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: