This document provides an example of regrouping in subtraction by framing it as making change from $2.53 for something that costs $1.97. It walks through subtracting 253 - 197 by first subtracting the ones place (3 - 7), realizing there are not enough pennies and trading a dime for ten pennies, then subtracting the dimes place and realizing there are not enough dimes so trading a dollar for ten dimes. The final answer is 56 with 1 dollar and 5 dimes remaining. In summary, regrouping in subtraction involves trading a higher place value for lower ones when there are not enough in the current place.

1. Mission: Math Boost Your Math Power!! Lesson 2-3 © 2010 Sandy Fleming Virtual Summer School Online

2. Let’s get started! Looks like you need to review the concepts related to regrouping in subtraction. Regrouping is simply naming numbers a little bit differently.

3. Our number system is specially designed to make it easy to work with larger numbers. Think of the challenges of adding and subtracting with Roman Numerals! VI + VIII = VVIIII??? It actually equals XIV !!

4. Then things changed…. Some wise person invented the base ten number system. Now we count using just ten digits, but the place that the numerals are written in makes a difference. The number 46 means we have four groups of ten and six single ones.

5. For many people, it’s easy to think of pennies, dimes and dollars. 253 is like two dollar bills, five dimes and three pennies. What if you had $2.53 and someone wanted you to pay $1.97? You can give them a dollar, but you don’t have 9 dimes or 7 pennies!

6. 253 - 197 You need to give up 7 pennies, but you only have three. We just traded one dime in for ten pennies!

7. 253 - 197 Now there are four dimes left and thirteen pennies. Take away the seven pennies, like this….. 4

8. 253 - 197 Now there are four dimes left and thirteen pennies. Take away the seven pennies, like this….. 4 6 and there are 6 left over.

9. 253 - 197 Now we can move the six leftover pennies to the bottom. 4 6 And there’s another problem! We must give up 9 dimes, but we only have four. Where can we get more dimes? Let’s trade in a dollar for ten dimes!

10. 253 - 197 Now we have one dollar bill left, and fourteen dimes. 4 6 That’s enough to get rid of 9. There are 5 dimes left. 1 5

11. 253 - 197 And one dollar take away one dollar is no dollars. 4 6 The answer to the subtraction problem is 56. 1 5 0

12. To review: Start with the ones column (on the right) Check to see if you have a larger number on the top. If the upper number is smaller than the lower one, you need to regroup or borrow from the next place to the left. Add ten to the top number and cross out the number you borrowed from. Put the new number there. Subtract. Repeat the process for the rest of the columns, working from left to right.

13. Practice, practice, practice! http://www.learn4good.com/games/kids/double_digits.htm http://www.simplekidsmath.com/Default.aspx?level=7 See you back here when you’re scoring at least 90% on subtraction regrouping problems!