7 + 5 = 12, carry 1-ten to the 10's place. Add the 10's column.
| ADDITION & SUBTRACTION PRIMER |
Adding: Carrying On
When we add small numbers -- say 3 and 4 -- together, we don't have to pay attention to the column or place in which to write the sum, because it is smaller than 10. We write it in the one's column. But, if our sum is greater than 10 -- say we have 7 + 9 -- the answer is 16 -- that's 1-ten and 6-ones. Since we're only allowed to put a single digit in each column -- we can't write 16 in the 1's column -- so we carry one 10 to its rightful place -- the 10's column -- and we write 16.
Though it is called Regrouping in many text books, this operation should be called CARRYING -- because we carry a ten over a column, to its proper place. We do the same with 100's, 1000's and gazillions of course. (There's no units called gazillions).
Examples:
1) carrying to the 10's column:
7 + 5 = 12, carry 1-ten to the 10's place. Add the 10's column.
2) carrying to the 100's column:
3) Carrying on:
.
Subtracting: Borrowing from a Neighbor
When we subtract a small number from a big one, say 9 – 4, we write 5 in the 1's column and we're done. However, say we have to find 65 – 37. Now, we have to subtract 7 from 5 in the one's column, but we can't do it, because 7 is bigger than 5. So, we borrow 10-ones from the neighboring number -- the 6 -- in the ten's column. We think of 65 as 5 tens + 15 ones -- and now we can subtract 7 from 15 in the 1's column, to get 8. The difference in the 10's column now is 50 – 30 or 20 because we borrowed 1 of the 6 tens from 60.
The answer is 28.
In order to check our subtraction, we add 28 to 37 to get 65.
Borrowing more than once:
Borrowing from Nothing
.
Regrouping in Addition is called CARRYING.
Regrouping in Subtraction is called BORROWING.
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
Practice Exercise 1: Addition
1) Use Addition with Carrying to find these sums:
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  |
h)  |
Practice Exercise 2: Subtraction
1) Use Subtraction with Borrowing to find these differences:
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  |
h)  |
i)  |
j)  |
.
Solutions
Practice Exercise 1: Addition
1) Use Addition with Carrying to find these sums:
a)  |
b)  |
c)  |
d)   |
e)  |
f)  |
g)  |
h)  |
Practice Exercise 2: Subtraction
1) Use Subtraction with Borrowing to find these differences:
| a)
|
b)
|
c)
|
d)
|
| e)
|
f)
|
g)
|
h)
|
| i).
|
j)
|
