1. Proportional and nonproportional relationshipsPg

2. 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

3. Proportional Relationships
Are these numbers proportional?
They are if their ratios are the same!
$ 𝑠𝑜𝑛𝑔 =$1.29 𝑝𝑒𝑟 𝑠𝑜𝑛𝑔.
$ 𝑠𝑜𝑛𝑔𝑠 = $1.29 per song.
$ 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

4. 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.

5. 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.
$ 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ =$6.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ
$ 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$5.75 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ
$ 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$5.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ
$ 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ𝑒𝑠 =$4.00 𝑝𝑒𝑟 𝑠𝑎𝑛𝑑𝑤𝑖𝑐ℎ
The cost of the sandwich is not the same each time so this is a NONPROPORTIONAL relationship.

6. 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