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Negative numbers are numbers less than zero. They are typically used in mathematics to represent things like debts or temperatures below zero. Understanding how they work is important when doing operations like multiplication. In multiplication:

• A positive number multiplied by a negative number results in a negative number (for example: \(5 \times -3 = -15\)).
• A negative number multiplied by another negative number results in a positive number (for example: \((-3) \times (-4) = 12\)).
• Multiplying any number by zero results in zero.

To keep track of the signs, remember that multiplying two numbers with the same sign gives a positive result, and multiplying two numbers with different signs gives a negative result. This rule is essential when dealing with equations like \(-1 \times 2 \times 7 \times -3\). It's crucial to proceed step-by-step and reassess signs at each step.

The order of operations is a standard rule in mathematics that determines the sequence in which calculations should be performed to ensure accurate results. When tasked with an expression that includes several operations, the order is:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order is commonly remembered by the acronym PEMDAS.
In our example, \(-1 \times 2 \times 7 \times -3\), we only have multiplication involved. Thus, we simply perform the operation from left to right. This means starting with \(-1\times 2\), then multiplying the result by \(7\), and finally multiplying by \(-3\). Properly following the order of operations ensures that we do not mix up calculations or signs.

Understanding how to go through each part of a problem step-by-step makes complex calculations approachable. With our expression, \(-1 (2) (7) (-3)\), breaking it down can make the task easier.In Step 1, start by tackling \(-1 \times 2\). This yields \(-2\), a straightforward multiplication of a negative and a positive number resulting in a negative.
In Step 2, multiply your result from the first step, \(-2\), with the next number, \(7\). This gives us \(-14\), since a negative times a positive remains negative.
In Step 3, the last multiplication involves \(-14\) and another negative number, \(-3\). Here, multiplying two negatives yields a positive, resulting in \(42\).
Step-by-step solutions are useful tools for complex problems, ensuring each operation is clearly understood and correctly performed.