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Adding and Subtracting Whole Numbers

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What is Addition?• Addition is just a final count of numbers or

items.

• Also called the “sum.”

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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.)

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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.

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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.

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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.

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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

+ 4 5 9

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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

+ 4 5 9

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.

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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

+ 4 5 9

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.

1

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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

+ 4 5 9

0

Now we will add the 3 and 5, and also the 1 since it was carried over.

1

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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

+ 4 5 9

9 0

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.

1

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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

+ 4 5 9

9 0

Now we will add the 2 and 4 that in the far left column.

1

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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

+ 4 5 9

6 9 0

Now we will add the 2 and 4 that in the far left column.

2+4=6

1

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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...

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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?

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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

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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

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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!

2+5+2+7+2=18

2

1

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5 0

1 2 9

7 8

+ 2 3

2 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

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5 0

1 2 9

7 8

+ 2 3

2 8 0

You got $280 in gifts!

Congratulations!!!

2

1

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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

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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?

Other ways to perform additions

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What about a blank number line

How do we mentally calculate 23 + 29?

23

+30

-1

53

52

=23 + 30 – 1=53 – 1=52

23 +29 is the same as 23+30-1SO…

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“Joining up our thinking” Mapping the partitioning strategy to our jottings.

54 + 38 80 12 80 10 2 92

50 + 4+ 30 + 8 80 +12

= 92

54 + 38

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?

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Subtraction

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What is Subtraction?

Subtracting whole numbers is the inverse operation of adding whole numbers.

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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

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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

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

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Another example

Always start with the ones.

5424- 756

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Step #1

Borrow a 10 from 2 tens

The problem becomes

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Step #2

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

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Step #3Borrow 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

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Let’s Try Some!

4,987

- 2,1583,230

- 320

177 212

9282, 1,9 1 0