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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Audrey Akins*

Audrey has more than a decade of experience teaching elementary. She has a bachelor's in journalism and a master's in education.

When you start adding multi-digit numbers together, the easiest and most common way to do this is through the use of the standard algorithm for addition. In this lesson, we will learn what that algorithm is and look at several examples.

Wait! Stop! Don't run away - it's not really as bad as it sounds! I know what happened. You heard the word algorithm and wanted nothing more to do with this lesson. Well, **algorithm** is just a fancy word for talking about a process used to solve problems. And **standard** just means something that is normally used. So, putting it all together, **standard algorithm** for addition simply means a normally used process to solve addition problems! Why can't we just say that in the first place, right?

The standard algorithm for addition has three simple rules:

**Rule 1:** Line up the numbers vertically by matching the place values - and start with the ones place.

To explain: When you add multi-digit numbers, the problem is typically written vertically - meaning one set of numbers is on top of the other. But, you can't just place the numbers anywhere - there is a proper placement of the numbers based upon place value. **Place value** is the place a number represents when a number is written in standard form. We will look at an example after we review the rest of the rules.

**Rule 2:** Add together the numbers that share the same place value - again, start with the ones place.

**Rule 3:** Regroup, if necessary.

OK. Now that we have the rules, let's practice!

Let's add 269 + 148.

Rule 1 tells us that you must line the numbers up starting with the digits in the ones place and then continue for the tens place and the hundreds place. For this problem, the numbers 9 and 8 are in the ones place, so we will put them one on top of the other, and the other place values will follow.

Rule 2 tells us to add together numbers that share the same place value beginning in the ones place. So, let's add 9 + 8 to get 17. Write the 7 in the ones places under the 9 and 8 and then, using Rule 3, regroup or carry over the 1 from the 17 to the tens place above the 6 and the 4.

Then add the numbers in the tens place. 6 + 4 + 1 = 11. Write the 1 in the tens place and write the other 1 in the hundreds place above the 2.

Finally, add the numbers in the hundreds place. 2 + 1 + 1 = 4. By this point you have 4 hundreds, 1 ten, and 7 ones, so your answer is 417.

Get a piece of paper and a pencil and try to solve this problem on your own. Don't look at the answer until you've tried it: 15 + 7.

No peeking!

Did your problem look like this?

I hope it did! Did you follow the rules?

- Line the numbers up vertically starting with the ones place
- Add together the numbers that share the same place value; and
- Regroup, if necessary

By learning the three simple rules of the standard algorithm for addition, you will be able to successfully add together very large numbers with no problems!

The standard algorithm for addition is a process that is normally used to solve multi-digit addition problems. The three rules of this algorithm are to: line the numbers up vertically based on place value (always start in the ones place); then begin adding together numbers that are in the same place value, and if you get an answer with two digits, use regrouping.

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Math for Kids23 chapters | 325 lessons

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