# 3-Digit Subtraction

This week my daughter taught me something about **subtraction**. I was amazed that I hadn’t thought of this earlier. The first thing that amazed me is that she already understood negative numbers. I don’t remember teaching her that concept. This must have been one of our random car conversations. However, she not only understood it, but knew when to apply it.

We’ve been working on 3 – **digit subtraction** for about 2 weeks now. We’re integrating **mental math** into the **math problems**, and it’s turning out to be a little harder than we both thought. Today however, we had a breakthrough. In a problem like:

852 – 581 = 271

There are a million ways to get to the right answer: The traditional way is to start in the ones place and subtract (2-1 = 1). Next, move to the tens place and subtract (15-8 = 7). Note that the 15 is from borrowing 100 from 800 and adding it to 50 to get 150. Next we move to the hundreds place and subtract (7-5 = 2). The final answer is 271.

However, the method my daughter and I use is to start in the hundreds place. Let me back up a little. Note that 852 is the same as 800 + 50 + 2. Also, 581 is the same as 500 + 80 + 1. This is really useful if you decide to add the two numbers or subtract the two numbers. If you add you would start with the hundreds; 800 + 500 = 1300. Then, go to the tens 50 + 80 = 130, and add the previous value for 1300 + 130 = 1430. Then, go to the ones place 2 + 1 = 3, and add the previous value for 1430 + 3 = 1433.

If you subtract, you can use the same idea. Start with the hundreds place and subtract (800-500 = 300). Next, move to the tens place and subtract (50-80 = -30), then subtract the previous value for 300 – 30 = 270. Next, move to the ones place and subtract (2-1 = 1), then add the previous value for 270 + 1 = 271.

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