1. Adding and Subtracting Whole Numbers
This is a powerpoint presentation about how to add and subtract positive whole numbers without the use of a calculator.

2. What is Addition? Addition is just a final count of numbers or items.
Also called the “sum.”
Addition is just a final count of numbers or items. Also called the “sum.”

3. Let’s add large numbers.
12 and 34 Line up numbers 12
+ 34
Line up the digits on top of each other starting with the number on the right (the rightmost digit, which is called the “ones” place.)
Take the numbers 12 and 24. If numbers have more than one digit, you must line up the place values on top of each other.

4. Let’s add large numbers.
12 and 34 Line up numbers 12
+ 34 6
Line up the digits on top of each other starting with the number on the right (the rightmost digit, which is called the “ones” place.)
Then add the numbers that are on top of each other like you normally would add numbers.

5. Let’s add large numbers.
12 and 34 Line up numbers 12
+ 34 6
Line up the digits on top of each other starting with the number on the right (the rightmost digit, which is called the “ones” place.)
Then add the numbers that are on top of each other like you normally would add numbers.

6. Let’s add large numbers.
12 and 34 Line up numbers 12
+ 34 46
Line up the digits on top of each other starting with the number on the right (the rightmost digit, which is called the “ones” place.)
And do the same for the other column of numbers.

7. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1
When adding numbers, You may have to “carry” numbers to the next column of numbers being added if the first column is over 9. Let’s look at an example. Let’s add 231 and Make sure to line up the digits in their respective places.

8. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1
Since 9+1=10, we will write the last digit of 10 (the zero) and “carry” the one above the 3 to the left to add it.
Then start with the far right column with the addition.

9. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1 1
Since 9+1=10, we will write the last digit of 10 (the zero) and “carry” the one above the 3 to the left to add it.
Since 9+1=10, we will write the last digit of 10 (the zero) and “carry” the one above the 3 to the left to add it. Then move to the next column to the left.

10. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1 1
Now we will add the 3 and 5, and also the 1 since it was carried over.
Now we will add the 3 and 5, and also the 1 since it was carried over.

11. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1
9 0 1
Now we will add the 3 and 5, and also the 1 since it was carried over =9 We do NOT need to carry here.
Now we will add the 3 and 5, and also the 1 since it was carried over =9 We do NOT need to carry here.

12. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1
9 0 1
Now we will add the 2 and 4 that in the far left column.
Now we will add the 2 and 4 that in the far left column.

13. Adding larger numbers...
You may have to “carry” numbers to the next column of numbers being added if the first column is over 9.
2 3 1
6 9 0 1
Now we will add the 2 and 4 that in the far left column.
2+4=6
Now we will add the 2 and 4 that in the far left column, which give you 6. The answer is 690.

14. With some practice, you will be able to successfully add positive whole numbers!
This will be useful in all aspects of this class AND in your everyday life.
Let’s look at a real-world example...

15. You graduated from Broward College!!!!
As some of your graduation gifts, you receive gifts from family and friends with the values of $50, $129, $78, and $23.
What is the total value of these gifts?

16. You will simply need to ADD all of those numbers up to get the total.
5 0
7 8

17. the places, add each column,
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
=20 2
5 0
7 8

18. the places, add each column,
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
=18 2
5 0
7 8
8 0 1

19. the places, add each column,
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
1+1=2 2
5 0
7 8 1

20. You got $280 in gifts! Congratulations!!! 5 0 1 2 9 7 8 + 2 3 2 8 0 2
5 0
7 8
2 8 0 1
You got $280
in gifts!
Congratulations!!!

21. Other things, you need to know…
Associative Property of Addition
When: (a + b) + c = a + (b + c)
Commutative Property of Addition
When: a + b= b + a
Zero Property of Addition
When: a + 0= a

22. Other ways to perform additions
We used the round to the nearest 10 and adjust strategy, for addition of 2 and 3 digit numbers
When adding numbers, you may also use the following strategy. You can round up to ten since counting by ten seems easier for most people.
How can we mentally calculate ?

23. What about a blank number line
How do we mentally calculate ?
is the same as
SO…
+30 52 53 23 -1
= – 1
=53 – 1
=52

24. “Joining up our thinking” Mapping the partitioning strategy to our jottings. 54
+ 38 80 12 10 2 92
Partitioning:
What is happening in our mind when we use this jotting?
50 + 4
80 +12
= 92
Partitioning:
What is happening in our mind when we use this jotting?

25. Subtraction

26. What is Subtraction?
Subtracting whole numbers is the inverse operation of adding whole numbers.

27. Subtractions with one digit are usually fairly easy
Subtractions with one digit are usually fairly easy. Things start getting complicated when you have more than one digit and you cannot remove the number at the bottom from the number on top such as when doing 85 − 8

28. Example
Since you could not remove 8 from 5, you borrowed a ten from 8 tens and add that to 5 to make it 15

29. You can also write the problem without the tens and the ones to make it look simpler as illustrated below

30. Another example
Always start with the ones.

31. Step #1
Borrow a 10 from 2 tens The problem becomes

32. Step #2
Borrow 1 hundred from 4 hundreds. 1 hundred = 10 tens. Then add 10 tens to 1 ten to make it 11 tens

33. Step #3
Borrow 1 thousand from 5 thousands. 1 thousand = 10 hundreds. Then add 10 hundreds to 3 hundreds to make it 13 hundreds Then, just subtract now since all numbers at the bottom are smaller than the number on top

34. Let’s Try Some! 7 17
3,230
- 320 2 12
4,987
- 2,158 1, 9 1 2, 8 2 9