Unit 5. Day 10.

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.

You CANNOT use this for every math problem You are about to see something special It only works in one situation CROSS MULTIPLICATION

Proportions A statement that two ratios (or rates) are equivalent 1 4 = 2 8 $3 2 𝑠𝑜𝑑𝑎𝑠 = $9 6 𝑠𝑜𝑑𝑎𝑠 60 𝑚𝑖𝑙𝑒𝑠 60 𝑚𝑖𝑛 = 1 𝑚𝑖𝑙𝑒 1 𝑚𝑖𝑛 3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒

Proportions: Cross Multiply 2 5 = 6 15 1 4 = 2 8 1 8 = 2 15 = 4 2 5 6 8 = 30 = 30 8 𝑎 𝑏 = 𝑐 𝑑 𝑎 𝑑 = 𝑏 𝑐 𝑎𝑑 = 𝑏𝑐

Proportions: Cross Multiply 𝐼𝑓 𝑇ℎ𝑒𝑛 𝑎 𝑏 = 𝑐 𝑑 𝑎𝑑=𝑏𝑐

Example A: Solve the proportion 𝑥 6 = 6 18 𝑥 6 = 6 18 6 6 𝑥 18 = 6 6 36 18 𝑥 = 18𝑥 = 36 18 18 𝑥 = 2 𝑥=2

Example B*: Solve the proportion 𝑦 5 = 21 35 𝑦 5 = 21 35 5 5 𝑦 35 = 5 21 105 35 𝑦 = 35𝑦 = 105 35 35 𝑦 = 3 𝑦=3

Example B*: Solve the proportion 𝑦 5 = 3 5 𝑦 5 = 3 5 𝑦 5 = 21 35 5 5 𝑦 5 = 5 3 𝑦 = 3 5𝑦 = 15 5 5 𝑦=3

Example C: Solve the proportion 8 9 = 40 𝑚 8 𝑚 = 9 40 8𝑚 = 360 8 8 4 5 8 3 6 0 𝑚=45 − 3 2 4 − 4 0

Example D*: Solve the proportion 7 11 = 𝑛 33 7 33 = 11 𝑛 231 = 11𝑛 11 11 2 1 21=𝑛 11 2 3 1 1 − 2 2 1 − 1 1

Example E: Solve the proportion 𝑎 8 = 9 10 𝑎 10 = 8 9 10𝑎 = 72 10 10 𝑎= 72 10 2∙2∙2∙3∙3 36 5 7 1 5 = = 𝑜𝑟 2∙5 𝑜𝑟 7.2

Example F*: Solve the proportion 10 4 = 9 𝑐 10 𝑐 = 4 9 10𝑐 = 36 10 10 𝑐= 36 10 2∙2∙3∙3 18 5 3 3 5 = = 𝑜𝑟 2∙5 𝑜𝑟 3.6

𝑥 4 ∙ 7 10 𝑥 4 ÷ 7 10 𝑥 4 + 7 10 𝑥 4 − 7 10 𝑥 4 = 7 10 Cross Multiply

Predicting with Proportions Cross Multiplication 5th grade simple method Unit Rate Graph 5th grade simple method Equation

Now we will use this fact to help us with word problems 𝐼𝑓 𝑇ℎ𝑒𝑛 𝑎 𝑏 = 𝑐 𝑑 𝑎𝑑=𝑏𝑐

𝑀𝑟. 𝐽𝑜𝑟𝑑𝑎𝑛 𝑐𝑎𝑛 𝑑𝑟𝑖𝑣𝑒 416 𝑚𝑖𝑙𝑒𝑠 𝑤𝑖𝑡ℎ 16 𝑔𝑎𝑙𝑙𝑜𝑛𝑠. Example A: Mr. Jordan was able to travel 130 miles on 5 gallons of gas. If he fills his tank (16 gallons), how many miles can he drive? 130 5 16 ? 𝑥 𝑚𝑖 𝑔𝑎𝑙 = 𝑚𝑖 𝑔𝑎𝑙 130 16 = 5 𝑥 2080 = 5𝑥 1 5 5 1 3 0 4 1 6 1 6 5 2 0 8 0 8 × 416 416 = 𝑥 − 2 0 1 7 8 1 3 ∎ + − 5 𝑀𝑟. 𝐽𝑜𝑟𝑑𝑎𝑛 𝑐𝑎𝑛 𝑑𝑟𝑖𝑣𝑒 416 𝑚𝑖𝑙𝑒𝑠 𝑤𝑖𝑡ℎ 16 𝑔𝑎𝑙𝑙𝑜𝑛𝑠. 2 8 3