Scientific Understanding

**What sections should I know before attempting to learn this section?**

–-> Equations

**How do you solve for an unknown?**

Besides multiplication and division, the most important mathematical skill you will need for this class is the ability to perform algebra manipulations to solve for an unknown variable like “x”. It is essential that you learn this skill early on in chemistry and continue to excel at it throughout the class. It is also useful in physics, if you plan to take that class in the future. If you get frustrated, keep in mind that I learned all I needed to know about math and solving for unknowns in a chemistry class and not in a math class. Anyone can learn this skill if they practice.

The central rule for algebra and solving for an unknown is that you always have to preform the same math function on both sides of an equal sign.

**FIRST ****EXAMPLE** if you have the equation:

45 = |
7 |

z |

You can multiply both sides by z (* z) like below

z * 45 = |
7 * z |

z |

**SECOND**** ****EXAMPLE** is if you had the equation:

3x = |
4 |

1 |
1 |

You can divide both sides by 3 like below

3x = |
4 |

3 |
3 |

Now that we know what is possible with equations, let us get to the core of how we should think about solving for unknowns. In my years of teaching, I have found a simple way to go about solving for unknowns that seems to make sense to almost every student I meet. It is a process that follows 2 goals.

**Goal One:** Get the unknown (the letter) into the numerator using multiplication or cross multiplication.

**Goal Two:** Get the unknown (the letter) alone on one side of the equation usually through the use of division.

That is it. Those are your only goals with 99% of the math problems you run across in chemistry. Now that we know what our goals are, let us take a look at some examples of using those goals. **REMEMBER ONLY SOLVE ONE STEP AT A TIME AND WRITE OUT EACH AND EVERY STEP**.

**VIDEO Solving for an Unknown Demonstrated Example 1**:

Given the equation, solve for the unknown X

5X = |
8 |

1 |
1 |

**Step 1:**

What is your first goal? Get the unknown into the numerator.

Has this been done? Yes, so we do not need to worry about it.

**Step 2:**

What is our second goal? Get the unknown alone on one side.

Has this been done? No.

So what do we need to do to achieve this? Divide both sides by 5 to move it away form the X.

5X = |
8 |

5 |
5 |

**Step 3:**

Cross out the 5 on the left side.

5X = |
8 |

5 |
5 |

**Step ****4****:**** **

Simplify

X = |
8 |

5 |

Is the unknown alone on one side? Yes. Okay then solve.

**Step ****5****:**

Solve: 8 / 5 = 1.6

COMPLETE ANSWER: X = 1.6

**VIDEO Solving for an Unknown Demonstrated Example ****2**:

Given the equation, solve for the unknown V

56 = |
8V |

9 |

**Step 1:**

What is your first goal? Get the unknown into the numerator.

Has this been done? Yes, so we do not need to worry about it.

**Step 2:**

What is our second goal? Get the unknown alone on one side.

Has this been done? No.

So what do we need to do to achieve this? Divide both sides by 8 to move it away form the V.

56 = |
8V |

9 * 8 |
8 |

**Step 3:**

Crossing out the 8 on the right side.

56 = |
8V |

9 * 8 |
8 |

**Step ****4****:**** **

Simplify

56 = |
V |

9 * 8 |

Is the unknown alone on one side? Yes. Okay then solve.

**Step ****5****:**

Solve: 56 / (9 * 8) =

COMPLETE ANSWER: V = 0.78

**VIDEO Solving for an Unknown Demonstrated Example ****3**:

Given the equation, solve for the unknown P

4 = |
7 |

P |
2 |

**Step 1:**

What is your first goal? Get the unknown into the numerator.

Has this been done? No.

So what do we need to do to achieve this? Cross multiply the P and the 2.

2 * 4 = |
7 * P |

P |
2 |

**Step 2:**

Cross out the P on the bottom left and the 2 on the bottom right.

2 * 4 = |
7 * P |

P |
2 |

**Step 3:**

Simplify

2 * 4 = |
7 * P |

1 |

Is the unknown in the numerator? Yes. Okay time to focus on our second goal.

**Step 4:**

What is our second goal? Get the unknown alone on one side.

Has this been done? No.

So what do we need to do to achieve this? Divide both sides by 7 to move it away form the P.

2 * 4 = |
7 * P |

7 |
7 |

**Step ****5****:**

Crossing out the 7 on the right side.

2 * 4 = |
7 * P |

7 |
7 |

**Step ****6****:**** **

Simplify

2 * 4 = |
P |

7 |

Is the unknown alone on one side? Yes. Okay then solve.

**Step ****7****:**

Solve: (2 * 4) / 7 = 0.86

COMPLETE ANSWER: P = 0.86

**VIDEO Solving for an Unknown Demonstrated Example ****4**:

Given the equation, solve for the unknown R

78 = |
3 * 5 |

R |

**Step 1:**

What is your first goal? Get the unknown into the numerator.

Has this been done? No.

So what do we need to do to achieve this? Multiply the R and to both sides.

R * 78 = |
3 * 5 * R |

R |

**Step 2:**

Cross out the R on the Right.

R * 78 = |
3 * 5 * R |

R |

**Step 3:**

Simplify

R * 78 = |
3 * 5 |

1 |

Is the unknown in the numerator? Yes. Okay time to focus on our second goal.

**Step 4:**

What is our second goal? Get the unknown alone on one side.

Has this been done? No.

So what do we need to do to achieve this? Divide both sides by 78 to move it away form the P.

R * 78 = |
3 * 5 |

78 |
78 |

**Step ****5****:**

Crossing out the 78 on the left side.

R * 78 = |
3 * 5 |

78 |
78 |

**Step ****6****:**** **

Simplify

R = |
3 * 5 |

78 |

Is the unknown alone on one side? Yes. Okay then solve.

**Step ****7****:**

Solve: (3 * 5) / 78 = 0.19

COMPLETE ANSWER: R = 0.19

**PRACTICE PROBLEMS**: Given the equation, solve for the unknown.

Given the equation solve for G

4G = |
9 |

1 |

Answer: 2.25

Given the equation solve for T

13 * 2 = |
5T |

1 |

Answer: 5.2

Given the equation solve for H

8 = |
5 |

H |
6 |

Answer: 9.6

Given the equation solve for K

2 * 9 = |
47 |

3 |
K |

Answer: 7.83

Given the equation solve for E

4 = |
16 |

E |

Answer: 0.25

Given the equation solve for

50 = |
8 * 6 |

B |

Answer: 0.96

**When you finish the lesson, try out the math review worksheet.**