Question

What is the sign of each product? Choose Positive or Negative.

Positive

Negative

−
3
⋅
(
−
15
)
−3⋅(−15)



3
(
−
5
)
3(−5)



−
5
⋅
(
−
2
)
⋅
(
−
1
)
−5⋅(−2)⋅(−1)



−
5

⋅
(
2
)
⋅
(
3
)
−5 ⋅(2)⋅(3)

Answer 1

To determine the sign of each product, we can apply the rules of multiplication for positive and negative numbers:

1. A positive number multiplied by a positive number is positive.
2. A positive number multiplied by a negative number is negative.
3. A negative number multiplied by a positive number is negative.
4. A negative number multiplied by a negative number is positive.
5. An even number of negative factors results in a positive product.
6. An odd number of negative factors results in a negative product.

Now let's analyze each expression:

1. **−3 ⋅ (−15)**:
- Two negatives multiply to give a positive.
- **Sign: Positive**

2. **3(−5)**:
- A positive and a negative multiply to give a negative.
- **Sign: Negative**

3. **−5 ⋅ (−2) ⋅ (−1)**:
- There are three factors: two negatives (which multiply to give a positive) and then multiplying by another negative gives a negative.
- **Sign: Negative**

4. **−5 ⋅ (2) ⋅ (3)**:
- One negative and two positives multiply to give a negative.
- **Sign: Negative**

Here is a summary of the signs:

1. Positive
2. Negative
3. Negative
4. Negative