Property of Multiplication

The Zero Property of Multiplication states that any number multiplied by zero is equal to zero. This is because zero times any quantity results in zero.
02

Apply the Zero Property

Apply the Zero Property of Multiplication to the given expression. This means multiplying 0 by \(\frac{8}{15}\).
03

Simplify the Expression

Using the Zero Property, simplify the expression: 0 \cdot \(\frac{8}{15}\) = 0.

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Key Concepts

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

Understanding Properties of Zero
The Properties of Zero are very straightforward yet powerful.
The most important one in multiplication is known as the Zero Property of Multiplication.
This property states: any number multiplied by zero is always zero.
It doesn鈥檛 matter how large or complicated the number might be. Whether it's a fraction, a whole number, or any other numeral, multiplying by zero will always result in zero.
This rule applies universally and helps us simplify many mathematical expressions easily.
Fundamental Multiplication Rules
To understand why the Zero Property of Multiplication works, let's look at some basic multiplication rules.
When we multiply two numbers, we are combining groups of things.
Let's say we have 3 groups of 5 apples. Multiplying 3 by 5 tells us there are 15 apples in total.
But what if we have 0 groups of 5 apples? It means we have no apples at all!
That's why any number multiplied by zero results in zero because you have zero groups of that number.
This rule helps us carry out multiplications effectively and is essential for simplifying expressions.
Simplifying Expressions with Zero Property
Simplifying expressions becomes much easier when you apply the Zero Property of Multiplication.
Let's take a practical example from the given exercise: 0 \cdot \( \frac{8}{15} \).
First, note the number you are multiplying by zero. It could be a fraction or any other number.
According to the Zero Property of Multiplication, no matter what the other number is, your expression simplifies directly to 0.
So, 0 \cdot \( \frac{8}{15} \) simplifies to 0 automatically.
This simplification rule helps to quickly solve and simplify complex mathematical problems involving multiplication.

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