Adding and Subtracting Whole Numbers What is Addition

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 12 + 34 6 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. ) 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 6 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. ) 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 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