Proportional and nonproportional relationships

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Proportional Relationships

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Presentation transcript:

Proportional and nonproportional relationships Pg. 272 - 275

Definitions Two quantities are PROPORTIONAL if they have a constant ratio. Look at the following data Write a ratio using the data 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑜𝑟𝑑𝑒𝑟 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐽𝑎𝑐𝑘𝑒𝑡𝑠 = $14 1 = $28 2 = $42 3 = $56 4 What do you notice? Each jacket ordered increases the cost of the order by $14. This relationship is proportional. Cost $14 $28 $42 $56 Number of jackets ordered 1 2 3 4

Proportional Relationships Are these numbers proportional? They are if their ratios are the same! $1.29 1 𝑠𝑜𝑛𝑔 =$1.29 𝑝𝑒𝑟 𝑠𝑜𝑛𝑔. $2.58 2 𝑠𝑜𝑛𝑔𝑠 = $1.29 per song. $3.87 3 𝑠𝑜𝑛𝑔𝑠 = $1.29 per song. Each relationship is the same. The numbers are proportional. Cost of an Apple Song Download $1.29 $2.58 $3.87 Number of songs 1 2 3

Definitions A relationship in which the ratio is not constant is NONPROPORTIONAL. To play at Rockin’ Play Center, they charge $5 per person to enter plus $3 for each hour. Is this relationship proportional? $8 1 ℎ𝑜𝑢𝑟 =$8 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 $11 2 ℎ𝑜𝑢𝑟𝑠 =$5.50 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 $14 3 ℎ𝑜𝑢𝑟𝑠 =$4.67 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 Cost $8 $11 $14 Hours of Play 1 2 3 These ratios are not the same, so this is a NONPROPORTIONAL relationship.

Proportional or nonproportional Jimmy’s sandwich shop listed the following prices for delivery sandwiches. 1 sandwich - $6.00, 2 sandwiches - $11.50, 3 sandwiches - $15 and 4 sandwiches - $16. Is the cost of the sandwiches proportional to the number ordered? Explain. $6.00 1 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ =$6.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ $11.50 2 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$5.75 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ $15.00 3 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$5.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ $16.00 4 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$4.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ The cost of the sandwich is not the same each time so this is a NONPROPORTIONAL relationship.

Proportional or nonproportional Which pricing guide is based on a constant unit price? Number of Fidgets 2 4 6 8 Total Cost ($) $5.00 $9.00 $13.00 $16.00 A Number of Fidgets 2 4 6 8 Total Cost ($) $5.00 $10.00 $15.00 $20.00 B Number of Fidgets 2 4 6 8 Total Cost ($) $6.00 $14.00 $24.00 $36.00 C