Scaling Factors
True or False:
Multiplying by a scale factor less than one will make the answer scale down.
True
Will multiplying a number by 1/5 make the answer scale up or down in size?
Scale down.
1/8 x 1/2 =
1/16
If 2/3 package of 12 pens have blue ink.
What will we be solving for in this problem?
How many pens have blue ink.
Describe a real world example of scaling.
Answers will vary:
Scale models, blueprints, food scales in the grocery store...
True or False:
Multiplying by a scale factor greater than one will result in no size change.
False
Will multiplying a number by 6/6 make the answer scale up or down in size?
The size will not change.
2/5 x 3/3 =
2/5
Veterinarian A treated 8 sick animals in one day shift. Veterinarian B treated 2 3/4 as many animals.
What are we figuring out in this problem? (HINT: 2 things!)
Which veterinarian treated more animals?
AND
How many animals did veterinarian B treat?
In what careers might someone use scaling?
Engineers, Architects, Chefs, Artists, Construction...
True or False:
Multiplying by a scale factor equal to one will make the answer scale up.
False
<, > or =
9/7 x 8 ___ 8
> (greater than)
6/3 x 8/2
8
Ethan and Gio are reading books in the library. Gio read for 5/6 the time that Ethan did. Ethan read for 54 minutes.
What are we solving for in this problem?
How long Gio read his book compared to Ethan's 54 minutes. (54 x 5/6)
Compare the two equations and fill the blank with
<, > or =
4/5 x 1/3 ____ 4/5 x 4/3
< (less than)
Give an example of a scale factor (in fraction form) that would make the answer scale up.
Answers will vary:
Any fraction or mixed number greater than 1.
Fill in the blank with a number to make the comparison true:
4 x __/6 < 4
Any number less than 6.
2/9 x 4 1/3
2/9 x 4 = 8/9
2/9 x 1/3 = 2/ 27
8/9 + 2/27 (common denominator: 27)
(8 x 3) / (9 x 3) = 24/27
24/27 + 2/27 = 26/27
dThe old dog park has a length of 80 feet and a width of 65 feet. Both the length and the width of the new dog park are 3 1/3 times greater than the length and width of the old dog park.
What are we figuring out in this problem?
The dimensions of the new dog park.
WITHOUT MULTIPLYING...Rank the following equations from least to greatest:
8/9 x 6/6
8/9 x 9/7
8/9 x 4/5
1. 8/9 x 4/5 (least)
2. 8/9 x 6/6
3. 8/9 x 9/7 (greatest)
Give an example of a scale factor (in fraction form) that would make the answer scale down.
Answers will vary:
Any fraction less than 1.
Fill in the blank with a number to make the comparison true:
53 x 4/__ > 53
Any number less than 4.
3 3/5 x 3 1/4
3 3/5 -> 18/5
3 1/4 -> 13/4
18/5 x 13/4 = 234/20 -> (234 ÷ 2)/(20 ÷ 2) = 117/10 =
11 7/10
In 2018, the average length of all the videos uploaded to YouTube were 12 minutes long. In 2023, the average length of videos were 7/8 as long.
What are we comparing in this problem?
The length of Youtube videos in 2018 compared to the length of Youtube videos in 2023.
Jackson worked 12 hours a week. Nadia worked 3/4 as many hours as Jackson. Amara worked 4/4 as many hours as Jackson. Vincent worked 4/1 as many as hours as Jackson.
WITHOUT MULTIPLYING, rank the four people from least number of hours to greatest.
(least) Nadia, Amara, Jackson, Vincent (most)