Question

Carlo is playing a game with the cards shown. He draws cards at random and multiplies the numbers.

a. Give an example of two cards Carlo could draw that have a positive product. Find the product.
A. 4 and 5, with a product of 20.
B. 0 and 3, with a product of 0.
C. -2 and -2, with a product of 4.
D. 1 and 1, with a product of 1.

Answer 1

To find two cards resulting in a positive product, Carlo should draw either two positive numbers or two negative numbers. Options A (4 and 5) and C (-2 and -2) both yield positive products of 20 and 4, respectively.

Step-by-step explanation:

The question we are addressing involves finding two cards that Carlo could draw from a game, resulting in a positive product when the numbers on the cards are multiplied together. We need to recall the basic rules of multiplication regarding the sign of the product:

• When two positive numbers multiply, the product is positive (e.g., 2x3 = 6).
• When two negative numbers multiply, the product is also positive (e.g., -2 x -2 = 4).
• When numbers with opposite signs multiply, the product is negative (e.g., -3 x 2 = -6).
• Multiplying by zero always results in a product of zero, regardless of the other number (e.g., 0 x 3 = 0).

Based on this, for Carlo to have a positive product, he should draw either two positive numbers or two negative numbers. From the options given:

1. Option A: 4 and 5, the product is 20, which is positive.
2. Option C: -2 and -2, the product is 4, which is positive.

Hence, both options A and C are correct examples where Carlo draws two cards that have a positive product.