1. Unit 3. Day 7.

2. Today’s Lesson
1) Review Unit Rate
2) Using Unit Rate to compare.
3) Introduction to proportions

3. 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟
Example A*: A car uses of a gallon to drive miles. What is the mileage of the car?
𝑚𝑖 𝑔𝑎𝑙
𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟
Example B*: Winston used gallons of paint to cover a wall that is square meters. How much area will one gallon of paint cover?
𝑚 𝑔𝑎𝑙
𝑔𝑎𝑙 𝑚 2 𝑜𝑟

4. 𝑚𝑖 1 𝑔𝑎𝑙 40 1 4 161 4 𝑚𝑖 23 8 𝑔𝑎𝑙 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 = 2 7 8 = = = = 14
Example A*: A car uses of a gallon to drive miles. What is the mileage of the car?
40 1 4
÷ 23 8
𝑚𝑖 𝑔𝑎𝑙
𝑚𝑖 1 𝑔𝑎𝑙
𝑚𝑖 𝑔𝑎𝑙
𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 =
2 7 8
÷ 23 8
161 4 ÷ 23 8
14 1
161 4 ∙ 8 23
2∙2∙2∙7∙23 = = = = 14 14 =
2∙2∙23

5. Example B*: Winston used gallons of paint to cover a wall that is square meters. How much area will one gallon of paint cover?
12 1 4
÷ 5 2
𝑚 𝑔𝑎𝑙
𝑚 2 1 𝑔𝑎𝑙
𝑚 𝑔𝑎𝑙
𝑔𝑎𝑙 𝑚 2 𝑜𝑟 =
2 1 2
÷ 5 2
49 4 ÷ 5 2
49 10
49 4 ∙ 2 5
98 20
2∙7∙7
4 9 10
4 9 10 = = = = =
2∙2∙5

7. Today’s Lesson
1) Review Unit Rate
2) Using Unit Rate to compare.
3) Introduction to proportions

8. 𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑎𝑐𝑟𝑒 1 ℎ𝑟 21 4 𝑎𝑐𝑟𝑒 7 2 ℎ𝑟 𝑎𝑐𝑟𝑒 ℎ𝑟 ℎ𝑟 𝑎𝑐𝑟𝑒 𝑜𝑟 = 𝑎𝑐𝑟𝑒 ℎ𝑟 = =
Example C*: Richard Ritter, Ms. Ritter’s dad, hired two people to help him on the farm. Drew plowed 5.25 acres in hours. Steven plowed an acre in 8 minutes. Which is the better (more efficient) worker?
5 1 4
21 4 𝑎𝑐𝑟𝑒 ℎ𝑟
÷ 7 2
5.25
𝑎𝑐𝑟𝑒 ℎ𝑟
ℎ𝑟 𝑎𝑐𝑟𝑒
𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑜𝑟 =
3 1 2
÷ 7 2
1 4
÷ 2 15
𝑎𝑐𝑟𝑒 ℎ𝑟
𝑎𝑐𝑟𝑒 1 ℎ𝑟
2 15
8 60
÷ 2 15
1 4 ÷ 2 15
1 4 ∙ 15 2
2∙3∙7
3∙5
1 1 2
1 1 2
1 7 8
1 7 8
21 4 ÷ 7 2
21 4 ∙ 2 7
42 28
15 8
3 2
15 8 = = = = = = = = = =
2∙2∙2
2∙2∙7

10. Today’s Lesson
1) Review Unit Rate
2) Using Unit Rate to compare.
3) Introduction to proportions

17. 8
Is this proportional?
𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛
8 12
Is this fair?
𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛
9 24 9 12 24
3 8
2 3
𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛
0. 6 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

18. 4
Is this proportional?
𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛
4 8
Is this fair?
𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛
15 30 15 8 30
1 2
1 2
0. 5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛
0.5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

19. Is this proportional?
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 9
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 15
Is this fair?
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 3 5
3 1
3 1

20. Is this proportional?
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 14
Is this fair?
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔
ℎ𝑜𝑢𝑟𝑠 𝑝𝑎𝑖𝑛𝑡𝑖𝑛𝑔 10 3 4
3.5 1

21. 3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒
$1 2 ℎ𝑜𝑢𝑟𝑠
$4 8 ℎ𝑜𝑢𝑟𝑠
A proportion is an stating that two ratios
(or rates) are equivalent.
equation =
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