Unit 3: Subtraction
Topic C: Renaming
When you subtract, you may need to rename. Renaming means changing from one place value to another.
For example:
- 1 ten can be renamed as 10 ones
- 1 hundred can be renamed as 10 tens
- 1 thousand can be renamed as 10 hundreds.
Renaming is an important part of subtracting. Sometimes the digit on top is smaller than the digit you are subtracting. This means that you will have to rename before you can subtract. This is also called borrowing.
Example A: 293
2 hundreds, 9 tens, 3 ones
renamed 2 hundreds, 8 tens, 13 ones
You borrow 1 ten. The 1 ten is renamed as 10 ones.
10 ones + 3 ones = 13 ones
Example B: 3782
3 thousands, 7 hundreds, 8 tens, 2 ones
Renamed 3 thousands, 6 hundreds, 18 tens, 2 ones
You borrow 1 hundred. The 1 hundred is renamed as 10 tens.
10 tens + 8 tens = 18 tens
Exercise One
Borrow from the number in the shaded box. Check your work using the answer key at the end of the exercise.
-
ten thousands thousands hundreds tens ones 423 4 2 3 4 1 13 -
ten thousands thousands hundreds tens ones 642 -
ten thousands thousands hundreds tens ones 1456 -
ten thousands thousands hundreds tens ones 5423 -
ten thousands thousands hundreds tens ones 6384
Answers to Exercise One
-
ten thousands thousands hundreds tens ones 642 6 4 2 6 3 12 -
ten thousands thousands hundreds tens ones 1456 1 4 5 6 1 4 4 16 -
ten thousands thousands hundreds tens ones 5423 5 4 2 3 5 4 1 13 -
ten thousands thousands hundreds tens ones 6384 6 3 8 4 6 2 18 4
Sometimes there is a zero in the place where you want to borrow from. You will need to move one more place value to the left and borrow from there.
Example C: 203
2 hundreds, 0 tens, 3 ones
renamed 1 hundreds, 10 tens, 3 ones
You borrow 1 hundred. The 1 hundred is renamed as 10 tens.
1 hundred, 9 tens, 13 ones
Then, you borrow 1 ten. The 1 ten is renamed as 10 ones.
10 ones + 3 ones = 13 ones
Example D: 30 782
3 ten thousands, 0 thousands, 7 hundreds, 8 tens, 2 ones
renamed 2 ten thousands, 10 thousands, 7 hundreds, 8 tens,
2 ones
You borrow 1 ten thousand. The 1 ten thousand is renamed as 10 thousands.
2 ten thousands, 9 thousands, 17 hundreds, 8 tens, 2 ones Then, you borrow 1 thousand. The 1 thousand is renamed as 10 hundreds.
10 hundreds + 7 hundreds = 17 hundreds
Exercise Two
Borrow from the number in the shaded box. Check your work using the answer key at the end of the exercise.
-
ten thousands thousands hundreds tens ones 403 4 0 3 3 10 3 3 9 13 -
ten thousands thousands hundreds tens ones 501 -
ten thousands thousands hundreds tens ones 904 -
ten thousands thousands hundreds tens ones 307
Answers to Exercise Two
-
ten thousands thousands hundreds tens ones 403 4 0 3 3 10 3 3 9 13 -
ten thousands thousands hundreds tens ones 501 5 0 1 4 10 1 4 9 11 -
ten thousands thousands hundreds tens ones 904 9 0 4 8 10 4 8 9 14 -
ten thousands thousands hundreds tens ones 307 3 0 7 2 10 7 8 9 14
Need more practice?
Ask your instructor for some play money. Using the one, ten, hundred, thousand, ten thousand and hundred thousand dollar bills, practice trading one of one type of bill for ten of the lesser place value.
Example:
| ABE bucks
$10 Ten |
= | ABE bucks
$1 One |
ABE bucks
$1 One |
| ABE bucks
$1 One |
ABE bucks
$1 One |
ABE bucks
$1 One |
|
| ABE bucks
$1 One |
ABE bucks
$1 One |
ABE bucks
$1 One |
|
| ABE bucks
$1 One |
ABE bucks
$1 One |
||
| ABE bucks
$1 One |
|||
| ABE bucks
$1 One |
|||
| ABE bucks
$1 One |
|||
| ABE bucks
$1 One |
|||
| ABE bucks
$1 One |
Topic C: Self-Test
Mark /12 Aim 10/12
- Borrow from the number in the shaded box. (6 marks)
-
ten thousands thousands hundreds tens ones 783 -
ten thousands thousands hundreds tens ones 827 -
ten thousands thousands hundreds tens ones 7942 -
ten thousands thousands hundreds tens ones 5364 -
ten thousands thousands hundreds tens ones 28634 -
ten thousands thousands hundreds tens ones 62751
-
- Borrow from the number in the shaded box. 6 marks.
-
ten thousands thousands hundreds tens ones 602 -
ten thousands thousands hundreds tens ones 805 -
ten thousands thousands hundreds tens ones 3075 -
ten thousands thousands hundreds tens ones 7048 -
ten thousands thousands hundreds tens ones 30478 -
ten thousands thousands hundreds tens ones 80946
-
Answers to Topic C Self-Test
-
-
ten thousands thousands hundreds tens ones 783 7 8 3 7 7 13 -
ten thousands thousands hundreds tens ones 827 8 2 7 8 1 17 -
ten thousands thousands hundreds tens ones 7942 7 9 4 2 7 8 14 2 -
ten thousands thousands hundreds tens ones 5364 5 3 6 4 5 2 16 4 -
ten thousands thousands hundreds tens ones 28634 2 8 6 3 4 2 7 16 3 4 -
ten thousands thousands hundreds tens ones 62751 6 2 7 5 1 6 1 17 5 1
-
-
-
ten thousands thousands hundreds tens ones 602 6 0 2 5 10 2 5 9 12 -
ten thousands thousands hundreds tens ones 805 8 0 5 7 10 5 7 9 15 -
ten thousands thousands hundreds tens ones 3075 3 0 7 5 2 10 7 5 2 9 17 5 -
ten thousands thousands hundreds tens ones 7048 7 0 4 8 6 10 4 8 6 9 14 8 -
ten thousands thousands hundreds tens ones 30478 3 0 4 7 8 2 10 4 7 8 2 9 14 7 8 -
ten thousands thousands hundreds tens ones 80946 8 0 9 4 6 7 10 9 4 6 7 9 19 4 6
-