Problem 12 - Fundamentals of Mathematics

Question

Use a calculator to find each value. $$ (-51.3) \cdot(-21.6) $$

Step-by-Step Solution

Answer

The result is 1108.08.

Step 1: Set Up the Expression

We need to multiply two negative numbers: \(-51.3\) and \(-21.6\). Write down the expression as \((-51.3) \cdot (-21.6)\).

Step 2: Determine the Sign of the Product

The product of two negative numbers is positive. Thus, the product will be positive.

Step 3: Multiply the Absolute Values

Use a calculator to multiply the absolute values: \(51.3 \times 21.6\). Input this into the calculator and compute the result.

Step 4: Obtain the Result

After entering 51.3 and 21.6 into the calculator, you should find that \(51.3 \times 21.6 = 1108.08\). Since the product of two negatives is positive, the result is \(1108.08\).

Key Concepts

Calculator Usage

Using a calculator for multiplying numbers, especially with decimals or large values, can simplify your calculations significantly. Calculators ensure accuracy and speed.

• Ensure your calculator is on; check the display for any unwanted entries before starting.
• Enter the numbers exactly as they appear, focusing on proper placement of negative signs where needed.
• Use the multiplication button, often denoted by "x" or "*", to input operations.
• Double-check by reviewing your equation on the display to minimize errors.

Let your calculator do the heavy lifting when it comes to complex multiplications, especially those with negative numbers.

Product of Negative Numbers

Understanding how to handle the product of negative numbers is crucial when working with multiplication. A general rule helps simplify this:

• The product of two negative numbers is always positive.
• This is because multiplying two negatives cancels out the negative sign, resulting in a positive result.

So when you multiply \((-51.3) \times (-21.6)\), the outcome is positive. Remembering this rule can help you to quickly predict the sign of your result, which is useful both with and without a calculator.

Absolute Value Multiplication

After determining the sign of the final product, you move on to multiplying the absolute values of the numbers. Absolute value reflects the magnitude of a number without considering the sign.

• Strip the negative signs, leaving you with \(51.3\) and \(21.6\).
• Input these values into your calculator as if they are positive.
• Multiplying absolute values directly contributes to finding the magnitude of the result.

In this exercise, the absolute values \(51.3\) and \(21.6\) were multiplied, resulting in \(1108.08\). Once computed, you apply the applicable sign to this product, remembering, in this case, it's positive.