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NMTA Essential Academic Skills Subtest Math (003): Practice & Study Guide43 chapters | 216 lessons | 11 flashcard sets

Instructor:
*Michael Quist*

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Algorithms are precise sets of instructions that tell us exactly how to do something. In this lesson, we will explore how to use algorithms to solve math problems.

You're staring blankly at two numbers that you're supposed to divide, and you just can't think of what to do first. If only you had a set of instructions!

An **algorithm** is a set of steps that, if you do it right, will always take you to the goal. It is like a set of instructions for building a model plane, or a recipe for making a cake. In mathematics, an algorithm will always point you toward the right answer.

A good example of using an algorithm for math is a 'left to right' approach for adding a column of numbers.

Say you start with an ugly group of numbers that you have to add together by hand (no calculator, PC, smart phone, etc.--you know, Stone Age stuff!)

You have 5280, 495, and 1520, and you want the total. So, you grab a piece of paper (or write on the cloth napkin, but don't tell anyone!), and you think about the algorithm.

Here's the algorithm:

- Put the numbers in a column, matching up the number places (you know, the 1's go with the 1's, the 10's with the 10's, etc.).
- Draw a line under them, to separate the numbers you're adding from your results.
- Add the 1000's column and write the total under the line in the 1000's column.
- Add the 100's column and write the total in the 100's column beneath your 1000's total.
- Add the 10's column and write that total in the 10's column beneath your 100's total.
- Add the 1's column and write that total in the 1's column beneath your 10's total.
- Adjust the 1's column: If the total of the 1's is more than 9, then you have one or more 10's in your 1's column. They have to be relocated to the 10's column. Write the number of 10's in the 10's column, and leave what's left in the 1's column.
- Adjust the 10's column: If you have any 100's in the 10's column, remove them from the 10's column and place that number of 100's in the 100's column.
- Adjust the 100's column: If there are any 1000's in the 100's column, relocate them to the 1000's column.
- Total up each of your column results, and write them next to each other in a row. You should now have the total (sum) of your original numbers.

Let's put these steps into action to solve our problem.

First, we'll put the numbers in a column for addition.

Then, draw a line underneath to set apart your results.

Looking at the 1000's column (the one on the far left), we can see that only two of the numbers actually have a digit for 1000's, so we'll add those together (5000 + 1000 = 6000). You can write in the 0's for the 1000's if you want to, but we'll just keep the number of 1000's in the 1000's column to show that the number represents 1000's.

Looking at the 100's column, we can see that there are two 100's in the first number, four 100's in the second one, and five 100's in the third number. Adding the 100's together, we get 11 of them, which we'll write in the 100's column under our 1000's total. Notice that we do have one 1000 in our 1100, but we'll deal with him later.

Next we'll add the 10's. We get 19 of them, or 190. We notice a 100 in that total, and we'll have to move him to the 100's column later, but let's check the 1's first.

Adding the 1's together (two 0's and a 5), we get a total of 5 for the 1's column. Now we're ready to start wrapping this up.

We'll pull the 5 down to the bottom. No 10's to carry over to the next column.

Moving over to our nineteen 10's we'll move one 100 to the next column, and bring the 9 down to the bottom.

Sliding to the hundreds place in our totals, we add the 100 we moved from the 10's column to the eleven 100's we already have there. That makes twelve 100's, so we'll pull 1000 out, moving him to the 1000's column, and put the two remaining 100's down at the bottom.

Finally, we total the 1000's, including the one we moved from the 100's total. Writing that 7 down at the bottom, we're done!

Now, this probably seems like a lot of extra steps to take for this problem, but realize that algorithms are meant to be precise sets of instructions that work every time. Sure, you can take shortcuts, but always make sure you're not missing something important when you're doing your math operations. Every step has a reason for being there!

There are algorithms for every kind of math operation you need to do. Many great web sites offer algorithms that will work for you, including steps and pictures. For example, say you need an algorithm for factoring a trinomial. A math text can offer a good set of steps, but you can also pull up videos and stuff on the Internet that will help a lot. If you do a search (using Google, Bing, etc.) using the terms 'algorithm' and 'trinomial', you'll see a whole list of sites that offer instructions for factoring trinomials. Pull the one you like, and you're ready to go!

**Algorithms** are precise sets of instructions that will lead you to a desired goal. In mathematics, they will give you exactly the steps you need to solve a problem. You can find useful algorithms in textbooks and on the Internet. The right algorithm is your key to solving any math problem you'll ever come across!

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NMTA Essential Academic Skills Subtest Math (003): Practice & Study Guide43 chapters | 216 lessons | 11 flashcard sets

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