Question

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how can you explain to a classmate how to determine the sign of the product when multiplying negative numbers?

Explanation:

To determine the sign of the product when multiplying negative numbers, we can use the following rule:

Step 1: Recall the rule for multiplying negative numbers

The product of two negative numbers is positive. For example, if we have \((-a) \times (-b)\) where \(a\) and \(b\) are positive numbers, then \((-a) \times (-b) = ab\) (positive).

If we multiply an odd number of negative numbers, the product is negative. For example, \((-a) \times (-b) \times (-c) = -abc\) (negative, since there are 3 negative factors, which is odd).

If we multiply an even number of negative numbers, the product is positive. For example, \((-a) \times (-b) \times (-c) \times (-d) = abcd\) (positive, since there are 4 negative factors, which is even).

Step 2: Explain with examples

• Two negative numbers: \((-2) \times (-3) = 6\) (positive, because 2 negative factors, even count).
• Three negative numbers: \((-2) \times (-3) \times (-4) = -24\) (negative, because 3 negative factors, odd count).
• Four negative numbers: \((-2) \times (-3) \times (-4) \times (-5) = 120\) (positive, because 4 negative factors, even count).

In summary, to determine the sign of the product of negative numbers:

• Count the number of negative factors.
• If the count is even, the product is positive.
• If the count is odd, the product is negative.

Answer:

The sign of the product of negative numbers is determined by the number of negative factors:

• If there are an even number of negative factors, the product is positive.
• If there are an odd number of negative factors, the product is negative.