Problem 305 - Prealgebra

Question

In the following exercises, simplify. $$947\cdot 0$$

Step-by-Step Solution

Answer

0

Step 1: Identify the Multiplication Operation

Recognize that the exercise requires multiplying the number 947 by 0.

Step 2: Apply the Multiplication Property of Zero

Recall that any number multiplied by 0 is 0. This is known as the Multiplication Property of Zero.

Step 3: Simplify the Expression

Using the Multiplication Property of Zero, simplify the expression: \[947 \times 0 = 0\]

Key Concepts

Basic Arithmetic

Basic arithmetic is the foundation of mathematics. It includes operations like addition, subtraction, multiplication, and division. Each arithmetic operation has its own set of rules and properties. Multiplication, for instance, involves calculating the product of two numbers.
One of the key properties in multiplication is the Multiplication Property of Zero. This property states that any number, no matter how large or small, multiplied by zero will always equal zero. It's a very useful shortcut in calculations.
For example, in the given exercise, we have to multiply 947 by 0. Using the Multiplication Property of Zero, we can directly conclude that the result is 0. No further calculations are needed.

Simplifying Expressions

Simplifying expressions involves reducing them into their most basic form. This often makes the expressions easier to work with and understand. In our exercise, we simplified the expression by applying the Multiplication Property of Zero.
Here’s a quick reminder on how to simplify expressions using this property:

• First, identify the multiplication operation.
• Recall that any number multiplied by 0 equals 0.
• Simplify the expression by applying this rule.

For example, when presented with \[947 \times 0\], we recognize that we can directly apply the multiplication property of zero, simplifying the expression to 0 with no further steps required. This saves us time and reduces complexity.

Prealgebra Concepts

Prealgebra sets the stage for higher mathematical learning. It introduces important principles and properties that will be frequently used in subsequent math courses. One crucial prealgebra concept is understanding the properties of numbers.
A key property introduced in prealgebra is the Multiplication Property of Zero. This property is fundamental and frequently appears in algebra and beyond. Knowing that any number multiplied by zero results in zero helps students simplify complex problems quickly.
Let's look at our example: \[947 \times 0\]. By applying our knowledge of the multiplication property of zero, we instantly know the result is 0. Recognizing and using such properties is a vital skill in prealgebra, making calculations quicker and more efficient.