Partial Products

We first learn to add and subtract. Then we learn to multiply. In Partial Products, we are multiplying but as we multiply, it is actually showing us how to do the multiplication. Partial Products is done in Base 10.

As you multiply each part in Partial products, you add them all together. The partial products method helps you keep track of each place value of each digit.

Let's say you want to multiply 243x5.
You should think of 243 as 200+40+3.
You start from the biggest place value to the smallest place value.

Then your first step is to multiply 200x5, which is 1000.
Then you multiply 40x5, which is 200.
Then you multiply 3x5, which is 15.
Then you add all the numbers you found together.
1000+200+15=1215.


Here is an example that shows you step by step what is happening.

Partial Sums

When we first learn how to add, we are just taught how to do it. Most of the time, the teacher did not take the time to explain why we are doing so or even how. With the partial sums method, you are personally learning how to add. It shows you how to add the non-shortcut way. It also shows you what is actually happening through out the problem.

Let's say you want to add 456+231. You would first add the 100's. 400+200=600. Then you would add the 10's. 50+30=80. Then, last but certainly not least, you would add the ones. 6+1=7. Finally you would add all of the partial sums together. 600+80+7=687.

You should do this method from left to right and add the columns.

In this example, it is actually showing you step by step what is happening in the problem:

The Egyptian Number System

The Egyptian Number System is the only system we did not learn in class. We were however, supposed to learn it in the book. Like the Attic-Greek System, this system is quite easy to understand.

The Egyptian System also, like all the others, uses symbols instead of numbers.

Here is some of the symbols of the Egyptian Number System to help you picture what it actually looks like:

The Egyptian Number system is also a non-postional number system, a base-10 number system, and does not have a symbol for zero. To be non-positional means that when you write down the symbols, it does not matter how you put them in order. The answer will still be the same. Base-10 means that the grouping of the numbers(symbols) is done by 10's. This system also doesn not have a symbol for zero, which makes it even less difficult to understand.

Here is a link to a website to help you learn more about the Egyptian Number system.

Examples:


                     

The Mayan Number System

In my opinion, the Mayan Number System is the hardest number system to comprehend. This system, like all the others, uses symbols to represent numbers. Even though this system uses lines and dots, it is alot more confusing than you would think.

Here is a picture of numbers 0-19 in Mayan Symbols to help you visualize the whole number system:

The Mayan Number System is postional, has a symbol for zero, and is a base 20 system. It is postional, which means that the symbols have to be in order for you to understand which number you are trying to figure out. This number system, unlike the others, has a symbol for the number zero. Also, this system is a base 20 system. This means that that numbers are grouped by 20's.

Here is a link to a website to help you better understand the Mayan Number System.

Examples:

The Babylonian Number System

As we learned in class, the Babylonian Number System is a little bit harder to understand than the Attic-Greek System. The Babylonian system also deals with symbols to represent numbers.

Here is a picture of the Babylonian System to help visualize what it looks like:

The Babylonian Number system is Contextual, positional, and a base 60 system. Contextual means to be determined by or in context. Depending on how many items you are counting, the symbols you are using could stand for higher numbers. In this system, the symbols are positional, which means that the order of the symbols is important. This system is a base 60 system. Base 60 means that the grouping of the numbers is done by 60's. There is also no zero involved in this system.


Here is a link to a website to better explain how the Babylonian System actually works.


Examples: 

The Attic-Greek Number System

Last week in class, we learned about 4 different number systems. The one that I personally found the easiest one to understand was the Attic-Greek Number System(Also known as the Roman System).

Here is a picture of the Attic-Greek System to help visualize what it looks like:

The Attic-Greek system is Non-Postional and does not have a zero involved in it. Non-positional means that no matter how you arrange the symbols when you write them down, the position of the numbers does not matter. Zeroes are not involved because that is just the way the Greek People decided to make it. This system is also a base ten system which means that the grouping of the numbers is done by 10's.

This site helps to show how each number is represented, how to find out what different numbers are, and it shows good graphics in how to write the symbols down.

Examples: