1. Unit 2. Day 5.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Adding & Subtracting Rational Numbers
7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers (fractions)

3. Today’s Lesson
Add/subtract: Mixed Numbers
Add/Subtract: Decimals
Add/subtract: Mixture of fractions/decimals

4. Example A: Add or subtract. Write in simplest form.
5 5 6 −7 1 2
5 5 6
7 1 2
35 6 − 45 6
− 5 3
35 6
15 2
−10
− 2∙5 − = = 6 = =
2∙3 6 2
−1 2 3
15 2 45 6
35 6 35 6   : 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 64 , 60 : 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20

5. Example B*: Add or subtract. Write in simplest form.
6 3 5 −9 1 10
6 3 5
9 1 10
33 5
91 10
66 10 − 91 10
−25
− 5 2
−5∙5 − = = 10 = = 5 10
2∙5
−2 1 2 66 10
91 10 91 10
33 5   : 5 , 10 , 15 , 20 : 10 , 20

7. Today’s Lesson
Add/subtract: Mixed Numbers
Add/Subtract: Decimals
Add/subtract: Mixture of fractions/decimals

8. Example C: +
5.8−8.7= − − 7
5 . 8 1
8 . 7 − −
8 . 7
5 . 8
2 . 9 2 . 9

9. Example D*:
1.8−7.5
1.89−7.5
Example E*:
Example F*:
−6.27−0.975

10. Example D*: +
1.8−7.5= − − 6
1 . 8 1
7 . 5 − −
7 . 5
1 . 8
5 . 7 5 . 7

11. Example E*: +
1.89−7.5= − − 1 6 4 1
7 . 5 − −
7 . 5 5 . 6 1
7 . 5 − −
7 . 5

12. Example F*:
−6.27−0.975= − − − 1 1 1 1 + + 7 .
7.245 2 4 5 7
7.245 . 2 4 5

13. Example G*:
−0.05−0.45
−0.301
Example H*:

14. Example G: −
−0.05−0.45= − − 1 1 + +
0.5 . 5
0.5 . 5

15. Example H*: +
−0.301 = − − 2 9 1 1 − −
0.298 . 2 9 8

16. Example I*:
Mr. Jordan did not realize his checking account had a balance of $200 when he used his debit card for a $ purchase. What is his checking account balance after the purchase? −
317.25 =
200.00 −
117.25 − 1 1 7 . 2 5

18. Today’s Lesson
Add/subtract: Mixed Numbers
Add/Subtract: Decimals
Add/subtract: Mixture of fractions/decimals

19. Q: What is a rational number?
A: A number that can be written as a fraction 𝑝 𝑞
− 5 7
− 5 7
2 3
2 3
−4 5 6
−4 5 6
0.875
0.875
−16. 3
−16. 3
Today: + +

20. − −2 1 2
3 4
− 2 1 2
Example --:
− −2 1 2
3 4
− 2 1 2
−2.4
−2.4
Which way is better?
− 24 10
3 4
− 5 2 +
−2.4 +
0.75
−2.5
−2.5
− 20 48 20 15
− 20 50 + −
−48+15−50 20 −
−50 20
−33 1 1 3 1 1
2 . 4 − +
2 . 5
−4 3 20
−83 1 . 6 5 . 20 = 4
4.15 1 5

21. −
2 3
Example -:
−0.8
− 8 10
2 3 +
− 30 24 30 20 + − −4
−2 15 = 30 =

22. Example -:
In my opinion, fractions are preferable … as this problem demonstrates. −
2 3
−0.8
−0.8 + … − 7 1
0 . 8
−2 15 − =
−0.1 3
0.13 . 1 3

23. Example J*: +
− − −2 5 6
−1 1 6
2 5 6
4.5
− 7 6
45 10
17 6 + +
− 30 35 30
135 85 30 + + −
6 1 6
37 6
185
100 = = 30 =

24. Groups

25. −5.2− −3.1 +5.2 Example K: Example L: Example M: Example N:
32 + −12 7 8
Example L:
− −5 5 6
Example M:
16 20 − −1.8 − 4 5
Example N:
S.51 Exercise 2

26. +
Example K*:
−5.2− −
3.1

27. Example L*:
32 + −12 7 8
−12 7 8 32
32 1
− 103 8 8
256
− 8
103
256−103 8
153 8 =

28. + + 9 29.3 + + Example M*: 3 1 6 +20.3 − −5 5 6 3 1 6 +20.3 − −5 5 6
− −5 5 6
− −5 5 6
3 1 6
5 5 6
3 1 6
5 5 6
20.3
20.3
19 6
203 10
35 6 + +
19 6
35 6 + 30 95 30
609
175 30 + + 6 54 9 +
879 30 = = =
29.3
29.3

29. Example N*: +
16 20 − −1.8 − 4 5
16 20
− 4 5
1.8
4 5
− 4 5
18 10
− 4 5
18 10 + 10 8 18 −8 10 10 + +
9 5
1.8
8+18−8 10
1 4 5 26
−8 10
9 5
1 4 5 18 = 10 = =