Contributed by:

Addition and Subtraction of Numbers

1.
Adding and Subtracting Whole

Numbers

Numbers

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

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

12

+ 34

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

12

+ 34

4.
Let’s add large

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

Then add the numbers

12 that are on top of each

other like you normally

would add numbers.

+ 34

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

Then add the numbers

12 that are on top of each

other like you normally

would add numbers.

+ 34

5.
Let’s add large

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

Then add the numbers

12 that are on top of each

other like you normally

would add numbers.

+ 34

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

Then add the numbers

12 that are on top of each

other like you normally

would add numbers.

+ 34

6.
Let’s add large

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

And do the same for the

12 other column of

numbers.

+ 34

12 and 34 Line

Line upup

the digits on top of

each other starting with

numbers the number on the right

(the rightmost digit, which

is called the “ones” place.)

And do the same for the

12 other column of

numbers.

+ 34

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.

231

You may have to “carry”

numbers to the next column of

numbers being added if the first

column is over 9.

231

8.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

column is overSince9.9+1=10, we will

write the last digit of 10

231 (the zero) and “carry” the

one above the 3 to the

left to add it.

0

You may have to “carry”

numbers to the next column of

numbers being added if the first

column is overSince9.9+1=10, we will

write the last digit of 10

231 (the zero) and “carry” the

one above the 3 to the

left to add it.

0

9.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is overSince9.9+1=10, we will

write the last digit of 10

231 (the zero) and “carry” the

one above the 3 to the

left to add it.

0

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is overSince9.9+1=10, we will

write the last digit of 10

231 (the zero) and “carry” the

one above the 3 to the

left to add it.

0

10.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 3

231 and 5, and also the 1

since it was carried over.

0

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 3

231 and 5, and also the 1

since it was carried over.

0

11.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 3

231 and 5, and also the 1

since it was carried over.

5+3+1=9 We do NOT

+459 need to carry here.

90

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 3

231 and 5, and also the 1

since it was carried over.

5+3+1=9 We do NOT

+459 need to carry here.

90

12.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 2

231 and 4 that in the far left

column.

90

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 2

231 and 4 that in the far left

column.

90

13.
Adding larger numbers...

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 2

231 and 4 that in the far left

column.

2+4=6

690

You may have to “carry”

numbers to the next column of

numbers being added if the first

1

column is over 9.

Now we will add the 2

231 and 4 that in the far left

column.

2+4=6

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

Let’s look at a real-world

able to successfully add positive

whole numbers!

This will be useful in all aspects of

this class AND in your everyday

Let’s look at a real-world

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?

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

1 2 9

7 8

+ 2 3

0

of those numbers up to get the

total.

5 0

1 2 9

7 8

+ 2 3

0

17.
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

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

18.
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

5 0

1

1 2 9

7 8

+ 2 3

8 0

the places, add each column,

and carry if the number

has more than one digit!

2+5+2+7+2=18

2

5 0

1

1 2 9

7 8

+ 2 3

8 0

19.
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

1

1 2 9

7 8

+ 2 3

2 8 0

the places, add each column,

and carry if the number

has more than one digit!

1+1=2

2

5 0

1

1 2 9

7 8

+ 2 3

2 8 0

20.
2

1

5 0

1 2 9

7 8

+ 2 3

28

You got $280

in gifts!

Congratulations!!!

1

5 0

1 2 9

7 8

+ 2 3

28

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

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

How can we mentally calculate 23 + 29?

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?

23.
What about a blank number line

How do we mentally calculate 23 + 29?

23 +29 is the same as 23+30-1

+30

52

53

23

-1

=23 + 30 – 1

=53 – 1

=52

How do we mentally calculate 23 + 29?

23 +29 is the same as 23+30-1

+30

52

53

23

-1

=23 + 30 – 1

=53 – 1

=52

24.
“Joining up our thinking” Mapping

the partitioning strategy to our

54 + 38 54 + 38

50 + 30 +4 +8 50 + 30 +4 +8

54

+ 38 Partitioning:

80 What is 50 + 4

12 + 30 + 8

happening

80 Partitioning: 80 +12

10

in our mind

What is when we

2 = 92

happening use this

92

in our mind jotting?

when we

use this

jotting?

the partitioning strategy to our

54 + 38 54 + 38

50 + 30 +4 +8 50 + 30 +4 +8

54

+ 38 Partitioning:

80 What is 50 + 4

12 + 30 + 8

happening

80 Partitioning: 80 +12

10

in our mind

What is when we

2 = 92

happening use this

92

in our mind jotting?

when we

use this

jotting?

25.

26.
What is Subtraction?

Subtracting whole

numbers is the inverse

operation of adding

whole numbers.

Subtracting whole

numbers is the inverse

operation of adding

whole numbers.

27.
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

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.
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 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

ones to make it look simpler as illustrated below

30.
Another example

5424

- 756

Always start

with the

ones.

5424

- 756

Always start

with the

ones.

31.
Step #1

Borrow a 10 from 2 tens

The problem becomes

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

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

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 2 12

4,987 3,230

- 2,158 - 320

2, 8 2 9 1, 9 1 0

7 17 2 12

4,987 3,230

- 2,158 - 320

2, 8 2 9 1, 9 1 0