Unit 2. Day 6.

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

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

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

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 = ∙ = −

− 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*:

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

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

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 ∙ = = −

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

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

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

5 6 Example D: When Mr. Jordan woke up, he had 5 6 of his battery left. During the day, he was using his calculator to do fun math problems. He used 3 8 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 = = =

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 = = =

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

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

∙ − − 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 ∙ = = −

Divide. Write in simplest form. − 2 3 ÷− 10 9 Example F*: − 15 16 ÷ 35 14 Example G*: 3 8 9 ÷−1 3 4 Example H*:

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 ∙ = =

Example G*: Divide. Write in simplest form. 35 − 15 16 ÷ 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 ∙ = =

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

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

5 8 5 12 Example I*: Mr. Jordan walked 5 8 miles in 5 12 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

Example J: Mr Jordan has 2 4 9 cups of jelly beans Example J: Mr Jordan has 2 4 9 cups of jelly beans. If he divides the jelly beans into 1 3 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

“How many times larger?” Word problems

Example K. : Mr Jordan makes breakfast and uses 5 1 4 cups of rice. Mr Example K*: Mr Jordan makes breakfast and uses 5 1 4 cups of rice. Mr. Yost only uses 3 4 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