Question

use the chip model to show the following.
a. (4)(2)
b. 4(-2)
c. -14 ÷ 7
d. -21 ÷ 3
(4)(2) = 8
b. let the first factor be the number of groups in the neutral space and let the second factor be the number of charges in a group. select the correct figure below.
(options with images of chip models labeled a, b, c, d)

Explanation:

Step1: Analyze the operation

The operation is \((4)(2) = 8\), which represents 4 groups (first factor) with 2 positive charges (second factor, since \(4\times2\) with positive values implies positive charges) each.

Step2: Evaluate the options

• Option A: Shows negative and positive, not matching \(4\times2\) (should be positive groups/charges).
• Option B: Shows two groups with positive charges, but the number of charges per group? Wait, no—wait, the first factor is number of groups, second is charges per group. For \(4\times2\), we need 4 groups? Wait, maybe I misread. Wait, the problem says "Let the first factor be the number of groups in the neutral space and let the second factor be the number of charges in a group". Wait, maybe the figures: Let's re-examine. Wait, the correct figure for \(4\times2\) (positive times positive) should have positive charge chips. Let's check the bottom right (Option B? Wait, the labels: The top right is A, top middle C, bottom right B, bottom middle D. Wait, the bottom right (B) has two groups of positive charges? Wait, no—wait, the first factor is 4? Wait, maybe the initial problem's part b is \((4)(2)=8\), so 4 groups (but maybe the figures have 2 groups? Wait, maybe the figures are simplified. Wait, looking at the options: Option B (bottom right) shows two groups of positive charge chips, each with multiple positive signs? Wait, no—wait, the correct model for positive multiplication (both factors positive) should have positive charge chips. Let's check the options:

• Option A (top left): Negative and negative? No.
• Option B (bottom right): Positive charge chips, two groups, each with positive charges. Wait, maybe the first factor is 2 groups (wait, maybe the problem's "first factor" is number of groups, second is charges per group. So \(4\times2\) would be 4 groups with 2 charges? But the figures show two groups. Wait, maybe a typo, but the correct figure for positive product should have positive charges. So Option B (the bottom right figure, labeled B) has positive charge chips, so that's the correct model for positive multiplication.

Answer:

B (the bottom right figure, labeled B)