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Chapter 7: Problem 174

Simplify using the properties of zero. 48\(\cdot 0\)

Short Answer

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Step by step solution

01

- Understand the Property of Zero

Any number multiplied by zero equals zero. This is known as the property of zero in multiplication.
02

- Apply the Property of Zero

Using the property of zero, simplify the multiplication. Here, 48 multiplied by 0 equals 0.

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Key Concepts

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

Multiplication
Multiplication is one of the fundamental operations in mathematics, along with addition, subtraction, and division. It's essentially repeated addition. For example:
When we say 3 multiplied by 4, it means adding 3 four times, like this: 3 + 3 + 3 + 3 = 12.

Multiplication is symbolized by different notations, such as the asterisk (*) or the multiplication dot (鈰�). For instance, we can write: 3 * 4 or 3鈰�4.

Multiplication has several key properties:
  • Commutative Property: a * b = b * a
  • Associative Property: (a * b) * c = a * (b * c)
  • Distributive Property: a * (b + c) = a * b + a * c
But one of the most impactful ones for this problem is the property of zero.
Zero Property
The zero property of multiplication states that any number multiplied by zero is zero. This holds true for all numbers, whether positive, negative, or even fractions.

For example:
  • 5鈰�0 = 0
  • -7鈰�0 = 0
  • 3.14鈰�0 = 0
This property is extremely useful in simplifying mathematical expressions, as it allows us to reduce complex multiplications quickly.

Understanding this property is vital because it shows the importance of zero in multiplication. Any term in a product that is zero ultimately makes the entire product zero. This brings us to our example.
Simplification
Simplifying an expression makes it easier to understand and work with.

In our example, we aim to simplify the expression 48鈰�0 using the zero property. Here鈥檚 how we do it:

Step 1: Recognize the property of zero in multiplication (any number multiplied by zero is zero).

Step 2: Apply this property to the given expression: Since 48 is being multiplied by zero, we directly use the zero property: 48鈰�0 = 0.

Therefore, the simplified form of 48鈰�0 is 0. Simplifying mathematical expressions highlights the simplicity behind seemingly complex operations, making problems much more approachable.

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