1. Unit 2. Day 6.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Multiplying Rational Numbers
7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers

3. Multiplying Fractions “Of” and word problems Dividing Fractions
Today’s Lesson
Multiplying Fractions
“Of” and word problems
Dividing Fractions

4. Example 6th Grade
6 7 ∙ 3 4
6∙3 18
2∙3∙3
9 14 = = = =
7∙4 28
2∙2∙7 18 28 2 9 4 7 3 3 2 2
6 7 ∙ 3 4
2∙3 3
9 14 = ∙ =
2∙2 7

5. Example 7th grade: Multiply. Write in simplest form.
6 7 ∙− 3 4
6∙3 18
2∙3∙3
9 14 = = = = −
7∙4 28
2∙2∙7 18 28 2 9 4 7 3 3 2 2
6 7 ∙− 3 4
2∙3 7
3 2∙2
9 14 = ∙ = −

6. − 7 8 ∙ 4 21 − 6 5 ∙− 15 16 Multiply. Write in simplest form.
Example A*:
− 6 5 ∙− 15 16
Example B*:
−2 5 8 ∙3 3 7
Example C*:

7. Example A*: Multiply. Write in simplest form.
− 7 8 ∙ 4 21
7∙4 28
2∙2∙7
1 6 = = = = −
8∙21
2∙2∙2∙3∙7
168
168 28 21 8 4 7 3 7 4 2 2 2 2 2
− 7 8 ∙ 4 21 7
2∙2
1 6 ∙ − = =
2∙2∙2
3∙7

8. Example B*: Multiply. Write in simplest form.
− 6 5 ∙− 15 16
6∙15 90
2∙3∙3∙5
9 8 = = = = +
5∙16
2∙2∙2∙2∙5 80 80 90 4 20 9 10 2 2 4 5 3 3 2 5 2 2
− 6 5 ∙− 15 16
2∙3 5
3∙5 2∙2∙2∙2
9 8
1 1 8 ∙ = = + 𝑜𝑟

9. Example C*: Multiply. Write in simplest form.
−2 5 8 ∙3 3 7
2 5 8
3 3 7
21 8
24 7
21∙24
504 = ∙ = =
8∙7 56
2∙2∙2∙3∙3 ∙7 =
2∙2∙2∙7
504 56 8
9 1 21 24 7 − = 𝑜𝑟 −9 4 2 3 7 4 6 2 2 2 2 2 3
3∙7 2∙2∙2
21 8 ∙ 24 7
2∙2∙2∙3 7
9 1 ∙ = = −

11. Multiplying Fractions “Of” and word problems Dividing Fractions
Today’s Lesson
Multiplying Fractions
“Of” and word problems
Dividing Fractions

12. “of” Word problems when multiplying fractions Half of $60  $30 1 2
60 1
Half of $60 ∙ 
$30
60 2 = = 30

13. “of” Word problems when multiplying fractions
5 8 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔. 𝑊𝑒 𝑒𝑎𝑡 ℎ𝑎𝑙𝑓 𝑜𝑓 𝑡ℎ𝑎𝑡.
5 8
1 2 ∙
5 16 =

14. 5 6
Example D: When Mr. Jordan woke up, he had of his battery left. During the day, he was using his calculator to do fun math problems. He used of his remaining battery life. What fraction of total battery power did he use?
3 8 ∙
15 48
3∙5 2∙2∙2∙2∙3
5 16 = = =

15. 1 2
Example E*: Mr. Jordan’s grandma dies and leaves half of a piece of land to Mr. Jordan’s mother, Julie. When Julie dies, she gives one-fourth of her inheritance to Mr. Jordan. What fraction of the land does Mr. Jordan inherit?
1 4 ∙
1 8
1 2∙2∙2
1 8 = = =

17. Multiplying Fractions “Of” and word problems Dividing Fractions
Today’s Lesson
Multiplying Fractions
“Of” and word problems
Dividing Fractions

18. 6th Grade 5
3 4
3 4 ÷ 5 8
5 8
3∙8 24
2∙2∙2∙3
6 5 ÷ = ∙ = = = = 8
4∙5 20
2∙2∙5 𝑜𝑟
1 1 5 24 20 4 6 4 5 2 2 2 3 2 2
3 4 ∙ 8 5
3 2∙2
2∙2∙2 5
6 5
1 1 5 ∙ = = 𝑜𝑟

19. ∙ − − 3 4 ∙ 8 5 3 2∙2 2∙2∙2 5 = = 7th Grade 5 − 3 4 ÷− 5 8 3 4 − 5 8 ∙
3∙8 24
2∙2∙2∙3
6 5 ÷ ∙ − = = = = = 8
4∙5 20
2∙2∙5 24 20 4 6 4 5 2 2 2 3 2 2
3 4 ∙ 8 5
3 2∙2
2∙2∙2 5
6 5 ∙ = = −

20. Divide. Write in simplest form.
− 2 3 ÷− 10 9
Example F*:
− ÷ 35 14
Example G*:
3 8 9 ÷−1 3 4
Example H*:

21. Example F*: Divide. Write in simplest form.10
− 2 3 ÷− 10 9
2 3
10 9
2∙9 18
2∙3∙3
3 5 ÷ = ∙ = = = = 9
3∙10 30
2∙3∙5 18 30 2 9 3 10 3 3 2 5
2 3 ∙ 9 10
2 3
3∙3 2∙5
3 5 ∙ = =

22. Example G*: Divide. Write in simplest form.35
− ÷ 35 14
15 16
35 14
15∙14
210
2∙3∙5∙7 ÷ = ∙ = = = 14
16∙35
560
2∙2∙2∙2∙5∙7
3 8 = −
560
210 35 16 15 14 5 7 4 4 3 5 2 7 2 2 2 2
15 16 ∙ 14 35
3∙5 2∙2∙2∙2
2∙7 5∙7
− 3 8 ∙ = =

23. Example H*: Divide. Write in simplest form.− 7
3 8 9 ÷−1 3 4
3 8 9
−1 3 4
− 7 4
35 9
35∙4
140
2∙2∙5∙7 = = ÷ ∙ = =
3∙3∙7 4
9∙7 63
20 9
2 2 9 = − 𝑜𝑟 − 63
140 9 7 4 35 3 3 5 7 2 2
5∙7 3∙3
35 9 ∙− 4 7
2∙2 7
− 20 9
−2 2 9 ∙ = = 𝑜𝑟

24. Speed
Word problems
30 𝑚𝑖𝑙𝑒𝑠 1ℎ𝑜𝑢𝑟
𝑘𝑚/ℎ
𝑚𝑖 ℎ
𝑘𝑚 ℎ
𝑚𝑖÷ℎ
𝑘𝑚÷ℎ

25. 5 8
5 12
Example I*: Mr. Jordan walked miles in hr. What is his speed?
Speed
𝑚𝑖 ℎ𝑟 : ÷ = 5
5 8 ÷ 5 12
5 8
5 12
5∙12
3 2 60
2∙2∙3∙5 ÷ = ∙ = = = = 12
8∙5 40
2∙2∙2∙5
1 1 2 = 60 40 6 10 4 10 2 3 2 5 2 2 2 5

26. Example J: Mr Jordan has 2 4 9 cups of jelly beans
Example J: Mr Jordan has cups of jelly beans. If he divides the jelly beans into cup containers, how many containers will he need?
2 4 9
2 4 9
1 3
1 3
22 9
3 1
66 9
2∙3∙11 3∙3
22 3 ÷ ÷ = ∙ = = =
7 1 3

27. “How many times larger?”
Word problems

28. Example K. : Mr Jordan makes breakfast and uses 5 1 4 cups of rice. Mr
Example K*: Mr Jordan makes breakfast and uses cups of rice. Mr. Yost only uses cup of rice. How many times larger is the amount of rice used by Mr. Jordan?
5 1 4
5 1 4
3 4
3 4
21 4
4 3
84 12
2∙2∙3∙7 2∙2∙3
7 1 ÷ ÷ = ∙ = = = = 7