Transcript Reda Berry Math Project

How to Teach Percentages
Using Proportions
Math For Life Situations
By
Reda Berry
Objectives
• Understand ratios
• Offer instructors an effective, easy, and
relevant way to teach percents using the
proportion method
What is a Ratio?
• A ratio is a comparison of two numbers
4 puzzle parts to 3 gears
How do you write a ratio?
• 4 puzzle parts to 3 gears
–
–
–
4 to 3
4:3
4/3
More about Ratios
• Ratios can be reduced by division
Example: 6/4 = 3/2 (when divided by 2/2)
6 to 4 = 3 to 2
6:4 = 3:2
• Ratios can be increased by multiplication
Example: 6/4 = 18/22 (when multiplied by 3/3)
6 to 4 = 18 to 22
6:4 = 18:22
Find the Ratio mistake
• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7
– 20 adults to 100 Children = 100: 20
– 25 female employees to 90 total employees =
5/18
Find the Ratio mistake
• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7 correct
– 20 adults to 100 Children = 100: 20 should be
20:100
– 25 female employees to 90 total employees =
5/18 correct 25/90 divided by 5 = 5/18
Proportions
• When two pairs of numbers have the same ratio, like the
numbers 2, 7 and 10, 35 we say they are proportional.
The equation 2/7 = 10/35 is a proportion
• In any proportion, the cross products are equal notice
that
2 x 35 = 7 x 10
70 = 70
Notice: We can use this fact to solve a proportion if one of
the 4 numbers is unknown
Word Problem #1
• If it takes 2 gallons of
paint to paint a room
which has 480 ft² to
be painted, how many
gallons will it take to
paint a room which
has 1200 ft² to be
painted?
Word Problem #1 solved
• If it takes 2 gallons of
paint to paint a room
which has 480 ft² to
be painted, how many
gallons will it take to
paint a room which
has 1200 ft² to be
painted?
•
•
•
•
2 gallons paint
480 ft² to be painted
How much paint?
1200 ft² to be painted
2/480 = x/1200
2 x 1200 = 480x
2400 = 480x
2400/480 = x
5 gallons of paint = x
Word Problem #2
• An 8 lb turkey breast
contains 36 servings
of meat. How many
pounds of turkey
breast would be
needed for 54
servings?
Word Problem #2 solution
• An 8 lb turkey breast
contains 36 servings
of meat. How many
pounds of turkey
breast would be
needed for 54
servings?
8 lb/36 = x lb/54
8 x 54 = 36x
432 = 36x
432/36 = 36/36x
12 = x
Check:
8 x 54 = 36 x 12
432 = 432
How do you introduce percents?
1. What is 20% of 40?
2. 45 is 45% of what number?
3. 35 is what percent of 70?
Students get confused on how to solve
these problems.
?????
1. When do I multiply?
2. When do I divide?
3. How do you multiply or divide with
percents?
4. Please, give me an easy way to do it!
The answer is a PROPORTION!
Basics of Percents
• All percent problems are composed of
three parts
– Percent
– Part
– Whole
• The answer lies in identifying which one is
missing.
The percent proportion
part
whole
*part is to whole as
percent number
100
part is to whole*
The percent proportion
using key words
is
of
%
100
Identifying Components
WH O L E
PERCEN T
8 is 20% of 40 • Clue Words
– IS = Part,
portion
– % = Percent
Symbol
– OF = Whole,
original
Identifying Components
8 is 20%
IS
OF
of 40
%
100
is
of
%
100
Identifying Components
is 20%
8
OF
of 40
%
100
is
of
%
100
Identifying Components
is 20%
8
40
of
%
100
is
of
%
100
Identifying Components
is
8
40
%
of
20
100
is
of
%
100
Using proportions to find answers
What is 20% of 40?
?
40
20
100
is
of
%
100
Using proportions to find answers
What is 20% of 40?
100
is
of
%
100
Using proportions to find answers
What is 20% of 40?
?
20
40
100
is
of
%
100
Using proportions to find answers
8 is 20% of what number?
100
is
of
%
100
Using proportions to find answers
8 is 20% of what number?
8
?
20
100
is
of
%
100
Using proportions to find answers
8 is what % of 40?
100
is
of
%
100
Using proportions to find answers
8 is what % of 40?
8
40
?
100
is
of
%
100
Basics of Percents
 Start with teaching students how to identify the
three components using CLUE WORDS
◦ Is – defines the part, or portion
◦ Of – defines the whole or original amount
◦ % symbol – defines percent
Percent Word Problem #1
• On average, about 40% of the
body weight of an adult male
is muscle. If a certain man
weights 225 lbs, how many
pounds should be muscle?
A. 325 lbs
B. 25 lbs
C. 90 lbs
D. 112.5 lbs
Percent Word Problem #1
Solved
• On average, about
40% of the body
weight of an adult
male is muscle. If a
certain man weights
225 lbs, how many
pounds should be
muscle?
x/225 = 40/100
100x = 225 x 40
100x = 9000
x = 9000/100
x = 90
Check:
100 x 90 = 225 x 40
9000 = 9000
Percent Word Problem #2
• Mrs. Jackson makes
$450 a week. She
pays $90 a week for
food. Money spent
for food is what
percent of Mrs.
Jackson’s income?
Contemporary GED Math, 2002
Percent Word Problem #2 solved
90/450 = x/100
• Mrs. Jackson makes
90 x 100 = 450x
$450 a week. She
9000 = 450x
pays $90 a week for
9000/450 = x
food. Money spent
for food is what
20% = x
percent of Mrs.
Check
Jackson’s income?
90 x 100 = 450 x 20
9000 = 9000
Contemporary GED Math, 2002
Percent Word Problem #3
• Eighteen people
attended David’s
evening math class.
This represents 75%
of the number
registered for the
class. How many
people are registered
for his class? Contemporary GED Math, 2002
Percent Word Problem #3 solution
• Eighteen people attended
18/x = 75/100
David’s evening math
18 x 100 = 75x
class. This represents
1800 = 75x
75% of the number
1800/75 = x
registered for the class.
24 = x
How many people are
registered for his class?
Check:
18 x 100 = 75 x 24
1800 = 1800
Contemporary GED Math, 2002
Advantages:
1. Multiplication? Division?
2. Eliminates the need to convert
percent into decimals.
3. Introduces students to variables.
4. Fractions, Unit conversions and
Geometry applications.