Problem 19 - Beginning and Intermediate Algebra

Question

Find each product. \(-0.5(0)\)

Step-by-Step Solution

Answer

0

Step 1: Identify the numbers to be multiplied

In the expression \(-0.5(0)\), identify the numbers involved. The two numbers are \(-0.5\) and \(0\).

Step 2: Multiply the numbers

Multiply \(-0.5\) by \(0\). Any number multiplied by zero is always zero. So, \(-0.5 \times 0 = 0 \).

Key Concepts

multiplication rules

Let's understand the basic rules of multiplication. Multiplication involves finding the product of two numbers.

- When you multiply two positive numbers, the result is positive.
- When you multiply two negative numbers, the result is also positive.
- When you multiply one positive number and one negative number, the result is negative.
- Finally, when either number is zero, the product is always zero.

So, in the given expression, we have \(-0.5(0)\). Since one of the numbers is zero, any multiplication rule involving zero tells us that the product will be zero.

zero property of multiplication

The zero property of multiplication is a key concept in understanding products involving zero. It states that any number multiplied by zero is always zero. This rule is simple but crucial. It applies to all real numbers, whether they are positive, negative, fractions, or whole numbers.

For instance: \ - \(5(0) = 0\ \), \(0(3) = 0\), \(\frac{1}{2}(0) = 0\).

In our exercise, we used this property: no matter the other number, including \(-0.5\) in this case, multiplying it by zero automatically makes the product zero.

identifying numbers in expressions

Identifying numbers correctly in an expression is essential for solving any problem. When you look at an expression, like \ -\(0.5(0)\), it’s important to recognize and separate out the numbers involved. Here’s how you do it:

- Spot each number and any signs (positive or negative) that accompany them.
- In \ -\(0.5(0)\), we have two key elements: -0.5 and 0.
- Understand what each number represents. Negative 0.5 means it is less than zero and moving towards the left on the number line.
- Zero, as a unique number, indicates no value or a null point on the number line.

Knowing which numbers you’re working with helps you apply the correct multiplication rules and properties, like the zero property discussed earlier.