Question

In a multiplication problem, the factors are the numbers that get multiplied. The commutative property of multiplication says that you can multiply these factors in any order, and you’ll always get the same product, or answer. This means that -5 times 3 will give you the same answer as 3 times -5.

a. 5 times 3 = 5 + 5 + 5
b. 5 times 3 = 5 / 1 / 3
c. 5 times 3 = (5 times 2) + 5
d. -5 times 3 = 3 times -5

Answer 1

In multiplication, the commutative property ensures that the order of factors does not change the product, as shown by both 5 times 3 and 3 times -5 resulting in the same absolute value but with a positive or negative sign based on the factors' signs.

Step-by-step explanation:

In mathematics, specifically when dealing with multiplication and its properties, understanding the sign rules is crucial. When two positive numbers multiply, such as 5 times 3, the product is positive, resulting in 15. This represents the commutative property of multiplication, where the order of factors does not affect the product; thus, 5 times 3 is the same as 3 times 5.

When we look at examples with different signs, such as -5 times 3, the product is negative, giving us -15. Likewise, 3 times -5 also yields -15, showcasing that the commutative property holds true regardlestrong> of sign. If we were to apply multiplication rules considering division and other operations, we would maintain a similar approach to signs: positive with positive yields positive, negative with negative yields positive, and mixing signs results in a negative product.

Vector multiplication, such as scalar or dot product, and vector or cross product, apply different rules. The scalar product is commutative, while the vector product is anti-commutative, implying that switching the order of vectors results in a product with an opposite sign.