Math Review

Reviewing Fractions

Adding & Subtracting The Rule: The denominator(s) must be the same Ex: 3 + 5 - 1 = ? 4 8 3 Common denominator is….. …..24 …. (8x3 & 6x4). Multiply each fraction to give you 24 on the bottom. Then you can add/subtract as needed.

Adding & Subtracting 18 + 15 - 8 = 25 24 24 24 24 18 + 15 - 8 = 25 24 24 24 24 Don’t forget to reduce!!!

Multiplying & Dividing DO NOT CROSS MULTIPLY!!!! Just multiply/divide across both the top and bottom. Then reduce as needed Ex: 1 x 3 x 5 x 7 = 105 or 1 x 3 x 5 x 7 = 35 2 4 6 8 384 2 4 6(2) 8 128 105 & 324 are both divisible by 3

Fractions Continued We don’t usually use just fractions in chemistry. However, when we solve “OUR” problems they will be set up just like multiplying fractions.

Fractions Continued EX. How many feet are in 8.7 km? (1 in = 2.54 cm) 8.7km x 1000m x 100 cm x 1in x 1 ft = 87000 = 3854.33 ft 1km 1m 2.54cm 12in 30.48 To solve you multiple across the top and the bottom separately and then divide. We won’t be using x for multiplying, we use a grid.

Problem Solving Worksheet 5

Solving for variables There are A LOT of formulas in Chemistry. You must be able to rearrange those formula’s to solve for the variable you need.

Solving for variables There are 2 basic rules that you must follow: 1. Whatever is done to one side MUST be done to the other 2. You CAN NOT solve for a variable in the denominator!! It must first be moved to the numerator (by multiplying)

Solving for variables For example: Solve for peace?

1st Multiply both sides by the sun Now, move the flower

Then divide both sides by the flower Finally symbols or letters are not as important as knowing how to rearrange the formula

Variable’s Cont. Now try it on these “real” chemistry formulas. Solve for volume D = m/v (Density) Solve for T PV=nRT (Ideal Gas Law) Solve for M2 M1V1 = M2V2 (Dilution Formula)

Answers V = m D T = PV nR M2 = M1V1 V2

Problem Solving Worksheet 10

Percents

3 Types Percent Error Percent Yield Percent Composition

Percent Error Percent Error tells you how accurate your results are.

Percent Error Percent Error = (Measured Value - Accepted Value) x 100

Example A student calculates the density of iron as 6.80 g/cm3 by using lab data for mass and volume. A handbook reveals that the correct value is 7.86 g/cm3. What is the percent error?

Precision versus Accuracy

Precision vs. Accuracy Precision- getting the same results again & again (reproducible) Accuracy- getting results close to the accepted or standard value

Precision vs Accuracy If the is the target or bulls-eye Which does this represent?

Precision vs Accuracy And this one?

Precision vs Accuracy You draw Accurate but not precise

Example The accepted value is 29.35. Describe the data below in terms of accuracy and precision Trial Measurement 1 29.48 2 28.97 3 29.27

Density D= Mass_ Volume Mass: put matter on balance Volume: - graduated cylinder - geometry volume formulas - displacement

Volume by Displacement

Example An unknown mineral has a mass of 16 grams. A graduated cylinder is filled with 10. mL of water. The mineral is dropped into the cylinder and the water level rises to 18 mL. What is the density of the mineral?

Exit Ticket #1 MUST SHOW YOUR WORK!!!! Solve for T2 P1V1 = P2V2 (Combined Gas Law) T1 T2