Comparing and Scaling
Problem 1.1 Ads That Sell
How many people took the taste test?
1.
2.
3.
4.
5.
17,139
11,426
28,565
5713
You can’t tell
From the statement #1, can you tell how many
people took the taste test?
A ratio is what kind of comparison?
1. Part to whole
2. Part to part
3. Whole to whole
From the statement #1, can you tell how many
people took the taste test?
A ratio is a part to part comparison.
Since Bolda comes first in the statement and
17,139 is the first number in the statement,
17,139 people preferred Bolda Cola.
How many people preferred Cola
Nola?
1.
2.
3.
4.
17,139
11,426
28,565
You can’t tell
From the statement #1, can you tell how many
people took the taste test?
A ratio is a part to part comparison.
Since Bolda comes first in the statement and
17,139 is the first number in the ratio, 17,139
people preferred Bolda Cola.
That means 11,426 people preferred Cola Nola
From the statement #1, can you tell how many
people took the taste test?
Bolda + Nola = Total
17,139 + 11,426 = 28,565
28,565 total people took the survey
What percent of the people surveyed preferred
Bolda Cola?
The information is given as a ratio. A
ratio is a part to part comparison.
A percent is what kind of a
comparison?
1. Part to part
2. Part to whole
3. Whole to whole
What percent of the people surveyed preferred
Bolda Cola?
The information is given as a ratio. A
ratio is a part to part comparison.
A percent is a is a part to whole comparison.
If 17,139 and 11,426 are the 2 parts,
what is the whole?
17,139 + 11,426 = 28,565
28,565 total people took the survey
What percent of the people surveyed preferred
Bolda Cola?
28,565 total people took the survey
part
Bolda 17,139
Percent 


 %  60%
w hole total
28,565
What percent of the people surveyed preferred
Bolda Cola?
What part does the percent ask about?
1.
2.
3.
4.
5.
Bolda
Nola
Dr. Pepper
Mug
You can’t tell
What percent of the people surveyed preferred
Bolda Cola?
28,565 total people took the survey
part
Bolda 17,139
Percent 


 %  60%
w hole total
28,565
17,139
28,565
1.
2.
3.
4.
5.
is what percent?
50%
60%
70%
80%
Not given
What percent of the people surveyed preferred
Bolda Cola?
28,565 total people took the survey
part
Bolda 17,139
Percent 


 17,139  28,565  .6  60%
w hole total
28,565
What fractional part of the people surveyed
preferred Cola Nola?
REMEMBER, 28,565 total people took the survey
part
Nola
11,426
4
Fraction 


 D  .4  F 
Simp
w hole Total 28,565
10
A fraction is what kind of a
comparison?
1. Part to part
2. Part to whole
3. Whole to whole
What fractional part of the people surveyed
preferred Cola Nola?
28,565 total people took the survey
part
Nola
11,426
4
Fraction 


 D  .4  F 
Simp
w hole Total 28,565
10
What “part” does the question ask
about?
What fractional part of the people surveyed
preferred Cola Nola?
1. Those who like
Bolda Cola
2. Those who like Cola
Nola
3. Those who like Dr.
Pepper
What fractional part of the people surveyed
preferred Cola Nola?
28,565 total people took the survey
part
Nola 11,426
4
2
Fraction 


 .4 
Simp 
w hole Total 28,565
10
5
Pd 4
What is the ratio of those surveyed that preferred
Bolda Cola to those that preferred Cola Nola in
simplest form? (reduced)
The comparison is given in ratio form
part Bolda 17,139
15
3
Ratio 


 1.5  F 
simp 
part
Nola
11,426
10
2
A ratio is what kind of comparison?
1. Part to whole
2. Part to part
3. Whole to whole
What is the ratio of those surveyed that preferred
Bolda Cola to those that preferred Cola Nola in
simplest form? (reduced)
The comparison is given in ratio form
part Bolda 17,139
15
3
Ratio 


 1.5  F 
simp 
part
Nola
11,426
10
2
What is the ratio of those surveyed that preferred
Bolda Cola to those that preferred Cola Nola in
simplest form? (reduced)
Which part goes on the top of the
ratio?
1.
2.
3.
4.
Bolda
Nola
A&W
Dr. Pepper
What is the ratio of those surveyed that preferred
Bolda Cola to those that preferred Cola Nola in
simplest form? (reduced)
The comparison is given in ratio form
part Bolda 17,139
15
3
Ratio 


 1.5  F 
simp 
part
Nola
11,426
10
2
What is the ratio in simplest terms?
11..
2.
23..
4.
3.
4.
part Bolda 17,139
8
Ratio 


.
part
Nola
11,426
5
.
.3
.2
417
371
17,139
11,426
What is the ratio of those surveyed that preferred
Bolda Cola to those that preferred Cola Nola in
simplest form? (reduced)
The comparison is given in ratio form
Ratios must be written with a number
on top and a number on the bottom!!
part Bolda 17,139
5 15
3
Ratio 


 1.5  1 
simp 
part
Nola
11,426
10 10
2
From statement #2 --You can only look at statement #2
What was the total number of people surveyed?
From statement #2 --You can only look at statement #2
How many more people preferred Bolda Cola?
From statement #2 --You can only look at statement #2
What percent of the people preferred
Bolda Cola?
From statement #2 --You can only look at statement #2
What fractional part of the people surveyed
preferred Cola Nola?
From statement #2 --You can only look at statement #2
What is the ratio of those that preferred Bolda
Cola to those that preferred Cola Nola in
simplest form? (reduced)
From statement #3 --You can only look at statement #3
What was the total number of people surveyed?
From statement #3 --You can only look at statement #3
How many more people preferred Bolda Cola?
If 60% prefer Bolda Cola, what
percent prefer Cola Nola?
1.
2.
3.
4.
60%
40%
100%
17.25%
From statement #3 --You can only look at statement #3
What percent of the people preferred Bolda Cola?
If 60% prefer Bolda Cola, then
100% - 60% = 40% prefer Nola Cola.
From statement #3 --You can only look at statement #3
What fractional part of the people
surveyed preferred Cola Nola?
If 60% prefer Bolda Cola, then 40% prefer
Nola Cola.
part
Cola Nola 40
4
2
fraction 




whole
total
100 10 5
What fractional “part” is the
question asking about?
What fractional part of the people
surveyed preferred Cola Nola?
1.
2.
3.
4.
Cola Nola
Coke
Bolda Cola
Sprite
From statement #3 --You can only look at statement #3
What fractional part of the people
surveyed preferred Cola Nola?
If 60% prefer Bolda Cola, then 40% prefer
Nola Cola.
Percent means “out of 100”
part
Cola Nola 40
4
2
fraction 




whole
total
100 10 5
From statement #3 --You can only look at statement #3
What is the ratio of those that preferred Bolda Cola to
those that preferred Cola Nola in simplest form?
(reduced)
If 60% prefer Bolda Cola, then 40% prefer
Nola Cola.
part Bolda Cola
60% .6 6 3
ratio 


  
part Cola Nola
40% .4 4 2
A ratio is what kind of comparison?
1. Part to whole
2. Part to part
3. Whole to whole
From statement #3 --You can only look at statement #3
What is the ratio of those that preferred Bolda Cola to
those that preferred Cola Nola in simplest form?
(reduced)
If 60% prefer Bolda Cola, then 40% prefer
Nola Cola.
part Bolda Cola
60% .6 6 3
ratio 


  
part Cola Nola
40% .4 4 2
From statement #4 --You can only look at statement #4
What was the total number of people
surveyed?
1.
2.
3.
4.
5 people
5713 people
23 people
You don’t know
From statement #4 --You can only look at statement #4
What was the total number of people surveyed?
From statement #4 --You can only look at statement #4
How many more people preferred
Bolda Cola?
1. 5 people
2. 1 person
3. 38 people
4. You don’t know
From statement #4 --You can only look at statement #4
How many more people preferred Bolda Cola?
From statement #4 --You can only look at statement #4
What percent of the people preferred Bolda Cola?
1.
2.
3.
4.
5.
6.
60%
40%
30%
20%
67%
150%
From statement #4 --You can only look at statement #4
What percent of the people preferred Bolda Cola?
part
Bolda 3
percent 

  %  60%
whole Total 5
A percent is what kind of a
comparison?
1. Part to part
2. Part to whole
3. Whole to whole
From statement #4 --You can only look at statement #4
What percent of the people preferred Bolda Cola?
part
Bolda 3
percent 

  %  60%
whole Total 5
What is the total in this statement?
1.
2.
3.
4.
5.
3
2
5
32
23
From statement #4 --You can only look at statement #4
What percent of the people preferred Bolda Cola?
part
Bolda 3 6
percent 

 
 60%
whole
Total 5 10
What fractional part of the people
surveyed preferred Cola Nola?
1.
2.
3.
4.
5.
2/3
3/2
3/5
2/5
You can’t tell
From statement #4 --You can only look at statement #4
What is the ratio of those that preferred Bolda Cola to
those that preferred Cola Nola in simplest form? (reduced)
.
1.
2.
3.
4.
.
.
.
.
.
1. Yes
2. No
•Yes, the difference in statement #2 is the same
as the difference in # 1
•If you change the data in #1 into the percent
that preferred Bolda, the answer is 60%, the
same as #3
•If you change the data in #1 into the ratio of
those that preferred Bolda to those that
preferred Nola, the reduced form would be 3
2
The same as #4.
Therefore all of the statements COULD
have come from the same data.
.
1.
2.
3.
4.
700 BC & 300 CN
600 CN & 400 BC
400 CN & 600 BC
300 BC & 700 CN
60%  1000

Bolda Cola
.6 x 1000 = 600
600  Bolda Cola
1000 total - 600 Bolda Cola  400 Cola Nola
400 people preferred Cola Nola