AFDA Notes
ANSWER KEY
Name ____________________
Ratios, Proportions, & Percent
Date ____________ Block ___
When relative comparisons are made between different values or quantities of the same kind,
the comparison is called a ratio. Ratios can be expressed in several forms: verbal, fraction,
division, or decimal.
Example 1
The following table summarizes Michael Jordan’s statistics during the six games of one of his
NBA championship series.
GAME
POINTS
FIELD GOALS
FREE THROWS
1
28
9 out of 18
9 out of 10
2
29
9 out of 22
10 out of 16
3
36
11 out of 23
11 out of 11
4
23
6 out of 19
11 out of 13
5
26
11 out of 22
4 out of 5
6
22
5 out of 19
11 out of 12
1. In the above table, which statistics are expressed as ratios?
Field Goals and Free Throws
2. In which game did Jordan score the most points?
Game 3
3. In which games(s) did he score the most field goals? The most free throws?
He scored 11 field goals in both games 3 & 5.
He scored 11 free throws in games 3, 4, & 6
Problem 3 focused on the actual number of Jordan’s successful field goals and free throws in
these six games. Another way of assessing Jordan’s performance is to compare the number of
successful shots to the total number of attempts for each game. This comparison gives you
information on the relative success of his shooting.
4. Use the free-throw data from the six games to express Jordan’s relative performance in
the given comparison formats (verbal, fraction, division, and decimal). The data from the
first game have been entered for you.
Jordan’s Relative Free-Throw Performance
GAME
VERBAL
FRACTION
DIVISION
DECIMAL
1
9 out of 10
9 10
0.90
2
10 out of 16
10 16
.625
3
11 out of 11
11  11
1.00
4
11 out of 13
11 13
.846
5
4 out of 5
4 5
0.80
6
11 out of 12
9
10
10
16
11
11
11
13
4
5
11
12
11  12
.917
5. a. For which of the six games was his relative free-throw performance highest?
His relative free throw performance is highest in game 3.
`
b. Which comparison format did you use to answer part a.? Why?
Answers will vary.
6. For which of the six games was Jordan’s actual free-throw performance the lowest?
In game 5 he made only 4 free throws.
7. For which of the six games was Jordan’s relative free-throw performance the lowest?
In game 2 his relative free throw performance was the lowest.
Proportional reasoning is the ability to recognize when two ratios are equivalent.
You can determine equivalent ratios the same way you determine equivalent fractions.
3 2 6
For example, 3 out of 4 is equivalent to 6 out 8, because  
4 2 8
8. Fill in the blanks in each of the following proportions.
a. 3 out 4 is equivalent to
9
b. 3 out 4 is equivalent to
24
c. 3 out 4 is equivalent to
out of 12
out of 32
75
out of 100
d. Write the resulting proportion from part c. using a fraction format.
3 75

4 100
9. a. Explain why the following ratios are equivalent.
i.
27 out of 75
They all equal
ii.
63 out of 175
iii.
36 out of 100
9
or .36
25
b. Write each ratio in fraction form.
27 63
36
9



75 175 100 25
c. Determine the “reduced” form of the equivalent fractions from part b.
9
25
The number 100 is a very familiar comparison. There are 100 cents in a dollar and often
100 points on a test. The Latin equivalent to the phrase “out of 100” is percent. Per means
“division” and cent means “100”, so percent means “divide by 100”.
So 70 out of 100 can be rephrased as 70 percent and written as 70%.
10.
Complete the following table using Michael Jordon’s field goal data from the
beginning of the notes.
Jordan’s Relative Field Goal Performance
GAME
VERBAL
FRACTION
1
9 out of 18
2
9 out of 22
3
11 out of 23
4
6 out of 19
5
11 out of 22
6
5 out of 19
9
18
9
22
11
23
6
19
11
22
5
19
DECIMAL
PERCENT
0.50
50%
.41
41%
.48
48%
.32
32%
.50
50%
.26
26%
Solving Proportions
a
and a given piece
b
a part
of information, either a “part” or a “total” value, resulting in the proportion: 
b total
The missing value can be determined by cross multiplying and solving the resulting equation,
(usually by dividing).
Examples
2 x

Solve 2 out of 3 =
out of 36
,
3x  72 ,
x  24
3 36
Problems that involve proportional reasoning usually include a known ratio
Solve
2 n

3 45
3n  90 ,
n  30
Solving Percent Problems
Percent problems are easily solved if thought of as a ratio.
Example
Your high school softball team won 80% of the games it played this year. If your team won 20
games, how many games did it play?
80
The 80 % can be written as the ratio of 80 parts out of a total of 100:
,
100
The 20 games won is the part out of the total games played, which we need to find and can be
20 parts
80 20
written as:
So now the proportion can be written as
we can solve for x

100 x
x total games
using “cross multiply and divide”
80x  2000 , x  25
The team played 25 games.