Unit 5. Day 11.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Cross Multiplication CCSS.MATH.CONTENT.7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.

Proportion Situations 1) 𝑆𝑢𝑟𝑣𝑒𝑦𝑠 𝑎𝑛𝑑 𝑝𝑜𝑙𝑙𝑠 2) 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑠𝑡𝑠 𝑇𝑜𝑑𝑎𝑦 3) 𝐵𝑎𝑘𝑖𝑛𝑔/𝐶𝑜𝑜𝑘𝑖𝑛𝑔 4) 𝑀𝑎𝑝𝑠 5) 𝐴𝑛𝑐𝑖𝑒𝑛𝑡 𝐺𝑟𝑒𝑒𝑐𝑒:𝑓𝑖𝑛𝑑 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 Any time you expect the ratios to be the same

ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑡𝑜𝑡𝑎𝑙 = ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑡𝑜𝑡𝑎𝑙 Example A: 3 out of 8 students surveyed said that they liked history class the best. If there are 328 7th graders at RMS, how many students like history most? 3 8 328 ? 𝑥 ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑡𝑜𝑡𝑎𝑙 = ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑡𝑜𝑡𝑎𝑙 123 7𝑡ℎ 𝑔𝑟𝑎𝑑𝑒𝑟𝑠 𝑙𝑖𝑘𝑒 ℎ𝑖𝑠𝑡𝑜𝑟𝑦 𝑡ℎ𝑒 𝑚𝑜𝑠𝑡. 3 8 = 𝑥 328 3 328 = 8 𝑥 984 = 8𝑥 8 8 984 8 2∙2∙2∙3∙41 2∙2∙2 = 𝑥 = = 123 123

𝑓𝑟𝑜𝑔𝑠 𝑎𝑐𝑟𝑒𝑠 = 𝑓𝑟𝑜𝑔𝑠 𝑎𝑐𝑟𝑒𝑠 Example B: Scientists want to know how many rare bush frogs live in a nature preserve. Scientists search 3 acres and find 5 frogs. How many frogs live in the nature preserve if the preserve is 50 acres? 3 5 ? 50 𝑥 𝑓𝑟𝑜𝑔𝑠 𝑎𝑐𝑟𝑒𝑠 = 𝑓𝑟𝑜𝑔𝑠 𝑎𝑐𝑟𝑒𝑠 5 3 = 𝑥 50 5 50 = 3 𝑥 8 83. 3 3 . 3 3 3 2 5 0 . 250 = 3𝑥 − 2 4 3 3 1 − 9 𝐴𝑏𝑜𝑢𝑡 83 𝑓𝑟𝑜𝑔𝑠 𝑙𝑖𝑣𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑒𝑟𝑣𝑒. 250 3 1 = 𝑥 − 9 1

Proportion Situations 1) 𝑆𝑢𝑟𝑣𝑒𝑦𝑠 𝑎𝑛𝑑 𝑝𝑜𝑙𝑙𝑠 2) 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑠𝑡𝑠 3) 𝐵𝑎𝑘𝑖𝑛𝑔/𝐶𝑜𝑜𝑘𝑖𝑛𝑔 4) 𝑀𝑎𝑝𝑠 5) 𝐴𝑛𝑐𝑖𝑒𝑛𝑡 𝐺𝑟𝑒𝑒𝑐𝑒:𝑓𝑖𝑛𝑑 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 Any time you expect the ratios to be the same

𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝑐𝑜𝑢𝑛𝑐𝑖𝑙 𝑛𝑒𝑒𝑑𝑠 𝑡𝑜 𝑠𝑒𝑙𝑙 7,500 ℎ𝑜𝑡𝑑𝑜𝑔𝑠 𝑡𝑜 𝑟𝑒𝑎𝑐ℎ 𝑡ℎ𝑒 𝑔𝑜𝑎𝑙 Example C: Student Council is selling hotdogs for a fundraiser. They sold 24 hotdogs and made $16 profit. How many hotdogs does student council need to sell in order to raise their $5,000 goal? 24 16 ? 5000 $ ℎ𝑜𝑡𝑑𝑜𝑔𝑠 = $ ℎ𝑜𝑡𝑑𝑜𝑔𝑠 16 24 = 5000 𝑥 𝑥 8 12 = 5000 𝑥 4 6 = 5000 𝑥 2 3 = 5000 𝑥 2 𝑥 = 3 5000 2𝑥 = 15000 2 2 𝑥 = 7500 7500 𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝑐𝑜𝑢𝑛𝑐𝑖𝑙 𝑛𝑒𝑒𝑑𝑠 𝑡𝑜 𝑠𝑒𝑙𝑙 7,500 ℎ𝑜𝑡𝑑𝑜𝑔𝑠 𝑡𝑜 𝑟𝑒𝑎𝑐ℎ 𝑡ℎ𝑒 𝑔𝑜𝑎𝑙

Example D: Kat was making cupcakes for fun Example D: Kat was making cupcakes for fun. She made 45 cupcakes and the ingredients cost her $18. Someone asked her if she would make 300 cupcakes for a wedding. How much will the ingredients cost? 45 18 ? 300 18 45 = 𝑥 300 $ 𝑐𝑢𝑝𝑐𝑎𝑘𝑒 = $ 𝑐𝑢𝑝𝑐𝑎𝑘𝑒 𝑥 6 15 = 𝑥 300 2 5 = 𝑥 300 2 300 = 5 𝑥 𝑇ℎ𝑒 𝑖𝑛𝑔𝑟𝑒𝑑𝑖𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 300 𝑐𝑢𝑝𝑐𝑎𝑘𝑒𝑠 𝑤𝑖𝑙𝑙 𝑐𝑜𝑠𝑡 $120 5𝑥 600 = 5 5 600 5 2∙2∙2∙3∙5∙5 5 = 𝑥 = = 120 120

Proportion Situations 1) 𝑆𝑢𝑟𝑣𝑒𝑦𝑠 𝑎𝑛𝑑 𝑝𝑜𝑙𝑙𝑠 2) 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑠𝑡𝑠 3) 𝐵𝑎𝑘𝑖𝑛𝑔/𝐶𝑜𝑜𝑘𝑖𝑛𝑔 4) 𝑀𝑎𝑝𝑠 5) 𝐴𝑛𝑐𝑖𝑒𝑛𝑡 𝐺𝑟𝑒𝑒𝑐𝑒:𝑓𝑖𝑛𝑑 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 Any time you expect the ratios to be the same

. 5𝑥 = 26 5 5 5 3 8 2 3 ? 𝑓𝑙𝑜𝑢𝑟 𝑤𝑎𝑡𝑒𝑟 = 𝑓𝑙𝑜𝑢𝑟 𝑤𝑎𝑡𝑒𝑟 𝑥 Example E: When baking bread, you use 5 parts flour to 3 parts water. If you use 8 2 3 cups of flour, how many cups of water do you use? 5 3 8 2 3 ? 8 2 3 26 3 𝑓𝑙𝑜𝑢𝑟 𝑤𝑎𝑡𝑒𝑟 = 𝑓𝑙𝑜𝑢𝑟 𝑤𝑎𝑡𝑒𝑟 𝑥 5 3 = 26 3 𝑥 5 5.2 . 2 3 1 26 3 3 26 3 5 2 6 . 5 𝑥 = − 2 5 1 5𝑥 = 26 5 5 𝑌𝑜𝑢 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 5 1 5 𝑐𝑢𝑝𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟. 𝑥= 26 5 5 1 5 5 1 5 =

𝑌𝑜𝑢 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 5 𝑐𝑢𝑝𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟. 1 1 2 Example F: When making rice, you use 1 1 2 parts water to 1 part dry rice. If you use 3 1 3 cups of rice, how many cups of water do you use? 1 3 1 3 ? 3 2 𝑥 𝑤𝑎𝑡𝑒𝑟 𝑟𝑖𝑐𝑒 = 𝑤𝑎𝑡𝑒𝑟 𝑟𝑖𝑐𝑒 10 3 3 2 1 = 𝑥 10 3 3 2 10 3 = 1 𝑥 30 6 = 𝑥 𝑌𝑜𝑢 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 5 𝑐𝑢𝑝𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟. 5 5=𝑥