Standard

# Equations

What is an equation?

Examples: 4 + 3  = 7        or        3x + 5 = 10

An equation is a number sentence. We call it an equation because it has an equal sign.

## The 5 Steps to Writing an Equation or Inequality

#### Step 5.Write the equations

Don’t forget our cool ‘dance’ we did to remember this!

WRITING EQUATIONS PRACTICE PROBLEMS:

## With Equations, Inequalities and Expressions we always want to combine like terms 1st!

Here is an example on how to do that:

Once all like terms have been combined then we can solve.

# Solving Equations with Models

MODELING EQUATIONS PRACTICE PROBLEMS:

# Solving Equations Algebraically

### Solve √(x/2) = 3

 Start With √(x/2) = 3 Square both sides: x/2 = 32 32 = 9: x/2 = 9 Multiply both sides by 2: x = 18

And the more “tricks” and techniques you learn the better you will get.

Here is an example of how we solved equations in class:

SOLVING EQUATIONS (with variables on both sides PRACTICE PROBLEMS:

Click here or here to practice Solving Equations online and get automatic feedback (it grades it)! 🙂

# Simple vs. Compound  Interest

### Introduction to interest:

http://www.mathsisfun.com/money/interest.html

### SIMPLE INTEREST

I = Prt

• I = interest owed  [\$] (this is ONLY the interest borrowed)
• P = amount borrowed (called “Principal”)  [\$]
• r = interest rate   [%] (you have to divide the percent by 100)  For information On Percents click here!
• t = time    [years]

Simple interest is money you can earn by investing some money (the principal). The interest (percent) is the rate that makes the money grow!

### COMPOUND INTEREST

A = P(1+r)^t

• A = All of it / Actual / total amount owed (this amount includes the interest and the principal)   [\$]
• P = amount borrowed (called “Principal”)    [\$]
• r = interest rate     [%]
• t = time    [years]

Compound interest is very similar to simple interest. The difference is that compound interest grows much faster! The reason it grows faster is because the interest (percent) has an exponent.

********** MAKE SURE TO READ THE QUESTION AND SEE EXACTLY WHAT IT IS ASKING DOES IT JUST WANT THE INTEREST OR THE TOTAL (All of it) ???????? *************************

For information on compound interest click here.

SIMPLE INTEREST PRACTICE PROBLEMS:

Click here or here to practice Simple Interest online and get automatic feedback (it grades it)! 🙂

COMPOUND INTEREST PRACTICE PROBLEMS:

Click here or here to practice Compound Interest online and get automatic feedback (it grades it)! 🙂

Standard

# Mean

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

# Absolute Value

Absolute Value means …

… only how far a number is from zero:

 “6” is 6 away from zero, and “−6” is also 6 away from zero. So the absolute value of 6 is 6, and the absolute value of −6 is also 6

# Mean Absolute Deviation

Mean absolute deviation (MAD) is about calculating the average distance from the mean.

Click here to watch a video from our 8th Grade Math textbook that goes in to detail and explain how to calculate the MAD.

MEAN ABSOLUTE DEVIATION:

The average/mean distance from the average/mean is the MAD.

Yes, we use “mean” twice: Find the mean … use it to work out distances … then find the mean of those!

### Three steps:

• 1. Find the mean of all values
• 2. Find the distance of each value from that mean (subtract the mean from each value, ignore negative signs)
• 3. Then find the mean of those distances

Like this:

### 3, 6, 6, 7, 8, 11, 15, 16

Step 1: Find the mean:

 Mean = 3 + 6 + 6 + 7 + 8 + 11 + 15 + 16 = 72 = 9 8 8

Step 2: Find the distance of each value from that mean:

Value Distance from 9
3 6
6 3
6 3
7 2
8 1
11 2
15 6
16 7

Which looks like this:

Step 3. Find the mean of those distances:

 Mean Deviation = 6 + 3 + 3 + 2 + 1 + 2 + 6 + 7 = 30 = 3.75 8 8

So, the mean = 9, and the mean deviation = 3.75

It tells us how far, on average, all values are from the middle.

In that example the values are, on average, 3.75 away from the middle.

### For deviation just think distance

MEAN ABSOLUTE DEVIATION Practice Problems:

## Random Sample

This is where everyone has an equal and fair chance of being selected.