Problem 61 - Algebra A Combined Function

Question

Perform the indicated operation. \(-2.1(-0.4)\)

Step-by-Step Solution

Answer

The product is 0.84.

Step 1: Identify the Numbers

We have two numbers: 1. 2.1 which is a negative number. 2. 0.4 which is a negative number. The operation we need to perform is multiplication.

Step 2: Determine the Sign of the Product

Multiplying two negative numbers gives a positive result. Thus, even though both -2.1 and -0.4 individually have negative signs, their product will be positive.

Step 3: Multiply the Absolute Values

Focus on the absolute values: 2.1 and 0.4. Multiply these numbers as if they were both positive: \[ 2.1 imes 0.4 = 0.84 \]

Step 4: Apply the Sign to the Product

From Step 2, we found that the product of two negative numbers is positive. So, the result from Step 3 becomes: 0.84.

Key Concepts

Sign of Product

When dealing with the multiplication of numbers, understanding the signs is crucial. In particular, when multiplying two negative numbers, the rule is that the product will always be positive. This might seem counterintuitive at first, but it helps to think about the rule for multiplying signs:

• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative = Negative

Therefore, in our exercise, multiplying (-2.1) and (-0.4) results in a positive product. This is because the two negative signs "cancel out," leading to a positive outcome.

Absolute Values

Absolute value is a concept that expresses the magnitude of a number regardless of its sign. For any number, the absolute value is non-negative. In simpler terms, it's the distance from zero on the number line. For the numbers involved in our exercise, the absolute values are:

• For -2.1, the absolute value is 2.1
• For -0.4, the absolute value is 0.4

When multiplying these numbers, you focus on their absolute values as if they were both positive. This simplifies the calculation process and ensures clarity when applying multiplication rules.

Operation Steps

Performing multiplication of negative numbers step-by-step simplifies complex calculations. Let's break it down for our exercise:

Step 1: Identify the Numbers

Start by recognizing both numbers to be multiplied. Here we have -2.1 and -0.4, both negative.

Step 2: Determine the Sign

Recall that multiplying two negative numbers results in a positive sign.

Step 3: Multiply the Absolute Values

Multiply the absolute values like normal positive numbers: 2.1 \( \times \) 0.4 equals 0.84.

Step 4: Apply the Sign to the Product

Finally, apply the positive sign derived in Step 2 to the product from Step 3, resulting in 0.84.

These steps guide you through the process from understanding the numbers to finding the final answer.

Product of Numbers

Finding the product of numbers involves multiplying them to arrive at an answer. In our example, the two numbers are -2.1 and -0.4. Through a methodical process, we've determined the product is derived by:

• First, understanding that their negative signs will produce a positive result
• Then, calculating the product of their absolute values (2.1 and 0.4)

The multiplication of these values yields 0.84. Thus, even though we initially started with negative numbers, their product is positive. This is a great illustration of handling not just the numbers but also the signs when it comes to multiplication.