1. M4.A.3 Compute accurately and fluently and make reasonable estimates.
M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally - straight computation only).

2. M4.A.3.2 Eligible Content
M4.A Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places).
M4.A Solve addition or subtraction problems with fractions with like denominators (denominators to 10, no simplifying necessary).

3. M4.A Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places).

4. PSSA Sample Item

5. Adding and Subtracting Decimals
When adding & subtracting numbers with decimals, stack the numbers on top of each other lining the decimals up. Remember, if a number doesn’t have a decimal, it comes at the end of the number.
EX: 
+ 5.2
I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

6. Adding and Subtracting Decimals
EX: 
102.64
I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

7. Addition of Decimals
2.35
+ 4.92

8. Addition Algorithm for Decimals
2.35
+ 4.92 7
Place Value: Start with smallest pieces (hundredths)
Basic Fact: 5 hundredths + 2 hundredths = 7 hundredths
Basic Fact: = 7
Rename: not needed

9. Addition Algorithm for Decimals1
2.35
+ 4.92
.27
Place Value: tenths
Basic Fact: 3 tenths + 9 tenths = 12 tenths
Basic Fact: = 12
Rename: 12 tenths as 1 one + 2 tenths

10. Addition Algorithm for Decimals1
2.35
+ 4.92
7.27
Place Value: ones
Basic Fact: 1 one + 2 ones + 4 ones = 7 ones
Basic Fact: = 7
Rename: not needed

11. 
+ 0.02
722.88
ON ADDITION, you don’t have to fill in 0’s but you can.
With SUBTRACTION, you need to fill in 0’s if the number is on top. EX: 8 – 2.54
8.00
2.54
5.46

12. 75 –  (add a decimal
& a couple 0’s)
75.00
0.24
74.76
Now try these:
b) 100 – 0.48
c) – d) 43 – 7.23

13. 72.3 – 4
89 – 42.36
44.2 – 39.67
66.23 – 44.97
Line up the decimals as shown below
These will all need 0’s added.

14. Lesson 35: Add, Subtract, Multiply & Divide Decimal Numbers
Rule for adding and subtracting decimals:
Line up the decimal point!!
Example 1: Add
3.6
+ .36
Add “0” if needed
to keep decimal
place.
3.60
+ 0.36
Answer: 3.96

15. Example 2: Subtract
Step 1: write the numbers vertical, aligning the decimal point
12.3
12.300
Add “0” to even out the places
Step 2: Subtract (be sure to borrow correctly when needed)
Answer:
7.733

16. Adding and Subtracting Decimals
LINE UP DECIMAL POINTS BEFORE YOU ADD OR SUBTRACT.
123.76
0.0009
123.76
0.0009
Now you can’t confuse the VALUE of each digit.
Now, just add or subtract as you normally would. You may add zeros to the end of a decimal to line up place values – just like comparing decimals.
Trying to add like this can be confusing, the place values are all mixed up

17. Subtracting Decimal Numbers
Ex) Max went to Wal-Mart with $ He then bought a television for $ How much money did he have left over?

18. Subtracting Decimal Numbers
Ex) Max went to Wal-Mart with $ He then bought a television for $ How much money did he have left over?
Solution: Line up the numbers vertically according to place value.

19. Subtracting Decimal Numbers

20. Subtracting Decimal Numbers

21. Subtracting Decimal Numbers4

22. Subtracting Decimal Numbers4

23. Subtracting Decimal Numbers4 3

24. Subtracting Decimal Numbers
1 4 3

25. Subtracting Decimal Numbers
1 14 3

26. Subtracting Decimal Numbers
1 14
6 3

27. Subtracting Decimal Numbers
1 14
. 6 3

28. Subtracting Decimal Numbers
. 6 3

29. Subtracting Decimal Numbers

30. Subtracting Decimal Numbers

31. Subtracting Decimal Numbers

32. Subtracting Decimal Numbers

33. Subtracting Decimal Numbers
Max had $ left.

34. Practice Adding Decimals
+ 5.6 b) c) d) e) f) g) h)

35. Practice Adding Decimals b) c) d) e) f) g) h)

36. Practice Subtracting Decimalsf) g)
h)  

37. Practice Subtracting Decimalsf) g)
h)  

38. M4.A Solve addition or subtraction problems with fractions with like denominators (denominators to 10, no simplifying necessary).

39. PSSA Sample Item

40. PSSA Sample Item

41. PSSA Sample Item

42. 3 4 Parts of a Fraction = the number of parts
= the total number of parts that equal a whole

43. Parts of a Fraction 3
= numerator 4
= denominator

44. Adding and Subtracting Fractions with like Denominators
You know that the bottom number of a fraction tells how may parts each whole is divided into.
In this picture each circle is divided into 4 parts so the bottom number for this fractions is 4. 4
We use or shade 5 parts so the top number of this fraction is 5. The picture shows the fraction
In a fraction the bottom number has a special name. The bottom number in a fraction is called the denominator. The denominator or the bottom number in a fraction tells how many parts each whole is divided into.

45. What are the denominators in these fractions?1 2
Two
Six
Eight
Five
Three
Remember the bottom number in a fraction is called the denominator. 4 6 7 8 7 5 2 3

46. You have learned to add fractions using pictures.
Fractions can be added and subtracted without using pictures.
Here’s a problem.
5 3
4 4
When you add and subtract fractions you do not work on the top and the bottom the same way. + = + = = +

47. Look at this problem. What is the denominator? Yes, it’s 4.
When you add and subtract fractions you COPY the denominator, then you work on the top. Remember, you copy the denominator and then you work on the top.
5 3
4 4
Look at this problem. What is the denominator?
Yes, it’s 4.
What do you do with the denominator?
Right, you copy it in the answer so the denominator in the answer is 4.
Now we can add the numbers on the top. What do we get when we add 5 + 3?
Correct, = 8.
We put the 8 on top in the answer so = 8 . + = 4

48. 5
Here’s a different problem. First look at the sign. We are subtracting in this problem.
Next look at the denominators. What do we do with the denominator?
Yes, we copy it in the answer.
On the top the sign tells us to subtract. 7 – 2, what’s the answer?
Right, 7 – 2 = 5. We put the 5 on top. - = 5 - =

49. Let’s try another problem.
4 3 2
First you copy the denominator then you work the top.
What is the denominator?
Yes, it’s 2.
Now work on the top. What is 4 – 3?
Right, it’s 1. So - = 2 - =

50. 4 4 4 Here’s a new problem. + = 2 3 + 4 =
2 3 4
What do we do with the denominator?
Yes, we copy the 4.
What do we get on top?
Good Job! = 5. + = + =

51. Subtracting Like Denominators
Only subtract the numerators
1/4
1/4 4 1 3 - = 4 4 4
1/4
1/4

52. Subtract these fractions
1/5
1/5 4 1 3 - =
1/5 5 5 5
1/5

53. Subtract these fractions
1/4
1/4 3 1 2 - = 4 4 4
1/4

54. Subtract these fractions1 1 1 6 6 6 5 2 3 - = 6 6 6 1 1 6 6

55. Subtract these fractions1 1 1 6 6 6 4 2 2 - = 6 6 6 1 6

56. Subtract these fractions5 3 2 - = 12 12 12

57. Subtract these fractions9 3 6 - = 10 10 10

58. Subtract these fractions4 3 1 - = 4 4 9 9 9

59. Subtract these fractions7 1 6 - = 5 5 8 8 8

60. Subtract these fractions8 2 6 - 4 3 = 1 9 9 9

61. - Check your work - - Your Turn
Copy these problems on your paper and write the answer. 6 5 - = 7 3 + =
Check your work 4 6 - = 7 4 - = 5 4 = +

62. You have learned to work problems this way.
You can also work fraction addition and subtraction problems when they are written this way.
5 8
8 3
2 2
7 6
Just like before check to see if you can work the problem the way it is written, copy the denominator, then add or subtract. - + = = + -

63. Your Turn

64. Your Turn 7 8 5 4 6 1 3 1 6