Problem 14 - Algebra A Combined Function

Question

Multiply. (-2)(-3)(-4)

Step-by-Step Solution

Answer

The product is -24.

Step 1: Multiply the First Two Numbers

Start by multiplying the first pair of numbers: \(-2 \times -3\). When you multiply two negative numbers, the result is positive, so: \(-2 \times -3 = 6\).

Step 2: Multiply the Result with the Third Number

Now take the result from Step 1 and multiply it by the next negative number: \(6 \times -4\).When you multiply a positive number by a negative number, the result is negative. So: \(6 \times -4 = -24\).

Key Concepts

Negative Numbers

Negative numbers represent values less than zero and are denoted with a minus sign. These numbers are a vital part of mathematics because they help explain debts, losses, and temperatures below zero, among other concepts. Understanding negative numbers can initially be confusing, but they become more intuitive the more you practice.

When dealing with negative numbers, it's essential to remember a few key points:

• Negative numbers are positioned to the left of zero on a number line.
• If two negative numbers are added together, the result becomes more negative, meaning the value decreases.
• When subtracting a negative number, it's equivalent to adding the positive counterpart.
• The opposite of a negative number is its positive equivalent.

Knowing these points makes working with negative numbers in calculations, such as multiplication, much easier.

Multiplying Integers

Integer multiplication, especially involving negative numbers, is an important arithmetic skill. Here, the focus is on understanding how signs affect the product:

• Multiplying two positive integers gives a positive product.
• Multiplying a positive integer and a negative integer results in a negative product.
• Multiplying two negative integers, however, produces a positive product.

To remember how sign rules work in multiplication, think of the rules like this:- If the signs are the same, the product is positive.- If the signs are different, the product is negative.

For example, multiplying egin{itemize} * \(-2 \times -3 = 6\) because both numbers are negative and their product is positive. * \(6\times -4=-24\) because the signs are different and the resulting product is negative. These rules simplify complex problems and ensure that any multiplication involving integers, whether positive or negative, can be tackled confidently.

Order of Operations

The order of operations ensures that mathematical expressions are solved correctly. When multiplying integers, following the proper order is crucial to obtaining an accurate result. The basic principle is often remembered using the acronym PEMDAS:

• P: Parentheses first
• E: Exponents (i.e., powers and square roots, etc.)
• M and D: Multiplication and Division (from left to right)
• A and S: Addition and Subtraction (from left to right)

In our original exercise, (-2)(-3)(-4), even though there are only multiplications, we still process them from left to right. So, you first multiply \(-2\) and \(-3\) to get \(6\), and then multiply the result by \(-4\) to get \(-24\). Sticking to this order prevents mistakes and ensures consistency in your calculations.

It's also crucial to note that while the order of multiplication and division should be from left to right, any operations within parentheses should be completed first. This principle helps maintain clarity and precision when solving mathematical expressions across various scenarios.