Evaluating Algebraic Equations

When we evaluate algebraic equations we substitute the variables with real numbers. When you know the value of the variables within the equation it becomes easier to find the correct answer that you are seeking.

For example: If you have an equation like w + c  when W = 8 and C = 9 you would replace the variables w and c with 8 and 9. You would then end up with 8 + 9 simple enough when you are just learning about algebra.

Another example would be 5xz if you put the numbers 8 and 9 into the equation you would end up with 5(8)(9); so in order to evaluate this equation you would first multiply 5 and 8 to get 40 then you would multiply 40 and 9 to come up with your final answer of 360.

Now, if y = 8 and t = 6 in the following equations what do you think the answer would be?

in y – t


in 8yt

By putting your numbers into the equation y – t you should come up with the equation 8 – 6 = 2; and in 8yt you should come up with  8(8)(6) = 64(6) = 384 you are just multiplying each of the numbers to come up with the end result.

Evaluating algebraic expressions is an easy concept to learn once you understand the variables, and insert the real numbers into your equation.

Here are some to evaluate

If a = 5, t = 7, c = 6, and d = 3

1. 6a + 9t

2. 8c + 6d

3. a3 + 7t

4. 8(a + d)

5. 15(c + a)

Using What You Learn

Learning Coding can be an interesting experience and rewarding. Especially, when you know what you are doing from the lessons that you have taken on coding. Some of the concepts that I have learned about in the process of learning about coding includes a variety of items.

  • html
  • CSS
  • JavaScript
  • jQuery
  • Python Syntax

Concepts that you Learn

All these concepts are somewhat easy to understand and you have to practice quite a bit to make sure that you understand the concepts that you are learning about throughout the process. Sometimes you also have to look at examples, and questions that other coder’s have asked about the same type of question that you are working on. Some people have a hard time understanding some of the concepts just like I did when I started some of it did not make sense but that is because I did not know anything about coding until looking into it earlier in the month of May.

What can you do with these concepts

Well you can work on many types of things like apps, websites, and learn just about anything that you want. You can also learn how to manipulate your blog posts on how you want your reader’s to see your posts. It is quite amazing that right now as I am writing this blog post I have used some of the concepts learned in coding. I know that there is only so much that you can write about coding but by using the concepts that you learn in something that you are working on gives you the ability to show off your new skills.

  • Engineer
  • NASA
  • Computer Science
  • Mathematics
  • Medical and Billing coding

Throughout the world there are many places that you can use these types of skills to obtain the information that you want out of your website, blog, apps, games or anything that you like. It is fascinating to me that more people are not interested in this type of information or want to learn about coding. I think that it is fun and I am excited to use my new skills on preparing this blog post with some of the interesting topics I have covered in the last couple of weeks.

I hope you have enjoyed reading my new work!

Maybe one day when I get good at this I can get a job doing this type of stuff



The zero is used to determine the positional value of a certain number within the mathematics world and to indicate the absence of quantity. The zero is needed in the positional number system that is used by people today. When you think about the position of any number in the positional numeral system it determines the value of that position. For example, in 567 the 5 stands for five hundred, and the 6 stands for six tens (sixty) and the 7 stands for seven ones or six units. In order to write the number five hundred six dollars you would have to include a zero to show that there are no tens in the number.

In school you learn that when you add a number to zero you get the original number. When you subtract you also get the original number. Multiplying a number by zero will automatically give you a zero. By dividing a number by zero it becomes indefinable. Yes it is just common sense to know these things.

It is believed that the Maya Indians invented the concept of Zero before 300 A.D. Several years later the Hindus developed the concept of the zero independently a few hundred years later after the Maya Indians did.

This ends the A to Z challenge it has been  a fun experience, and I am looking forward to the next challenge of writing. Adding more articles to my blog for the viewer’s to enjoy.

Basic Algebra

In actual Junior high school she was never good at math it was not until she reached her Associate’s degree that she started enjoying math. Your associate’s degree is nothing more than rehashing the things that you learned in Junior high school and high school.

To many this is just common sense however, to other’s who have math anxiety, and issues understanding the concepts of basic algebra this might come in handy for them to understand the concepts of learning such algebraic expressions.

Basic algebra is using the same methods like addition, subtraction, multiplication, and division. However, algebra also uses letters to represent numbers in the algebraic equations.

Addition in algebra

x + y would mean the sum of x and y equals a certain number

For example: The sum of a and 5 would be written as a + 5

The sum of y and 8 would be written as y + 8

If L plus W it would be written as L + W

So in writing with symbols you could use the following examples to practice writing algebraic equations in addition.

The sum of x and 5    x + 5

9 more than Y     9 + y

a plus b     a + b

Z increased by 7   z + 7


Some problems for you to practice with on your own:

1. The sum of x and y

2. t plus z

3. b plus 9

4. The sum of b and n

5. 15 more than y

6. x increased by 5

7. 9 more than k

8. 100 increased by z

When you learn the words that are used within the algebraic equations it becomes easier to learn how to solve the problem to obtain the right answer.


Subtraction in Algebra

Subtraction is almost the same as addition but the words that you will see for subtraction our a little different.

Some writing expressions that would indicate subtraction would include:

w minus t would be written   w – t

w decreased by 9 would be written  w – 9

9 less than b would be written 9 – b

The difference of t and 15 would be written  t – 15

Some of the problems that you will see throughout your experience in algebra may not make sense to you in the beginning and learning the terms is something that you need to practice so that you do not have issues with the problems on tests or quizzes.

Therefore, here are some problems for you to work on your own:

1. 8 less than p

2. 10 less than t

3. y decreased by w

4. d minus l

5. y minus 9

6. z decreased by 7

7. c decreased by 4

8. t less than 15


I hope that you are still with me here in learning algebraic equations with addition and subtraction. Therefore, we will discuss multiplication, and division.

Multiplication in algebra

There are a variety of ways to write algebraic equations when you are using the multiplication symbol.

a ∙ b



These examples indicate that the product of a and b or a times b

Now, the words that you might see in multiplication expressions would include:

7 times b could be written like  7 ∙ b   (7)(b)   7b

twice c is written as 2c

6 more than the product of 8 and x would be written like 8x + 6

The product of 8, t, z would be written like 8tz

The product of 6 and the sum of x and w would be written as 6(x + w)

Therefore, here are some problems that you can work on your own.

1. t times z

2. The product of r and w

3. The product of 9, c, and d

4. The sum of twice t and z

5. The product of 8 and the sum of c and t

6.  9 times a

7. The product of 10 and the sum of z and r

8. twice the sum of t and z

Once, you learn the words that are involved with multiplication expressions it becomes easier to spot what you need to do to solve the algebraic equations.


Division in Algebra

w/t means that w divided by t or the quotient of w and y

Therefore, if you see these terms within an algebraic expression you need to divide the numbers.

y divided by 8 is written as y/8

the quotient of z plus t divided by 9 would be written like     z + t/9

The sum of r plus z divided by the difference of w minus a would be written like                   r + z/w-a

Furthermore, when you are just learning algebra and the meanings behind the expressions it becomes easier as you are learning. The problems become easier as you go along because you are understanding the meanings behind the words in the problems.

Therefore, here are some problems for you to work on your own.

1. w divided by 15

2. The quotient when x is divided by 9

3. The sum of s and 6 divided by 3

4. The difference of t and q divided by 8

5. The sum of t and x divided by the difference of a and 6

6. The difference of  y minus t divided by 4

7. The quotient of c plus r divided by 9

8. The sum of y and 5 divided by the difference of y and 5

Within these examples, and problems I hope that you have understood some of the information that I have provided. Homeschooling children can be a fun experience or it can be a total flop. Understanding the information that is before you is the main key to succeeding in learning algebraic expressions.

More to come! The problems will get more complex but I believe that this type of information is good for our children to understand what they are learning in Basic algebra….

Any questions feel free to email me at tammyhopkinson@aol.com

Mean, Mode, and Median

Does all statistical data have a mean, median, or mode? Why? When is the mean the best measure of central tendency? When is the median the best measure of central tendency?

The mean is an average of a set of data and in order to find the mean you would simply add the numbers together and divide by the total number of inputs that were available to find the mean of those numbers. As a homeschool teacher I have to use this to find the mean of one of the students grades by adding all of the grades together and dividing the numbers by how many assignments were done. The median is the middle number that is given within the set of data and has been organized in ascending order to give me the median of the assignments. The mode of this example would be the number that occurs more frequently in the data. Statistical data does not always have a mean, mode, or median but should have at least one of these statistical measures. Using average is the best measure of a central tendency because it depends on the set of data and whether or not it has outliner’s. Furthermore, if there are not many outliner’s mean can be a good measure but if outliner’s are present within the data median is the better measure to use because it would not skew the information based on the outliner’s data. In contrast, most statistical data has a mean, median, mode, or all three, but there are some instances in which certain calculations cannot be made or are arbitrary.

Frequency Distribution

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What is the purpose of developing a frequency distribution? What is the relationship between the relative frequency and the cumulative frequency? Could a frequency distribution contain qualitative data? Why? In thinking about frequency distribution which, shows various data that is divided into different classes within a business. It also divides the occurrences in each of the specific classes. These frequency distributions are used in quantitative, and qualitative data analysis within any type of business. Many of the graphs, histograms, pie charts, and bar charts can be used within the frequency distribution to keep track of how well any product or service is doing within the business. The relationship between the relative and cumulative frequency is that the relative frequency counts the total number of counts on a certain product or service. While the cumulative frequency sums up the number of counts on the product or service provided. In my opinion this would be a good tool to use because of the data that it would provide for any business. Especially to see how well a product or service is doing within that business. It is also used to see how many times a certain event would happen over the course of a certain period of time. If the data that has been collected over that period of time is quantitative then the data will be used within the frequency distribution.


What is an independent variable? What is a dependent? What is the relationship between independent and dependent variables? What is the purpose of differentiating these terms?

Independent variables are mathematical factor’s that will vary and can be manipulated by the researcher because they would want a certain outcome. A dependent variable is a mathematical factor that would change depending on the researcher’s independent variable. Throughout math we learn that x is the independent variable and y is the dependent variable. By differentiating these two terms can be used in order to find two different numbers within the equation. Throughout the workplace we use variables on a daily basis. For example the current place that I am working for just came out with some new entrée’s to offer to the customer’s. We could take one of the new entrée’s and use it as an example our Mixed Grill is delicious. This entrée would be considered the independent variable because this entrée would rely on the customer’s purchasing the entrée. The sales/revenue that is created from this entrée would be the dependent variable because it would change based on the performance and demand of the entrée. By putting two and two together I now get a better understanding on how important it is to research and gather as much information about the entrée and how it would affect the business. A manager must have a clear understanding of mathematical equations in order to make it through one day of being a manager. Just because there are programs that can do this type of math does not mean that you are always going to get the right answer without doing a little bit of research along with the numbers.