Problem 64 - Algebra 1: Concepts and Skills

Question

Use the distributive property and mental math to simplify the expression. $$ -8(2.80) $$

Step-by-Step Solution

Answer

-22.4

Step 1: Identify Operation

We first identify that this is a simple multiplication of -8 by 2.80.

Step 2: Multiply

We then proceed to multiply -8 by 2.80, making sure to preserve the relevance of the decimal digits.

Step 3: Write Down the Result

Finally, we write down the result obtained from the multiplication.

Key Concepts

Mental Math

Mental math is an essential skill that helps simplify complex calculations without the need for a calculator or pen and paper. When thinking about mental math in the context of the given exercise, the goal is to break down numbers into manageable parts. For the expression \(-8 imes 2.80\), you can break down 2.80 into simpler components like 2 and 0.80. This method makes it easier to handle numbers and reduces the chance of errors.

• First, think of \(2.80\) as \(2 + 0.80\).
• Next, apply \(-8\) to each component separately.
• Calculate \(-8 imes 2\) which equals \(-16\), and \(-8 imes 0.80\) which equals \(-6.4\).

Now, you combine these results to get the final answer of \(-16 - 6.4 = -22.4\). This showcases how mental math, along with the distributive property, can simplify multiplication involving decimals.

Multiplication

In the context of multiplication, especially when applied to the distributive property, it's crucial to know the core operation rules. Multiplication involves combining groups of equal size. In our expression, \(-8 imes 2.80\), we are determining how much is in \(-8\) groups of \(2.80\). The multiplication operation is straightforward because:

• Each part of the expression is multiplied separately.
• The negative sign in \(-8\) indicates that our groups will be negative, affecting the final result.

Understanding the role of multiplication within the distributive property simplifies complex expressions and leads to accurate results.

Simplification

Simplification is the process of reducing an expression to its simplest form, making calculations easier and quicker. In our exercise involving \(-8(2.80)\), simplification is achieved by:

• Breaking down the problem using the distributive property to handle \(2.80\) as \(2 + 0.80\).
• Performing two smaller multiplications, \(-8 imes 2\) and \(-8 imes 0.80\).
• Combining the results to form a simpler answer.

This method not only helps in finding the result more efficiently but also aids in understanding and mental visualization of mathematical concepts. Simplification is not just about altering the numbers but is also about using the steps to reach the simplest true form of an expression, ensuring clarity and accuracy.