2. What is Addition? 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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
20. 2 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
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?
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
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?
25.
26. What is Subtraction? 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
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
29. You can also write the problem without the tens and the ones to make it look simpler as illustrated below
30. Another example 5424 - 756 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
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