Problem 20 - Beginning and Intermediate Algebra

Question

Find each product. \(-0.3(0)\)

Step-by-Step Solution

Answer

0

Step 1: Understanding the Multiplication Property

Multiplying any number by zero always results in zero. This is known as the zero property of multiplication.

Step 2: Applying the Zero Property

In the given problem, \(-0.3(0)\), the number \(-0.3\) is being multiplied by zero. According to the zero property, the product will be zero.

Key Concepts

multiplication

Multiplication is one of the basic operations in arithmetic. It involves finding the product of two numbers. The numbers involved in multiplication are called 'factors'. When you multiply numbers, you are essentially adding the same number multiple times.
For example, if you multiply 3 by 4, you are adding 3 four times: \(3 + 3 + 3 + 3 = 12\).

Key points to remember about multiplication:

• Any number multiplied by 1 remains unchanged. This is called the identity property of multiplication.


• Multiplication is commutative. This means the order of factors doesn’t change the product: \(a \cdot b = b \cdot a\).

Multiplication is also associative: \((a \cdot b) \cdot c = a \cdot (b \cdot c)\). Understanding these properties helps make multiplication simpler and ensures you're applying the operation correctly.

properties of numbers

Numbers have unique properties that govern how they interact with one another. These properties help us perform arithmetic operations more efficiently. Let's explore a few key properties relevant to our exercise:

• Zero Property of Multiplication: This property states that any number multiplied by zero results in zero, as seen in the problem \(-0.3(0) = 0\).


• Identity Property: The product of any number and 1 remains that number, e.g., \(7 \cdot 1 = 7\).

Using these properties can simplify problem-solving and make arithmetic operations easier to understand.

basic arithmetic

Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division. These operations are the foundation for most math problems you'll encounter.
Here’s a brief overview of each:

• Addiction: Combining two or more numbers to get a sum.


• Subtraction: Determining the difference between numbers by removing one from another.


• Multiplication: Repeated addition of the same number.


• Division: Splitting a number into equal parts.

Each arithmetic operation follows specific rules and properties, like the zero property of multiplication, to make calculations consistent and predictable. By mastering these basics, you’ll be better equipped to tackle more complex math problems.