Transcript Adding and Subtracting Whole Numbers

Adding and Subtracting Whole
Numbers
What is Addition?

Addition is just a final count of numbers or items.

Also called the “sum.”
Let’s add large numbers.
12 and 34
12
+ 34
Line up numbers
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.)
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.
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.
Let’s add large numbers.
12 and 34
12
+ 34
46
Line up numbers
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.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
231
+459
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
231
+459
0
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.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
1
231
+459
0
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.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
1
231
+459
0
Now we will add the 3 and 5,
and also the 1 since it was
carried over.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
1
231
+459
90
Now we will add the 3 and 5,
and also the 1 since it was
carried over. 5+3+1=9 We do
NOT need to carry here.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
1
231
+459
90
Now we will add the 2 and 4
that in the far left column.
Adding larger numbers...
You may have to “carry” numbers to the
next column of numbers being added if
the first column is over 9.
1
231
+459
690
Now we will add the 2 and 4
that in the far left column.
2+4=6
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...
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?
You will simply need to ADD all
of those numbers up to get the
total.
5 0
1 2 9
7 8
+
2 3
0
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
0+9+8+3=20
2
5 0
1 2 9
7 8
+
2 3
0
Keep in mind to line up
the places, add each column,
and carry if the number
has more than one digit!
2+5+2+7+2=18
2
1
5 0
1 2 9
7 8
+
2 3
8 0
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
1
5 0
1 2 9
7 8
+
2 3
2 8 0
2
1
5 0
1 2 9
7 8
+
2 3
280
You got $280
in gifts!
Congratulations!!!
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
Other ways to perform additions
We used the round to the nearest 10 and
adjust strategy, for addition of 2 and 3
digit numbers
How can we mentally calculate 23 + 29?
What about a blank number line
How do we mentally calculate 23 + 29?
23 +29 is the same as 23+30-1
SO…
+30
52
53
23
-1
=23 + 30 – 1
=53 – 1
=52
“Joining up our thinking” Mapping
the partitioning strategy to our
jottings.
54 + 38
54
+ 38
80
12
80
10
2
92
50 + 30 +4 +8
Partitioning:
What is
happening in
our mind
when we use
this jotting?
54 + 38
50 + 30 +4 +8
Partitioning:
What is
happening in
our mind
when we use
this jotting?
50 + 4
+ 30 + 8
80 +12
= 92
Subtraction
What is Subtraction?
Subtracting whole numbers is
the inverse operation of
adding whole numbers.
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
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
You can also write the problem without the tens and the
ones to make it look simpler as illustrated below
Another example
5424
- 756
Always start
with the ones.
Step #1
Borrow a 10 from 2 tens
The problem becomes
Step #2
Borrow 1 hundred from 4 hundreds. 1
hundred = 10 tens. Then add 10 tens
to 1 ten to make it 11 tens
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
Let’s Try Some!
7 17
2 12
4,987
- 2,158
3,230
- 320
2, 8 2 9
1, 9 1 0