Problem 23 - Introductory Algebra for College Students

Question

perform the indicated multiplication. $$(-5)(-2)(3)$$

Step-by-Step Solution

Answer

The answer to the multiplication \((-5)(-2)(3)\) is \(30\).

Step 1: Multiply the first Two numbers

in this step, we would multiply the first two numbers, which are both negative. The multiplication of two negative numbers gives a positive number. So, \( -5 \times -2 = 10\)

Step 2: Multiply the Result with the Third Number

Now, combine the product from step 1 with the next number given. Multiply \(10 \times 3 = 30\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-). In mathematics, negative numbers are often used to indicate values below a certain reference point, such as temperature below freezing or financial losses.
When you multiply two negative numbers, the negative signs cancel each other out, resulting in a positive product. This is an important rule to remember:

• Multiplying two negative numbers gives a positive result.
• For example, \(( -5 ) \times ( -2 ) = 10\).

Understanding this concept is crucial in handling negative numbers in various mathematical operations, especially in integer multiplication.

Positive Numbers

Positive numbers are greater than zero and are usually written without a sign. These numbers include all the natural numbers starting from one upwards, like 1, 2, 3, and so on.
They are straightforward to work with in multiplication since the result remains positive:

• When you multiply a positive number with another positive number, the outcome is also a positive number.
• For instance, multiplying 3 and 10 gives 30.

This property makes positive numbers intuitive to handle, as the result will always be a positive integer unless mixed with negative numbers or zero.

Integer Multiplication

Integer multiplication refers to multiplying whole numbers, both positive and negative, and it follows certain fundamental rules:

• Multiplying two positive integers or two negative integers results in a positive integer.
• Multiplying a positive integer by a negative integer will produce a negative result.

To visualize integer multiplication, let's look at our example:1. We start with two negative numbers, \(-5\) and \(-2\), multiplying them gives us a positive integer, 10.2. Next, multiply this result by 3, a positive integer. The final result is 30, a positive integer.This step-by-step approach illustrates how understanding the rules of integer multiplication can simplify complex calculations by breaking them down into manageable steps.