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Understanding negative numbers is essential in algebra. A negative number is a number less than zero and is represented with a minus sign \-\ like \-2\. When you multiply a positive number by a negative number, the product is always negative. For example, \(2 \times (-2) = -4\). When you multiply two negative numbers, the product is positive: \((-2) \times (-3) = 6\). Remember these rules:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative

Practice with different combinations of positive and negative numbers to get comfortable with these rules. It will make solving problems much easier!

Grouping numbers is a useful strategy in algebra to make calculations easier. In the exercise, we grouped the numbers \(2 \times (-2)\) and \(25 \times 67\) together. Grouping helps to simplify the multiplication process by breaking it down into smaller, manageable parts.
Here's why it's helpful:

\1. \ Group pairs of positive and negative numbers: This allows you to quickly determine the sign of the result (positive or negative).
\2. \ Simplify large numbers: Grouping can turn complex multiplications into easier ones – for example, breaking down 67 into (60 + 7).

Try grouping numbers in different ways to see which method works best for you. It’s all about finding the most efficient path to the solution.

Multiplication problems, especially with multiple numbers, can be tackled effectively using a step-by-step approach. This method breaks down complicated problems into a series of simpler operations:

1. First, identify pairs of numbers to group. In our exercise, we grouped \(2 \times (-2)\) and \(25 \times 67\).
2. Multiply the first group: \(2 \times (-2) = -4\). Since one number is negative, the product is negative.
3. Next, multiply the second group: Break it down if necessary. \(25 \times 67 = 25 \times (60 + 7)\), which further breaks down to \(25 \times 60 + 25 \times 7\).
\ We calculated \(25 \times 60 = 1500\) and \(25 \times 7 = 175\). Adding these results gives us \(1500 + 175 = 1675\).
4. Finally, multiply the results of the two groups: \(-4 \times 1675 = -6700\).

This method not only helps in computing the correct result but also provides a clear understanding of the multiplication process. Practice with different problems to master this strategy!