1. Unit 5. Day 11.

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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
= 𝑥 𝑥
8 12 = 𝑥
4 6 = 𝑥
2 3 = 𝑥
2 𝑥 = 2𝑥 =
15000 2 2 𝑥 =
7500
7500
𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝑐𝑜𝑢𝑛𝑐𝑖𝑙 𝑛𝑒𝑒𝑑𝑠 𝑡𝑜 𝑠𝑒𝑙𝑙 7,500 ℎ𝑜𝑡𝑑𝑜𝑔𝑠 𝑡𝑜 𝑟𝑒𝑎𝑐ℎ 𝑡ℎ𝑒 𝑔𝑜𝑎𝑙

8. 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
= 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

9. 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

10. . 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 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 = 𝑥 5
5.2 . 2 5
2 6 .
5 𝑥 = −
2 5 1 5𝑥 = 26 5 5
𝑌𝑜𝑢 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 𝑐𝑢𝑝𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟.
𝑥= 26 5
5 1 5
5 1 5 =

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