Question

If our problem is 3 × (-4), we can think of it as 3 groups of -4. But when our problem is -4 × 3, it’s strange to think about "negative 4 groups" of 3. Instead, we can think of the negative sign as "the opposite of." Two integers are opposites if they’re the same distance away from 0 on opposite sides of the number line. So, -4 × 3 is "the opposite of" 4 × 3. We can model this on the number line by jumping 3 units to the right, 4 times, and then jumping to "the opposite of" our product: -12. Wilbur says that -7 × 5 is the same as 7 × 5. What would you tell Wilbur?"

Answer 1

Wilbur is mistaken. -7 × 5 is not the same as 7 × 5; the correct product is -35 due to the rule that multiplying a negative number by a positive one results in a negative product.

Step-by-step explanation:

When dealing with multiplication involving negative numbers, it's essential to consider the concept of opposites and the direction on the number line. In the case of -7 × 5, we can interpret it as starting at 0, moving 5 units to the right four times (since -7 is the opposite of 7), and ending up at -35. This aligns with the rule that the product of a negative and a positive number is negative.

The misunderstanding might arise from the commutative property of multiplication, which states that the order of the factors doesn't affect the product. However, this property doesn't apply to the sign of the factors.

In the example given, reversing the order to 5 × -7 would still yield -35, but Wilbur's assertion that -7 × 5 is the same as 7 × 5 is incorrect. Multiplying by a negative number involves considering the opposite direction on the number line, leading to a different result.