Problem 13 - Algebra A Combined Function

Question

Multiply. (-1)(-3)(-5)

Step-by-Step Solution

Answer

The product is -15.

Step 1: Multiply the first two numbers

Start by multiplying the first two numbers: \(-1 \times -3\). Multiplying two negative numbers results in a positive number. Thus, \((-1) \times (-3) = 3\).

Step 2: Multiply the result with the third number

Now multiply the result from Step 1 with the third number:\(3 \times -5\). When you multiply a positive number by a negative number, the result is negative. Therefore, \(3 \times -5 = -15\).

Key Concepts

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division. Each of these operations has rules that dictate how we perform them and what outcomes we expect.

Multiplication, for example, is essentially repeated addition. If you multiply 3 by 4, it is the same as adding 3 together four times (3 + 3 + 3 + 3 = 12). This principle extends to all numbers, whether they are positive, negative, or zero.

Understanding these operations is crucial because they form the foundation for more advanced mathematical concepts. Once you grasp how to work with basic arithmetic, tackling complex problems becomes easier.

Negative Numbers Multiplication

When multiplying negative numbers, we follow specific rules. One of the key rules is that multiplying two negative numbers results in a positive number. This might seem a bit counterintuitive at first, but it helps to think of it in terms of direction and vectors.

Imagine walking backwards (negative direction) and then turning around and walking backwards again. You end up moving forward, hence a positive direction. In terms of multiplication:

• Negative x Negative = Positive
• Example: \((-1) \times (-3) = 3\)

This rule is consistent and will help you solve problems involving negative numbers efficiently.

Positive and Negative Numbers

Understanding the difference between positive and negative numbers can greatly help in arithmetic calculations.
Positive numbers are those that are greater than zero, like 5, 12, or 200, while negative numbers are less than zero, like -5, -12, or -200.

When multiplying different signs, you may follow another set of rules:

• Positive x Negative = Negative
• Negative x Positive = Negative
• Example: \(3 \times -5 = -15\)

It's crucial to always keep track of the signs. This ensures accuracy, especially as calculations become more complex.