Question

4 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.

b. give an example of two cards carlo could draw that have a negative product. find the product.

Explanation:

Part a

Step1: Recall sign rules for multiplication

To get a positive product, we multiply two numbers with the same sign (both positive or both negative). Let's assume there are cards with positive and negative numbers. Suppose we have a card with \( -2 \) and another with \( -3 \) (we can infer possible card values, or maybe from the shown cards, if one is \( -2 \) and another negative, or two positives). Wait, the shown cards have \( -2 \) and \( 0 \), but maybe there are other cards? Wait, maybe the original problem has more cards, but since two cards with same sign: if we take two negative cards, say \( -2 \) and \( -5 \) (assuming another negative card), but maybe the given cards (from the image) have \( -2 \) and maybe a positive? Wait, maybe the user's image has more, but let's proceed. Alternatively, if there's a \( 3 \) and \( 4 \), but from the shown, maybe \( -2 \) and another negative. Wait, maybe the problem has cards like \( -2 \), \( 0 \), and others. Let's assume two negative cards: \( -2 \) and \( -3 \). Then product is \( (-2)\times(-3) = 6 \). Or two positive cards, like \( 2 \) and \( 3 \), product \( 6 \). Let's take \( -2 \) and \( -4 \) (hypothetical, but following sign rule).

Step2: Calculate the product

Take two negative numbers, e.g., \( -2 \) and \( -3 \). Then \( (-2)\times(-3) = 6 \). Or if there's a \( 2 \) and \( 3 \), \( 2\times3 = 6 \).

Step1: Recall sign rules for multiplication

To get a negative product, we multiply two numbers with different signs (one positive, one negative).

Step2: Calculate the product

Take a positive and a negative number, e.g., \( -2 \) and \( 3 \). Then \( (-2)\times3=-6 \). Or \( 2 \) and \( -3 \), product \( -6 \).

Answer:

(example):
Cards: \( -2 \) and \( -3 \); Product: \( 6 \) (or other same - sign cards, e.g., \( 2 \) and \( 3 \), product \( 6 \))

Part b