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Regrouping (Borrowing) in Subtraction

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- 1. Warm Up <ul><li>How much money do I have? </li></ul>3 Ten Dollar Bills 2 One Dollar Bills 1 Quarter 1 Nickel 2 Pennies 1 Five Dollar Bill 1 One Dollar Bill 1 Dime 2 Nickels 4 Pennies
- 2. Remember, that each digit in a number has a value. 7 Hundreds 700 4 Tens 40 5 Ones 5 Add them 745 I could BORROW 1 ten from the ten’s column and add it to the ones column. The value of the 4 is really 40, 4 tens. The value of the 1 is really 10, so 40 – 10 = 30, or 3 tens. 5 4 7 Ones Tens Hundreds 5 + 10 4 - 1 7 Ones Tens Hundreds 15 3 7 Ones Tens Hundreds
- 3. We can BORROW from the Hundred’s Column too. 7 Hundreds 700 4 Tens 40 5 Ones 5 Add them 745 40 + 100 = 140 4 tens + 1 hundred = 140 The value of the 4 is really 40, 4 tens. 5 4 7 Ones Tens Hundreds 5 4 + 100 7 - 1 Ones Tens Hundreds 5 14 6 Ones Tens Hundreds
- 4. Even after I’ve borrowed from the Hundreds place and put it in the Tens column, I can then borrow from the Tens column and give it to the Ones column 14 Tens = 14 x 10 = 140 6 Hundreds 600 13 Tens 130 15 Ones 15 Add Them 745 Original Number 5 14 6 Ones Tens Hundreds 5 + 10 14 - 1 6 Ones Tens Hundreds 15 13 6 Ones Tens Hundreds 5 4 7 Ones Tens Hundreds
- 5. <ul><li>Regrouping is also called Borrowing. </li></ul><ul><li>When you can’t subtract easily, then Borrow from a higher column that can support lending. </li></ul><ul><li>Look at the ones column. Can you subtract 7 from 5 and get a positive number? No. So borrow. </li></ul><ul><li>Look at the tens column. Can you you subtract 2 from 4 and get a positive number? Yes? Then borrow from the 4. </li></ul>Subtraction Symbol 5 4 7 7 2 5 Ones Tens Hundreds
- 6. Regrouping is also called Borrowing. When you can’t subtract easily, then Borrow from a higher column that can support lending. 3. After borrowing, then just subtract. 745 – 527 = 218 5 + 10 4 - 1 7 7 2 5 Ones Tens Hundreds 15 3 7 8 1 2 7 2 5 Ones Tens Hundreds
- 7. Now, lets try borrowing from the Hundreds so that we can subtract from the Ones column. 621 – 345 = ? <ul><li>Look at the Ones Column, can’t subtract 5 from 1 and get a positive number. </li></ul><ul><li>Look at the Tens Column, can’t subtract 4 from 2 and get a positive number, soooooo… </li></ul><ul><li>Look at the Hundreds Column, I can subtract 3 from 6 and get a positive number so I’m going to borrow from the Hundred’s Column. </li></ul>1 2 6 5 4 3 Ones Tens Hundreds
- 8. 621 – 345 = 276 1 + 10 = 11 ones 2 + 100 = 20 + 100 = 120 = 12 tens Now to borrow: 12 – 1 = 11 tens 6 – 1 = 5 hundreds 5 4 3 Ones Tens Hundreds 11 11 5 6 7 2 5 4 3 Ones Tens Hundreds
- 9. Here is a little cheat that most people like to use while borrowing. 5 6 2 - 3 4 8 Follow the same steps from earlier, look at each column until you can subtract from it and get a positive number. <ul><li>Can’t subtract 8 from 2. </li></ul><ul><li>Look at Tens Column, I CAN subtract 4 from 6, therefore I can borrow from 6 and give to the 2 in the Ones Column. </li></ul>3. Cross out the 6 and make it a 5. (It is the same thing as subtracting 1) 5
- 10. Here is a little cheat that most people like to use while borrowing. 5 6 2 - 3 4 8 Follow the same steps from earlier, look at each column until you can subtract from it and get a positive number. 4. Now add a 1 to the 2 in the Ones Column to make it 12. (It is the same as adding 1 ten to the ones column, adding 10 + 2, which equals 12). 5 1 5. Now the problem is 5 hundreds, 5 tens, and 12 ones, minus 3 hundreds, 4 tens, and 8 ones, and you can subtract! 2 1 4
- 11. Here is a problem without the steps. Lets talk them out as we go. 8 2 1 - 5 5 2
- 12. 8 2 1 - 5 5 2 7 Here is a problem without the steps. Lets talk them out as we go. I couldn’t subtract 2 from 1 in the ones column, and I couldn’t subtract 5 from 2 in the tens column, so I had to borrow from the hundreds column. 1 Now I add the 1 I’ve taken away from the Hundreds Column and add it to the Tens Column. Changing the 2 to a 12.
- 13. 8 2 1 - 5 5 2 7 Here is a problem without the steps. Lets talk them out as we go. I couldn’t subtract 2 from 1 in the ones column, and I couldn’t subtract 5 from 2 in the tens column, so I had to borrow from the hundreds column. 1 Now I add the 1 I’ve taken away from the Hundreds Column and add it to the Tens Column. Changing the 2 to a 12. 11 Borrow from the 12 in the tens column and make it 11, then add the 1 to the 1 in the ones column. 1 2 6 9 Now, subtract!!!

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