Rationalize the Denominator

Thursday, May 9, 2024

Many times you may need to rationalize the denominator which means there will not be an irrational number as the denominator.
Rationalizing the denominator involves rewriting a fraction so that the denominator is a rational number. This can be done by multiplying both the numerator and denominator of the fraction by a suitable expression.

For example, to rationalize the denominator of the fraction 1/√2, we can multiply both the numerator and denominator by √2: 1/√2 * √2/√2 = √2/√4 = √2/2
Now the denominator is a rational number, 2.

Let's rationalize the denominator of 1/√3

rationalize denominator

The Outer Planets-Jovian Planets

Friday, April 26, 2024

The Outer Planets which are also called the Gas Giants include Jupiter, Saturn, Uranus, and Neptune. These planets are also called the Jovian Planets. The term Jovian means Jupiter like. The Jovian planets, also known as gas giants, are the four largest planets in the Solar System: Jupiter, Saturn, Uranus, and Neptune. They are all composed primarily of hydrogen and helium, and have thick atmospheres and no solid surfaces.

Largest planet in the Solar System Has a thick atmosphere with a Great Red Spot Has 79 known moons

Saturn Second largest planet in the Solar System Has a thick atmosphere with a hexagonal-shaped polar vortex Has 62 known moons
Uranus Third largest planet in the Solar System Has a thick atmosphere with a unique tilt Has 27 known moons
Neptune Fourth largest planet in the Solar System Has a thick atmosphere with a Great Dark Spot Has 14 known moons

Properties of Nonmetals

Thursday, January 25, 2024

Nonmetals are found on the right of the periodic table and tend to gain electrons.

There are 17 nonmetals Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Chlorine Argon Phosphorus Sulfur Selenium Bromine Krypton

They range from brittle solids to gasses at room temperature. Because their outer shells are filled with electrons they tend to gain electrons.

They share some of these properties.

Nonmetals share these properties

  • Low density

  • Poor conductors of heat and electricity

  • Not malleable or ductile

  • Brittle solids or gasses at room temperature

  • React with metals to form salts

11 Body Systems in 3 minutes

Friday, January 12, 2024

If you could take a look inside this person riding the skateboard you would see an amazing team of different body systems working together.

body systems

There are at least 11 body systems that work together to help keep the human body alive. 

The integumentary system is made up of our skin, which is the largest organ of the body. It acts as a barrier which protects us from the outside world, helps prevent water loss, and regulates our temperature. In addition, it allows us to touch our surroundings.

The skeletal system is made up of our bones, ligaments which attach bone to bone, tendons which attach muscle to bone and our joints. The skeletal system helps with movement and protection. 

The muscular system is responsible for movement inside and out of the body. There are three major types of muscles, skeletal muscles which are muscles attached to bones, smooth muscles which are involuntary muscles found inside the stomach, the intestines and several other places, and cardiac muscle which are muscles of the heart. 

The urinary system filters blood through the kidneys where it works to filter out waste and produces urine. 

The function of the respiratory system is to exchange oxygen and carbon dioxide between the atmosphere and the blood. The lungs are a major organ of this system.

The digestive system breaks down food so nutrients can be absorbed by the body. It has three main functions, ingest food, break food down so that nutrients can be absorbed, and eliminate what can't be digested. 

The endocrine system sends chemical messages throughout the body. This system is composed of glands that produce hormones that act as chemical messengers of the body. For example adrenaline is a hormone that causes you to have a sudden burst of energy. 

The reproductive system is responsible for producing offspring. 

The lymphatic system includes organs and cells that filter lymph and blood and destroy foreign microorganisms.Lymph is the fluid that leaks out of the capillaries. This fluid circulates among the tissue cells and is collected by lymphatic vessels and returned to the veins.

The nervous system sends electrical signals throughout your body. These signals may cause your arm to move or your heart to be this system is composed of two major divisions. The central nervous system, which is the brain and the spinal cord, and the peripheral nervous system which consists of the nerves that branch out from the brain and the spinal cord. 

The circulatory system pumps blood throughout your body. It consists of your heart veins that carry blood to the heart arteries that carry blood away from the heart and capillaries which connect the veins and the arteries.

A Guide to Improving Your Grades

Monday, December 25, 2023

Here is a simple plan that will help you stay organized, learn to be proactive, and apply new study habits. Here is how it works. Take about 10 minutes a day,watch the video as apply what it asks you to do.

Here is a breakdown of each day.
Day 1. Restock your pencil pouch and backpack. Here are some suggestions to help keep you well supplied.
Sharpen pencils, replace notecards, replace any missing materials.
Items you should have in your pencil pouch. Pencils Colored pencils Eraser Notecards Day 2. Read over the list of 5 memory tools and see if you can apply any right now. Mnemonics Journey Method Mind map Song Picture
This video go over these memory techniques.
Memory Techniques for School https://youtu.be/SKmI5me-GdY
Day 3. Learn to be proactive
What is one activity you can complete know that will make your life easier in the future? Example: I hung up a key hanger. I use this everyday so I can always find my keys. A couple more examples,
Lay your clothes out the night before. Look over your agenda and note if you have any tests coming up.
Each of these activities are proactive and help you keep from being reactive. Day 4 Watch the video on 45 study tips and apply one this week.

Day 5 Review your current study goals and add one new study goal . Here are several example goals. I will start my homework within 1 hour of getting home. I will review class notes within 24 hours of taking them. I will start a study group. I will study at least 1 hour every day.
These are just examples of some study goals.
Day 6 If you use 3 ring binders go through all the papers in each of your notebooks.
Follow this rule
Only handle them once You will either file in the correct section Set up an archive box and either put the paper in the archive box or throw the paper away.

One thing I learned from teaching almost 30 years is that if you can use a spiral notebook for your subjects it is easier and more effective that a 3 ring binder. Day 7 Read over your reflective questions and add one new reflective questions from the list that you like. The first time you will pick one reflective question and write this reflective goal in your agenda.
Examples of reflective questions.
What do I need to do today to help me achieve my goals tomorrow? Do I focus on what is important? Do my friends make a positive or negative impact on my life? What is my next step to achieve school success? What can I do to improve? Day 8 Do a random act of kindness for someone and remember kindness multiplies kindness. Day 9 Clean out your backpack using DIRT

D Dump everything out.
I Inventory what you have.
R Repack your backpack.
T Throw out all your thrash
Day 10 Take a Rest

Function Notation and Evaluating Functions

Thursday, December 21, 2023

Function notation is a shortened method way to write functions.
Let's go over the parts of function notation.

function notation

The f is the name of the function. f is usually used but any letter can be used. 
The x is the input value. 
It is read f of x and not f times x.

When you are asked to evaluate a function you substitute a value for x which is the input in order to find the output.

Evaluate  f(x) = 4x + 5 when x is 2
f(2) = 4 ( 2 ) + 5
f(2) = 8 + 5
f(2) = 13

If you evaluate f(x) = 5x + 2r when x = -4r + 3m
You simply plug in the value for x 
f(-4r + 3m ) = 5( -4r + 3m ) + 2r 

How to Calculate Mean-Median-Mode and Range

Wednesday, December 20, 2023

Numbers and groups of numbers  are all around us.

For example, what is the total number of students at your school?

Who is the oldest student or the youngest student?

Who runs the fastest mile and who has the highest test average?

A measure of central tendency is one way to organize data so you can figure out what it is telling you.

Three Measures of  Central Tendencies include: MEAN, MEDIAN & MODE.

A measure of central tendency is a single number that is used to summarize all the values of a data set.

For example, you have this group of people. You may want to know if they are all close to the same age, or what is the average height or how many have dark hair ?

mean median mode

Let’s work an example.

What is the mean median and mode of this family?

mean median mode example

The ages are 68,10,7,40,36,2.12,65

MEAN - the  average of a set of numbers.

Mean and average are the same.


1. Add all of the numbers in the data set 

2. Divide by the total number of items in the data set 

3. If there is a ZERO, it must be included!

Let's find the mean of the average ages of the family.

Let’s add the ages together 68,10,7,40,36,2.12,65 = 240

Now let’s divide by the number of numbers in the data set.

If there was a zero it would be included and we have 8 members.

So 240 divided by 8 = 30 so the average age is thirty

Now let’s calculate median

MEDIAN - the number in the center of a data set when the numbers are in order from least to greatest.


1. Arrange the numbers from least to greatest order.

2. Cross off the greatest and least numbers in the list (at the

same time) until you are left with just one number in the

middle - this is the MEDIAN!

3. If there are two numbers left in the middle, you have to find

the MEAN or AVERAGE of the two numbers.

Find the median of the ages of the family.


Let's arrange from least to greatest

Since we have an even number we need to take the average of the numbers in the middle.

So the mean or average of 12 and 36 is 48 divided by 2 which equals 24.

If you had an odd number it would just be the number in the middle.

Mode equals the number which occurs most often in a data set. There might be one mode, no mode, or many modes.


Arrange the numbers from least to greatest order.

See if any numbers repeat.

The number that repeats most often is the mode.

What is the mode of the family?

Let’s arrange from least to greatest


So no number repeats so you have no mode.

If you had this,


Then 7 would be the mode.

Finally let’s figure out the range for this data set.

RANGE  is NOT a measure of central tendencies, it is a MEASURE OF VARIATION.

It is a measure of the variation between the greatest and lowest numbers in a data set.

Find the greatest number and SUBTRACT the least number.

What is the range of of the family?

Let"s order from least to greatest.


So the range is 68 -2 which equals 66

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