Problem 40 - Elementary Algebra

Question

Simplify. $$ -24(0) \div 8 $$

Step-by-Step Solution

Answer

The simplified expression is 0.

Step 1: Identify the Expression

The expression to simplify is \(-24(0) \div 8\). This involves a multiplication by zero and a division.

Step 2: Multiplication by Zero

Any number multiplied by zero equals zero. Therefore, \(-24 \times 0 = 0\).

Step 3: Division of Zero

Zero divided by any non-zero number is zero. So, \(0 \div 8 = 0\).

Step 4: Final Simplification

After performing these operations, the expression simplifies to zero.

Key Concepts

Multiplication by Zero

In algebra, multiplication by zero is a very straightforward operation. When any number, whether positive or negative, is multiplied by zero, the result is always zero. This is because zero represents the absence of quantity. For example, think about taking any number of groups of nothing—no matter how many groups you have, if there's nothing in each group, you still end up with nothing at all. Therefore, when we have -

• -24 multiplied by zero,

like in the original problem, the outcome is simply zero. This basic rule helps simplify expressions and solve equations efficiently.

Division in Algebra

Division in algebra is distributing a number equally into groups. It's crucial in algebra to understand how division interacts with other operations like multiplication, especially where zero is involved. When we divide zero by a non-zero number, the result is always zero. This concept can be considered in terms of sharing: if you have zero apples and share them among any number of people, each person still ends up with zero apples. This is shown when the original exercise simplifies to -

• zero divided by eight,

and we conclude that -

• the answer is zero.

On the other hand, remember that division by zero is undefined because dividing something into zero parts doesn't make sense. Understanding these principles helps streamline algebraic problem-solving.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Each has its own set of rules and behaviors that are fundamental to understanding more complex algebraic concepts. While addition combines quantities, subtraction takes them apart. Multiplication, as previously mentioned, is like repeated addition, and division breaks them into parts. For example, when dealing with multiplication and division in algebraic expressions:

• Multiplying any number by zero always results in zero
• Dividing zero by a non-zero number ends in zero

These rules make it easier to navigate algebraic simplifications such as in the original exercise where both operations lead to -

• a final result of zero.

Being comfortable with these rules is crucial for tackling algebra with confidence and precision.