What multiplication patterns can you see from each situation? Fill in the chart below according to the signs of the factors and products.

Question

Hint: Use the Desmos Scientific Calculator to test numbers that you choose.

(4 points)

Answer 1

To analyze multiplication patterns based on the signs of factors, we can categorize the products based on whether the factors are positive or negative. Here are the general patterns when multiplying two factors:

| Factor 1 | Factor 2 | Product | |----------|----------|----------| | Positive (+) | Positive (+) | Positive (+) | | Positive (+) | Negative (-) | Negative (-) | | Negative (-) | Positive (+) | Negative (-) | | Negative (-) | Negative (-) | Positive (+) |

Here’s a breakdown of the patterns:

1. Positive × Positive = Positive

   • Example: 3 × 4 = 12

2. Positive × Negative = Negative

   • Example: 3 × -4 = -12

3. Negative × Positive = Negative

   • Example: -3 × 4 = -12

4. Negative × Negative = Positive

   • Example: -3 × -4 = 12

Conclusion:

The sign of the product depends on the signs of the factors:

• If both factors have the same sign (both positive or both negative), the product is positive.
• If the factors have different signs (one positive and one negative), the product is negative.

You can use the Desmos Scientific Calculator to test these rules with any integers you choose, but the patterns will hold true for all real numbers.