Problem 25 - Algebra 1

Question

Find the product. $$(13)(-2)(-3)$$

Step-by-Step Solution

Answer

The product of these numbers is 78.

Step 1: Identify the Numbers

Notice that we have three numbers in the expression: 13, -2, and -3. Two of these numbers are negative (-2 and -3) and one of them is positive (13).

Step 2: Multiply the Numbers

Now, we'll multiply them one by one. First, multiply 13 by -2 to get -26. Then, multiply -26 by -3.

Step 3: Calculate the Final Product

The multiplication of -26 and -3 gives us 78. Remember that the product of two negative numbers is a positive number, so -26 times -3 equals 78.

Key Concepts

Understanding Negative Numbers in Multiplication

When multiplying numbers, dealing with negative numbers can seem tricky at first. A negative number is any number less than zero. In multiplication, negative numbers follow specific rules that help determine the sign of the product.

- **Negative times Positive**: The result is negative. Example: \((13) \times (-2) = -26\).
- **Negative times Negative**: The result is positive, as shown by \((-26) \times (-3) = 78\).

Think of negative signs as direction changes. Multiplying two negatives cancels out the negative effect, leading to a positive product.

Mastering the Order of Operations

The order of operations is essential in solving math problems correctly. It's like following a recipe, where steps must be done in the right order to get the correct outcome. The standard order is:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

In this exercise, we focus on multiplication. We multiply from left to right: first \(13 \times -2\), then the result \(-26\) is multiplied by \(-3\). This ensures the calculations are accurate and follow standard procedures.

Exploring Integer Arithmetic

Integer arithmetic involves whole numbers, both positive and negative, and zero. It's important to understand how to work with integers, especially when doing multiplication.

Steps in Integer Multiplication:
- **Identify the Integers**: Recognize positive and negative numbers.
- **Apply Rules**: Use multiplication rules for negative and positive integers.

In this case, we started with three integers: 13, -2, and -3. By understanding and following the multiplication rules of integers, we successfully computed the product to be 78. Integer arithmetic is foundational in math and helps in understanding more complex concepts.