Question

Activity

An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms? Complete the steps below to solve this problem and others like it.
Part A
Three electrons are removed from each of 4 atoms. Write an expression to represent the net change on the charge for the group of atoms.

Part B
Simplify the expression obtained in part A and explain what the answer represents.

Part C
Here’s a similar problem. Write an expression for the net change in charge if two electrons are added to each of six atoms in a group. Also, write an expression that represents removing two protons each from a group of six atoms.

Part D
Simplify the two expressions in part C.

Part E
How are the two products in part D related?

Part F
Think about multiplying any two rational numbers. Based on this activity and your previous work, write a set of rules for finding the sign of the product based on the sign of the two numbers being multiplied.

Answer 1

A)

The charge of each electron is -1, so the charge of three electrons is -3. Removing something is denoted by a negative sign. The expression that represents the removal of three electrons from each of four atoms is (-3)(-4).

B)

(-3)(-4) = (-1)(3)(-1)(4) = (-1)(-1)(3)(4) = 12

The net change in the charge for the group of atoms is 12 (or +12); that is, the charge of the atoms increases by 12.

C)

Adding two electrons to each of six atoms results in a net change in charge of (-2)(6). Removing two protons from each of six atoms results in a net change in charge of (2)(-6).

D)

(-2)(6) = (-1)(2)(6) = (-1)(12) = -12

(2)(-6) = (2)(6)(-1) = (12)(-1) = -12

E)

The products are the same: -12.

F)

If the signs of the numbers are the same, the product is positive. If the signs of the numbers are different, the product is negative.

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Answer 2

Step-by-step explanation:

A: The charge of each electron is -1, so the charge of three electrons is -3. Removing something is denoted by a negative sign. The expression that represents the removal of three electrons from each of four atoms is (-3)(-4).

B: (-3)(-4) = (-1)(3)(-1)(4) = (-1)(-1)(3)(4) = 12

The net change in the charge for the group of atoms is 12 (or +12); that is, the charge of the atoms increases by 12.

C: Adding two electrons to each of six atoms results in a net change in charge of (-2)(6). Removing two protons from each of six atoms results in a net change in charge of (2)(-6).

D: (-2)(6) = (-1)(2)(6) = (-1)(12) = -12

(2)(-6) = (2)(6)(-1) = (12)(-1) = -12

E: The products are the same: -12.

F: If the signs of the numbers are the same, the product is positive. If the signs of the numbers are different, the product is negative.