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Multiplication is a basic mathematical operation that is essentially repeated addition. For example, if you have 3 groups of 4 apples, you can write this as a multiplication problem:

• 3 multiplied by 4, written as \(3 \times 4\).
• This equals 12, because you have 3 groups of 4, which is the same as adding 4 three times (4 + 4 + 4 = 12).

When multiplying two numbers, you combine them into a larger group, represented by a single product. This operation is extremely versatile and applies to much more than simple counting, as you'll see it used with various types of numbers, including those that are negative or fractions.

In the expression given, \(0(-12)(-5)\), we're looking at a real-world example of multiplication involving both zero and negative numbers. Understanding the order is crucial; you follow the expression starting from left to right, combining numbers as per basic multiplication rules.

Negative numbers represent a value less than zero, typically used to denote a decrease. Imagine having a debt of 5 dollars. This situation can be represented with the number -5. When we multiply numbers, and one or both are negative, we have specific rules to remember:

• Multiplying two negative numbers gives a positive result.
• Multiplying a positive number by a negative one, or vice versa, will give a negative result.

In our exercise, there are negative numbers involved: -12 and -5. In the absence of multiplication by zero, \((-12) \times (-5)\) would result in a positive number, specifically 60, because \((-12) \times (-5) = 60\). However, the presence of zero changes this outcome, as we'll see next.

Following a step-by-step approach ensures we don't miss any crucial operations, especially in exercises involving multiple rules like the zero property and multiplication of negatives.

Step 1: Understand the Expression

We have the expression \(0(-12)(-5)\). The aim here is to process these multiplications in order, focusing on how each number interacts, especially with zero being involved.

Step 2: Apply the Zero Property of Multiplication

Use the zero property, which states that any number multiplied by zero is zero. This simplifies the equation dramatically, since:

• Once zero multiplies by anything, particularly the first number -12, the answer immediately becomes 0: \(0 \times (-12) = 0\).

Step 3: Complete the Multiplication

Lastly, you multiply the zero outcome by the final number, which is -5:

• \(0 \times (-5) = 0\).

Conclusion

With every multiplication involving zero, the result remains zero. Following this clear, step-by-step breakdown helps to reinforce understanding of how different properties and rules in mathematics are applied in practical terms.