Using Multiples
to Introduce
Percents
Answer Key
Susan Mercer
Teaching Tips
Before introducing this unit students need to practice writing multiples. Ideally,
three rows of ten multiples each but it can be five or ten rows too. It is a great
practice for students who have low math skills.
I have students write multiples as a warm-up. Every day they have to write a
different multiple and whatever they do not finish in class is homework.
After couple of weeks, I give students the tenth multiple and ask them what
multiples they are going to use and why. Students get really good at determining
what multiple to write given the tenth multiple. This is key to developing a better
understanding of percents.
Example:
50
In this example students need to write multiples of 5 to get to 50.
Review of Multiples
Write multiples of 10, ending in 300
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
Write multiples of 2, ending in _60___
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
Write multiples of 5, ending in _150___
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
© S. Mercer - Using Multiples to Introduce Percents
Page - 1
Review of Multiples
Write multiples of 4, ending in _120___
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100
104
108
112
116
120
Write multiples of 7, ending in _210___
7
14
21
28
35
42
49
56
63
70
77
84
91
98
105
112
119
126
133
140
147
154
161
168
175
182
189
196
203
210
Write multiples of 9, ending in _270___
9
18
27
36
45
54
63
72
81
90
99
108
112
126
135
144
153
162
171
180
189
198
102
216
225
234
243
252
261
270
© S. Mercer - Using Multiples to Introduce Percents
Page - 2
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
0
0•3
0
3
1•3
3
6
2•3
3+3
9
3•3
3+3+3
12
4•3
3+3+3+3
15
5•3
3+3+3+3+3
18
6•3
3+3+3+3+3+3
21
7•3
3+3+3+3+3+3+3
24
8•3
3+3+3+3+3+3+3+3
27
9•3
3+3+3+3+3+3+3+3+3
30
10 • 3
3+3+3+3+3+3+3+3+3+3
What patterns do you see?
ANSWERS WILL VARY
© S. Mercer - Using Multiples to Introduce Percents
Page - 3
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
0
0•7
0
7
1•7
7
14
2•7
7+7
21
3•7
7+7+7
28
4•7
7+7+7+7
35
5•7
7+7+7+7+7
42
6•7
7+7+7+7+7+7
49
7•7
7+7+7+7+7+7+7
56
8•7
7+7+7+7+7+7+7+7
63
9•7
7+7+7+7+7+7+7+7+7
70
10 • 7
7+7+7+7+7+7+7+7+7+7
What patterns do you see?
ANSWERS WILL VARY
© S. Mercer - Using Multiples to Introduce Percents
Page - 4
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
0
0•4
0
4
1•4
4
8
2•4
4+4
12
3•4
4+4+4
16
4•4
4+4+4+4
20
5•4
4+4+4+4+4
24
6•4
4+4+4+4+4+4
28
7•4
4+4+4+4+4+4+4
32
8•4
4+4+4+4+4+4+4+4
36
9•4
4+4+4+4+4+4+4+4+4
40
10 • 4
4+4+4+4+4+4+4+4+4+4
What patterns do you see?
ANSWERS WILL VARY
© S. Mercer - Using Multiples to Introduce Percents
Page - 5
Teaching Tips
Teacher needs to model how to complete this page. First have students write
multiples of 10 and multiples of 3. Next, using the table students answer the
questions. It is very important to emphasize that 100% is the whole. I have my
students color it and writing besides it WHOLE.
Multiples and Percents
Multiples
of 10
Multiples
of
3
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
3
6
9
12
15
18
21
24
27
30
X
33
36
39
42
45
48
51
54
57
60
Using the table, answer the following questions:
•
What is 100% of 30? _30___
•
What is 50% of 30? _15___
•
27 is what percent of 30? _90%___
•
12 is what percent of 30? _40%___
•
What is 40% of 30? _12 ___
•
24 is what percent of 30? _80%___
•
What is 110% of 30? _33___
•
What is 0% of 30? _ 0___
•
60 is what percentof 30? _200%___
•
65% of 30 is between what two number? _18___ and _21__
•
99% of 30 is close to what number? _30___
•
16% of 30 is between what two numbers? _3__ and _6___
•
Is 50% of 30 bigger than 30? Yes or No Why? It is smaller than 30 because
50% is less one whole therefore less than 30
•
What is 200% of 30? _60___
© S. Mercer - Using Multiples to Introduce Percents
Page - 6
Multiples and Percents
Multiples
of 10
Multiples
of
6
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
6
12
18
24
30
36
42
48
54
60
X
66
72
78
84
90
96
102
108
114
120
Using the table, answer the following questions:
•
What is 100% of 60? _60___
•
54 is what percent of 60? _90%___
•
What is 70% of 60? _42___
•
24 is what percent of 60? _40%__
•
What is 110% of 60? _66___
•
What is 0% of 60? _ 0___
•
90 is what percentof 60? _ 150%___
•
25% of 60 is between what two number? _12__ and _ 18___
•
99% of 60 is close to what number? _60___
•
128% of 60 is between what two numbers? _72___ and
•
Is 75% of 60 bigger than 60? Yes or No Why? because 75% is less than
_78___
the whole 100% therefore 75% of 60 is less than 60___
•
Is 170% of 60 bigger than 60? Yes or No Why? because 170% is more
than the whole 100%_therefore 170% of 60 is more than 60__
•
What is 200% of 60? _120___
•
180 is what percent of 60? __300%___
© S. Mercer - Using Multiples to Introduce Percents
Page - 7
Multiples and Percents
Multiples
of 10
Multiples
of
8
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
8
16
24
32
40
48
54
64
72
80
X
88
90
104
112
120
128
134
144
152
160
Using the table, answer the following questions:
•
What is 100% of 80? _80___
•
32 is what percent of 80? _40%___
•
What is 10% of 80? _ 8___
•
What is 200% of 80? _160___
•
64 is what percent of 80? _ 80%___
•
What is 130% of 80? _104___
•
What is 0% of 80? __ 0___
•
120 is what percentof 80? _150%___
•
35% of 80 is between what two number? _24___ and _32___
•
101% of 80 if close to what number? _ 80___
•
167% of 60 is between what two numbers? _128__ and __134__
•
Is 86% of 80 bigger than 80? Yes or No Why? because 86% is less than
the whole 100% therefore 86% of 80 is less than 80
•
Is 130% of 80 bigger than 80? Yes or No Why? because 130% is more
than the whole 100% therefore 130% of 80 is more than 80
© S. Mercer - Using Multiples to Introduce Percents
Page - 8
Multiples and Percents
Multiples
of 10
Multiples
of
40
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
40
80
120
160
200
240
280
320
360
400
X
440
480
520
560
600
640
680
720
760
800
Using the table, answer the following questions:
•
What is 100% of 400? _400___
•
320 is what percent of 400? _80%___
•
What is 20% of 400? _80___
•
120 is what percent of 400? _ 30%___
•
What is 140% of 400? __560___
•
What is 0% of 400? _ 0___
•
600 is what percentof 400? _150%___
•
75% of 400 is between what two number? _280___ and _320___
•
49% of 400 is close to what number? _200___
•
179% of 400 is between what two numbers? _680___and _720___
•
Is 50% of 400 smaller than 400? Yes or No Why? because 50% is less
than the whole 100% therefore 50% of 400 is less than 400
•
Is 170% of 400 bigger than 400? Yes or No Why? because 170% is more
than the whole 100% therefore 170% of 400 is more than 400
•
What is 200% of 400? _800___
© S. Mercer - Using Multiples to Introduce Percents
Page - 9
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
7
14
21
28
35
42
49
56
63
70
X
77
84
91
98
105
112
119
126
133
140
Using the table, answer the following questions:
•
What is 100% of 70? ____70____
•
What is 10% of 70? ____7____
•
How do you obtain 10% of 70 given 100%?
•
80% is what percent of 70? ____56____
•
What is 150% of 70? ____105____
•
21 is what percent of 70? ____30%____
•
What is 0% of 70? ____0____
•
45% of 70 is between what two number? ____28____ and ____35____
•
59% of 70 if close to what number? ____42____
•
137% of 70 is between what two numbers? ____91____ and ____98____
•
Is 45% of 70 smaller than 70? Yes or No Why? because 45% is less
70 divided by 10
than the whole 100% therefore 45% of 70 is less than 70
•
Is 125% of 70 bigger than 70? Yes or No Why? because 125% is more
than the whole 100% therefore 125% of 70 is more than 70
© S. Mercer - Using Multiples to Introduce Percents
Page - 10
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
0
15
30
45
60
75
90
105
120
135
150
X
165
180
195
210
225
240
255
270
285
300
Using the table, answer the following questions:
•
What is 100% of 150? ____150____
•
What is 10% of 150? ____15____
•
How do you obtain 10% of 150 given 100%? ___divided 150 by 10____
•
30 is what percent of 150? ____20%____
•
What is 150% of 150? ___225____
•
90 is what percent of 150? ____60%____
•
What is 20% of 150? ____30____
•
15% of 150 is between what two number? ____15____ and ____30____
•
99% of 150 if close to what number? ____150____
•
151% of 150 is between what two numbers? ____225____and ____240____
•
What is 1% of 150? ____1.5____
How did you calculate 1% of 150? ___divide 150 by 100 or_divide 15 by 10
© S. Mercer - Using Multiples to Introduce Percents
Page - 11
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
0
50
100
150
200
250
300
350
400
450
500
X
550
600
650
700
750
800
850
900
950
1000
Using the table, answer the following questions:
•
What is 100% of 500? ____500____
•
What is 10% of 500? ____50____
•
How do you obtain 10% of 500 given 100%? ____500 divided by 10____
•
200 is what percent of 500? ____40%____
•
What is 150% of 500? ____750____
•
400 is what percent of 500? ____80%____
•
What is 60% of 500? ____300____
•
15% of 500 is between what two number? ____50____ and ____100____
•
49% of 500 if close to what number? ____250____
•
198% of 500 is between what two numbers? ___950____and ____1000____
•
What is 1% of 500? ____5____
How did you calculate 1% of 500? __divide 500 by 100 or_divide 50 by 10
© S. Mercer - Using Multiples to Introduce Percents
Page - 12
Percents and Multiples
Percent
Multiples
Multiples
as a product
Multiples
as an addition
0%
0
0•6
0
10%
6
1•6
6
20%
12
2•6
6+6
30%
18
3•6
6+6+6
40%
24
4•6
6+6+6+6
50%
30
5•6
6+6+6+6+6
60%
36
6•6
6+6+6+6+6+6
70%
42
7•6
6+6+6+6+6+6+6
80%
48
8•6
6+6+6+6+6+6+6+6
90%
54
9•6
6+6+6+6+6+6+6+6+6
100%
60
10 • 6
6+6+6+6+6+6+6+6+6+6
© S. Mercer - Using Multiples to Introduce Percents
Representa
tion
Page - 13
Percents and Multiples
Percent Multiples
Multiples
as a
product
Multiples
as an addition
0%
0
0 • 14
0
10%
14
1 • 14
14
20%
28
2 • 14
14 + 14
30%
42
3 • 14
14 + 14 + 14
40%
56
4 • 14
14 + 14 + 14 + 14
50%
70
5 • 14
14 + 14 + 14 + 14 + 14
60%
84
6 • 14
14 + 14 + 14 + 14 + 14 + 14
70%
98
7 • 14
14 + 14 + 14 + 14 + 14 + 14 + 14
80%
112
8 • 14
14 + 14 + 14 + 14 + 14 + 14 + 14 + 14
90%
126
9 • 14
14 + 14 + 14 + 14 + 14 + 14 + 14 + 14 + 14
100%
140
10 • 14
14 + 14 + 14 + 14 + 14 + 14 + 14 + 14 + 14 + 14
© S. Mercer - Using Multiples to Introduce Percents
Representat
ion
Page - 14
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
9
18
27
36
45
54
63
72
81
90
X
99
108
117
126
135
144
153
162
171
180
Using the table, answer the following question:
•
How did you complete the table? Describe step by step.
ANSWERS MAY VARY _first you take 50% and you double it to find 100% that is 45 times
two 90, next you take 100% and divide it by 10 to find out what
multiples to use.
Write 5 percent questions that can be answered with the table and answer them.
Question 1: __
ANSWERS WILL VARY
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 15
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
6
12
18
24
30
36
42
48
54
60
X
66
72
78
84
90
96
102
108
114
120
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
ANSWERS WILL VARY
Write 5 percent questions that can be answered with the table and answer them.
Question 1: __
ANSWERS WILL VARY
______________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 16
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20%
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
12
24
36
48
60
72
84
96
108
120
X
132
144
156
168
180
192
204
216
228
240
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
ANSWERS WILL VARY
Write 5 percent questions that can be answered with the table and answer them.
Question 1: __
ANSWERS WILL VARY
______________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 17
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
2
4
6
8
10
12
14
16
18
20
X
22
24
26
28
30
32
34
36
38
40
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
ANSWERS WILL VARY
Write 5 percent questions that can be answered with the table and answer them.
Question 1: _
ANSWERS WILL VARY
______________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 18
Percent Practice and Review
1)
100% of 70
7
5
7
7
5
5 •6 = 30
7 •10 = 70
20% of 30
Write the answer as a
mulitplication.
90% of 20
4)
3
2
3
50% of 150
15
15
Write the answer as a
mulitplication.
2
2
2
15 15
15
Write the answer as a
mulitplication.
8 8
8
8
8
9)
8 8
8 • 9 = 72
150 % of 250
25 25 25
25
25
25
25
25 25 25
Write the answer as a
mulitplication.
4
4
90 % of 80
8
2 • 9 = 18
4 4
15 • 5 = 75
8
2
70 % of 40
6)
4
7)
Write the answer as a
mulitplication.
2 2
2
2
3•2=6
5)
Write the answer as a
mulitplication.
5 5
5
5
7
7
7
60% of 50
2)
7 7
7
7
3)
Write the answer as a
mulitplication.
Write the answer as a
mulitplication.
25 25 25
25
25
4 4
120 % of 110
8)
11 11 11
11
11
11
11
11 11 11
11
11
11 • 12 = 132
5
5
5
5
5
Write the answer as a
mulitplication.
5 5
5
© S. Mercer - Using Multiples to Introduce Percents
Write the answer as a
mulitplication.
200 % of 50
10)
5
25 •15= 375
4 • 7 = 28
5 5
5
5
5
5
5
5
5
5 5
5 •20=100
Page - 19
Percent Practice and Review
1)
100% of 160
Write the answer as a
mulitplication.
16 16 16
16
16
16
16
16 16 16
7
7
Write the answer as a
mulitplication.
9 • 4 = 36
80% of 120
4)
Write the answer as a
mulitplication.
7
7
7
140% of 20
2
2
2
9)
Write the answer as a
mulitplication.
7 7
7 • 7 = 49
270 % of 50
8)
2
2
2 2
110% of 220
22 22 22
22
22
22
22
22
22 22
Write the answer as a
mulitplication.
5 • 27 = 135
2
2
2
Write the answer as a
mulitplication.
7 7
18 • 5 = 90
2
12 • 8 = 96
70% of 70
6)
18 18 18
18
18
2
Write the answer as a
mulitplication.
12 12 12
12
12
12
12 12
7
50% of 180
2
9
16 •10= 160
7 • 4 = 28
7)
Write the answer as a
mulitplication.
9
7
5)
9
9
40% of 70
3)
40% of 90
2)
2
2 • 14= 28
Write the answer as a
mulitplication.
5
5
5 5 5
10)
5
5
5
5
5
5 5 5
5 5
70 % of 10
1
5 5 5
5
5
5
5
5
5
5
5 5
Write the answer as a
mulitplication.
1
1
1
1
22
22•11= 242
© S. Mercer - Using Multiples to Introduce Percents
1 1
1•7= 7
Page - 20
Problem:
What is 80% of 120?
120
What is the whole? _____
?
What is the part? ______
80%
What is the percent? _____
Solve the problem using multiples
The whole (100%) is 120.
120 ÷ 10 = 12. Complete the table using multiples of 12.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
12
24
36
48
60
72
84
96
108
120
132
80% of 120 is 96
Solve the problem using
proportions
1.
2.
3.
4.
part
%
whole
100
x
80
120
100
x • 100 = 80 • 120
x • 100 = 9600
Steps to solve the
proportion
1. Set the proportion
2. Cross Multiply
3. Divide
4. Answer the question
x = 9600 ÷ 100
x = 96
80 % of 120 is 96
© S. Mercer - Using Multiples to Introduce Percents
Page - 21
Problem:
What is 20% of 60?
60
What is the whole? _____
?
What is the part? ______
20%
What is the percent? _____
Solve the problem using multiples
The whole (100%) is 60.
60 ÷ 10 = 6. Complete the table using multiples of 6.
0%
0
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
6
12
18
24
30
36
42
48
54
66
72
60
20% of 60 is 12
Solve the problem using
proportions
1.
2.
3.
4.
part
%
whole
100
x
20
60
100
x • 100 = 60 • 20
x • 100 = 1200
Steps to solve the
proportion
1. Set the proportion
2. Cross Multiply
3. Divide
4. Answer the question
x = 1200 ÷ 100
x = 12
20 % of 60 is 12
© S. Mercer - Using Multiples to Introduce Percents
Page - 22
Problem:
What is 150% of 40?
40
What is the whole? _____
?
What is the part? ______
150%
What is the percent? _____
Solve the problem using multiples
The whole (100%) is 40.
40 ÷ 10 = 4. Complete the table using multiples of 4.
0%
0
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
28
32
36
4
8
12
16
20
24
44
48
52
56
60
64
40
150% of 40 is 60
Solve the problem using
proportions
1.
2.
3.
4.
part
%
whole
100
x
150
40
100
x • 100 = 40 • 150
x • 100 = 6000
Steps to solve the
proportion
1. Set the proportion
2. Cross Multiply
3. Divide
4. Answer the question
x = 6000 ÷ 100
x = 60
150 % of 40 is 60
© S. Mercer - Using Multiples to Introduce Percents
Page - 23
Problem:
11 is 10% of what number?
?
What is the whole? _____
11
What is the part? ______
10%
What is the percent? _____
Solve the problem using multiples
10% is 11.
Complete the table using multiples of 11.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
11
22
33
44
55
66
77
88
99
110
121
11 is 10% of 110
Solve the problem using
proportions
1.
2.
3.
4.
part
%
whole
100
11
10
x
100
11 • 100 = x • 10
1100 = x • 10
Steps to solve the
proportion
1. Set the proportion
2. Cross Multiply
3. Divide
4. Answer the question
1100 ÷ 10 = x
x = 110
11 is 10% of 110
© S. Mercer - Using Multiples to Introduce Percents
Page - 24
Problem:
160 is what percent of 80?
80
What is the whole? _____
160
What is the part? ______
?
What is the percent? _____
Solve the problem using multiples
80 is the whole, 100%. 80 ÷ 10 = 8.
Therefore, need to complete the table using multiples of 8.
0%
0
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
8
16
24
32
40
48
54
64
72
80
88
96
104
112
120
128
134
144
152
160
160 is 200% of 80
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
160
80
x
100
160 • 100 = x • 80
16000 = x • 80
3.
16000 ÷ 80 = x
x = 200
4.
160 is 200% of 80
© S. Mercer - Using Multiples to Introduce Percents
2. Cross Multiply
3. Divide
4. Answer the question
Page - 25
Problem:
24 is what percent of 30?
30
What is the whole? _____
24
What is the part? ______
?
What is the percent? _____
Solve the problem using multiples
30 is the whole, 100%. 30 ÷ 10 = 3.
Therefore, need to complete the table using multiples of 3.
0%
0
10 %
20 %
3
30 %
6
9
40 %
50 %
60 %
70 %
80 %
90 % 100 %
12
15
18
21
24
27
30
24 is 80% of 30
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
3.
4.
24
30
x
100
24 • 100 = x • 30
2400 = x • 30
2. Cross Multiply
3. Divide
4. Answer the question
2400 ÷ 30 = x
x = 80
24 is 80% of 30
© S. Mercer - Using Multiples to Introduce Percents
Page - 26
Problem:
A Middle School has 300 girls. 40% of the girls play an instrument.
How many girls play an instrument?
300
What is the whole? _____
?
What is the part? ______
40%
What is the percent? _____
Solve the problem using multiples
All the girls in the school are the whole, 100%. 300 ÷ 10 = 30.
Therefore, need to complete the table using multiples of 30.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
30
60
90
120
150
180
210
240
270
300
40% of 300 is 120.
Therefore, 120 girls play an instrument.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
3.
4.
x
300
40
100
40 • 300 = x • 100
12000 = x • 100
2. Cross Multiply
3. Divide
4. Answer the question
12000 ÷ 100 = x
x = 120
40% of 300 is 120
© S. Mercer - Using Multiples to Introduce Percents
Page - 27
Problem:
A Middle School has 250 boys. 60% of the boys play soccer. How
many boys play soccer?
What is the whole? 250
What is the part? ______
?
What is the percent? _____
60%
Solve the problem using multiples
All the boys in the school are the whole, 100%. 250 ÷ 10 = 25.
Therefore, need to complete the table using multiples of 25.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
25
50
75
100
125
150
175
200
225
250
60% of 250 is 150.
Therefore, 150 boys play soccer.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
3.
4.
x
250
60
100
60 • 250 = x • 100
15000 = x • 100
2. Cross Multiply
3. Divide
4. Answer the question
15000 ÷ 100 = x
x = 150
60% of 250 is 150
© S. Mercer - Using Multiples to Introduce Percents
Page - 28
Problem:
Sabrina gets an allowance of $20 a week. She saves 30%. How
much does she save each week?
What is the whole? 20
What is the part? ______
?
What is the percent? _____
30%
Solve the problem using multiples
The weekly allowance is the whole, 100%. 20 ÷ 10 = 2.
Therefore, need to complete the table using multiples of 2.
0%
0
10 %
20 %
2
30 %
4
6
40 %
8
50 %
60 %
70 %
80 %
90 % 100 %
10
12
14
16
18
20
30% of 20 is 6.
Therefore, Sabrina saves $6 a week.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
x
20
30
100
30 • 20 = x • 100
600 = x • 100
3.
600 ÷ 100 = x
x = 6
4.
30% of 20 is 6
© S. Mercer - Using Multiples to Introduce Percents
2. Cross Multiply
3. Divide
4. Answer the question
Page - 29
Problem:
Sean has $70. He used $49 to buy a CD player. What percent of his
money did he spend?
49
What is the part? ______
What is the whole? 70
What is the percent? _?_
Solve the problem using multiples
Sean’s money is the whole, 100%. 70 ÷ 10 = 7.
Therefore, need to complete the table using multiples of 7.
0%
0
10 %
7
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
14
21
28
35
42
49
56
63
70
49 is 70% of 70
Therefore, Sean spent 70% of his money on a CD player
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
3.
4.
49
70
x
100
49 • 100 = x • 70
4900 = x • 70
2. Cross Multiply
3. Divide
4. Answer the question
4900 ÷ 70 = x
x = 70
49 is 70% of 70
© S. Mercer - Using Multiples to Introduce Percents
Page - 30
Problem:
A $1200 computer is on sale for $840. What is the percent of discount?
840
What is the part? ____
What is the whole? 1200
What is the percent? _?_
Solve the problem using multiples
The price of the computer is the whole, 100%. 1200 ÷ 10 = 120.
Therefore, need to complete the table using multiples of 120.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
0
120
240
360
480
600
720
840
960
90 % 100 %
1080
1200
840 is 70% of 1200
Therefore, the percent of discount is 30%
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
840
1200
x
100
2. 840• 100 = x • 1200
84000 = x • 1200
3.
4.
2. Cross Multiply
3. Divide
4. Answer the question
84000 ÷ 1200 = x
x = 70
840 is 70% of 1200
© S. Mercer - Using Multiples to Introduce Percents
Page - 31
Problem:
Sabrina’s restaurant bill is $50. She leaves a 15% tip. How much is
the tip?
What is the whole? 60
What is the part? __?__
What is the percent? _15%_
Solve the problem using multiples
The restaurant bill is the whole, 100%. 60 ÷ 10 = 6.
Therefore, need to complete the table using multiples of 6.
0%
0
10 %
6
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
12
18
24
30
36
42
48
54
60
15% of 60 is between 6 and 12. The middle number
between 6 and 12 is 9. Therefore, the tip is $9.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
x
60
15
100
60• 15 = x • 100
900 = x • 100
3.
900 ÷ 100 = x
x = 9
4.
9 is 15% of 60
© S. Mercer - Using Multiples to Introduce Percents
2. Cross Multiply
3. Divide
4. Answer the question
Page - 32
Problem:
The retail price of a TV is $400. The discount is 25%. How many
dollars is the discount?
What is the whole? 400
What is the part? __?__
What is the percent? _25%_
Solve the problem using multiples
The price of the TV is the whole, 100%. 400 ÷ 10 = 40.
Therefore, need to complete the table using multiples of 40.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
40
80
120
160
200
240
280
320
360
400
25% of 400 is between 80 and 120.
The middle number between 80 and 120 is 100.
Therefore, the discount is $120.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
2.
x
400
25
100
400 • 25 = x • 100
1000 = x • 100
3.
1000 ÷ 100 = x
x = 100
4.
100 is 25% of 400
© S. Mercer - Using Multiples to Introduce Percents
2. Cross Multiply
3. Divide
4. Answer the question
Page - 33
Problem:
What is 260% of 120?
What is the whole? 120
What is the part? __?__
What is the percent? 260%_
Solve the problem using multiples
120 is the whole, 100%. 120 ÷ 10 = 12.
Therefore, need to complete the table using multiples of 12.
0%
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 % 100 %
0
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228
240
252
164
276
288
300
312
260% of 120 is 312.
Solve the problem using
proportions
part
%
whole
100
Steps to solve the
proportion
1. Set the proportion
1.
x
120
260
100
2. 120 • 260 = x • 100
31200 = x • 100
3.
31200 ÷ 100 = x
x = 312
4.
312 is 260% of 120
© S. Mercer - Using Multiples to Introduce Percents
2. Cross Multiply
3. Divide
4. Answer the question
Page - 34
Summary
Discovering Shortcuts
Throughout this unit you have used multiples to solve percent problems. Review all the
problems to discover “easy ways” to calculate the specific percents without having to write the
multiples or setup a proportion. For each percent, explain how you can calculate it quickly without
setting up a proportion and give an example:
Percent
Shortcut or easy way to calculate it
10%
take the whole (100%) and divide it by 10
10% of 40 is 4 because 40 ÷ 10 = 4
50%
take the whole (100%) and divide it by 2
50% of 40 is 20 because 40 ÷ 2 = 20
100%
is the whole (100%)
100% of 40 is 40 because 40 is 100%
200%
take the whole (100%) and multiple it by 2 200% of 40 is 80 because 40 x 2 = 80
20%
Example
One way is to divide the whole by 10 to
20% of 40 is 8 because
obtain 10%, then you multiply 10% by 2 to 40 ÷ 10 = 4 (10%) and 4 x 2 = 8 (20%)
get the 20%.
or
A different way is to multiply the whole by 40 x 2 = 80 (200%) and 80 ÷ 10 = 8 (20%)
2 to obtain 200% and then divide 200% by
10 to get 10%.
One way is to divide the whole by 10 to
obtain 10%, then divide 10% by 2 to get
the 5%.
5%
A different way is to divide the whole by 2
to obtain 50% and then divide 50% by 10
to get 5%.
© S. Mercer - Using Multiples to Introduce Percents
5% of 40 is 2 because
40 ÷ 10 = 4 (10%) and 4 ÷ 2 = 2 (5%)
or
40 ÷ 2 = 20 (50%) and 20 ÷ 10 = 2 (5%)
Page - 35
Using Multiples
to Introduce
Percents
Name: ____________________
Period: ________
Date: ______________________
Review of Multiples
Write multiples of 10, ending in 300
10
20
100
300
Write multiples of 2, ending in _____
2
4
6
Write multiples of 5, ending in _____
5
10
15
© S. Mercer - Using Multiples to Introduce Percents
Page - 1
Review of Multiples
Write multiples of 4, ending in _____
Write multiples of 7, ending in _____
Write multiples of 9, ending in _____
© S. Mercer - Using Multiples to Introduce Percents
Page - 2
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
0
0•3
0
3
1•3
3
6
2•3
3+3
9
3•3
3+3+3
What patterns do you see?
© S. Mercer - Using Multiples to Introduce Percents
Page - 3
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
0
7
14
21
What patterns do you see?
© S. Mercer - Using Multiples to Introduce Percents
Page - 4
Review of Multiples
Multiples
Multiples
as a product
Multiples
as an addition
36
40
What patterns do you see?
© S. Mercer - Using Multiples to Introduce Percents
Page - 5
Multiples and Percents
Multiples
of 10
Multiples
of
3
%
%
%
%
%
%
%
%
%
%
X
Using the table, answer the following questions:
•
What is 100% of 30? ________
•
What is 50% of 30? _______
•
27 is what percent of 30? _______
•
12 is what percent of 30? ______
•
What is 40% of 30? ______
•
24 is what percent of 30? _______
•
What is 110% of 30? ______
•
What is 0% of 30? _______
•
60 is what percentof 30? ______
•
65% of 30 is between what two number? ______ and ______
•
99% of 30 is close to what number? _______
•
16% of 30 is between what two numbers? _____ and ______
•
Is 50% of 30 bigger than 30? Yes or No Why? ____________________
____________________________________________________________________
•
What is 200% of 30? ______________
© S. Mercer - Using Multiples to Introduce Percents
Page - 6
%
Multiples and Percents
Multiples
of 10
Multiples
of
6
%
%
%
%
%
%
%
%
%
%
X
Using the table, answer the following questions:
•
What is 100% of 60? ________
•
54 is what percent of 60? ______
•
What is 70% of 60? ______
•
24 is what percent of 60? _______
•
What is 110% of 60? ______
•
What is 0% of 60? _______
•
90 is what percentof 60? ______
•
25% of 60 is between what two number? ______ and ______
•
99% of 60 is close to what number? _______
•
128% of 60 is between what two numbers? _____ and ______
•
Is 75% of 60 bigger than 60? Yes or No Why? ____________________
____________________________________________________________________
•
Is 170% of 60 bigger than 60? Yes or No Why? ____________________
____________________________________________________________________
•
What is 200% of 60? ______________
•
180 is what percent of 60? _______
© S. Mercer - Using Multiples to Introduce Percents
Page - 7
%
Multiples and Percents
Multiples
of 10
Multiples
of
8
%
%
%
%
%
%
%
%
%
%
X
Using the table, answer the following questions:
•
What is 100% of 80? ________
•
32 is what percent of 80? ______
•
What is 10% of 80? ______
•
What is 200% of 80? _____
•
64 is what percent of 80? _______
•
What is 130% of 80? ______
•
What is 0% of 80? _______
•
120 is what percentof 80? ______
•
35% of 80 is between what two number? ______ and ______
•
101% of 80 if close to what number? _______
•
167% of 80 is between what two numbers? _____ and ______
•
Is 86% of 80 bigger than 80? Yes or No Why? ______________________
____________________________________________________________________
•
Is 130% of 80 bigger than 80? Yes or No Why? _____________________
____________________________________________________________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 8
%
Multiples and Percents
Multiples
of 10
Multiples
of
40
%
%
%
%
%
%
%
%
%
%
X
Using the table, answer the following questions:
•
What is 100% of 400? ________
•
320 is what percent of 400? ______
•
What is 20% of 400? ______
•
120 is what percent of 400? _______
•
What is 140% of 400? ______
•
What is 0% of 400? _______
•
600 is what percentof 400? ______
•
75% of 400 is between what two number? ______ and ______
•
49% of 400 is close to what number? _______
•
179% of 400 is between what two numbers? _____ and ______
•
Is 50% of 400 smaller than 400? Yes or No Why? ____________________
____________________________________________________________________
•
Is 170% of 400 bigger than 400? Yes or No Why? ____________________
____________________________________________________________________
•
What is 200% of 400? ______________
© S. Mercer - Using Multiples to Introduce Percents
Page - 9
%
Multiples and Percents
Based on the information provided complete the table.
0%
%
%
%
%
%
%
%
%
% 100 %
70
0
X
Using the table, answer the following questions:
•
What is 100% of 70? ________
•
What is 10% of 70? _____
•
How did you obtain 10% of 70 given 100%? __________________________
•
Does this always work? _______ Why? ________________________________
•
80% is what percent of 70? ______
•
What is 150% of 70? _____
•
21 is what percent of 70? _______
•
What is 0% of 70? _______
•
45% of 70 is between what two number? ______ and ______
•
59% of 70 if close to what number? _______
•
137% of 70 is between what two numbers? _____ and ______
•
Is 45% of 70 smaller than 70? Yes or No Why? ______________________
____________________________________________________________________
•
Is 125% of 70 bigger than 70? Yes or No Why? _____________________
____________________________________________________________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 10
Multiples and Percents
Based on the information provided complete the table.
0%
%
%
%
%
%
%
%
%
% 100 %
150
0
X
Using the table, answer the following questions:
•
What is 100% of 150? ________
•
What is 10% of 150? _____
•
How do you obtain 10% of 150 given 100%? __________________________
•
Does this always work? _______ Why? ________________________________
•
30 is what percent of 150? ______
•
What is 150% of 150? _____
•
90 is what percent of 150? _______
•
What is 20% of 150? _______
•
15% of 150 is between what two number? ______ and ______
•
99% of 150 if close to what number? _______
•
151% of 150 is between what two numbers? _____ and ______
© S. Mercer - Using Multiples to Introduce Percents
Page - 11
Multiples and Percents
Based on the information provided complete the table.
0%
%
%
%
%
%
%
%
%
% 100 %
500
0
X
Using the table, answer the following questions:
•
What is 100% of 500? ________
•
What is 10% of 500? _____
•
How do you obtain 10% of 500 given 100%? __________________________
•
Does this always work? _______ Why? ________________________________
•
200 is what percent of 500? ______
•
What is 150% of 500? _____
•
400 is what percent of 500? _______
•
What is 60% of 500? _______
•
15% of 500 is between what two number? ______ and ______
•
49% of 500 if close to what number? _______
•
198% of 500 is between what two numbers? _____ and ______
•
What is 1% of 500? _________
How did you calculate 1% of 500? _______________________________________
______________________________________________________________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 12
Percents and Multiples
Percent
Multiples
Multiples
as a product
Multiples
as an addition
Representation
0%
10%
100%
60
© S. Mercer - Using Multiples to Introduce Percents
Page - 13
Percents and Multiples
Percent
Multiples
Multiples
as a product
Multiples
as an addition
Representation
0%
10%
100%
140
© S. Mercer - Using Multiples to Introduce Percents
Page - 14
Multiples and Percents
Based on the information provided complete the table.
0%
%
%
%
%
0
50 %
%
%
%
% 100 %
45
X
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
________________________________________________________________________
________________________________________________________________________
Write 5 percent questions that can be answered with the table and answer them.
Question 1: ________________________________________________________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 15
Multiples and Percents
Based on the information provided complete the table.
0%
10 %
%
%
%
%
%
%
%
% 100 %
0
X
66
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
________________________________________________________________________
________________________________________________________________________
Write 5 percent questions that can be answered with the table and answer them.
Question 1: ________________________________________________________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 16
Multiples and Percents
Based on the information provided complete the table.
0%
0
%
20%
%
%
%
%
%
%
% 100 %
24
X
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
________________________________________________________________________
________________________________________________________________________
Write 5 percent questions that can be answered with the table and answer them.
Question 1: ________________________________________________________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 17
Multiples and Percents
Based on the information provided complete the table.
0%
%
%
%
%
0
%
%
%
%
90 % 100 %
18
X
Using the table, answer the following question:
•
How did you complete the table? Describe step by step. ____________________
________________________________________________________________________
________________________________________________________________________
Write 5 percent questions that can be answered with the table and answer them.
Question 1: ________________________________________________________________________
Answer: __________________
Question 2: ________________________________________________________________________
Answer: __________________
Question 3: ________________________________________________________________________
Answer: __________________
Question 4: ________________________________________________________________________
Answer: __________________
Question 5: ________________________________________________________________________
Answer: __________________
© S. Mercer - Using Multiples to Introduce Percents
Page - 18
Percent Practice and Review
1)
100% of 70
Write the answer as a
mulitplication.
2)
60% of 50
Write the answer as a
mulitplication.
3)
20% of 30
Write the answer as a
mulitplication.
4)
90% of 20
Write the answer as a
mulitplication.
5)
50% of 150
Write the answer as a
mulitplication.
6)
___ % of ___
Write the answer as a
mulitplication.
4 4
4
4
4
___ % of ___
7)
Write the answer as a
mulitplication.
8
8
9)
11 11 11
11
11
11
11
11 11 11
8
8
8
8 8
___ % of ___
25 25 25
25
25
25
25
25 25 25
___ % of ___
8)
8 8
4 4
Write the answer as a
mulitplication.
25 25 25
25
25
© S. Mercer - Using Multiples to Introduce Percents
Write the answer as a
mulitplication.
11
11
___ % of ___
10)
5
5 5
5
5
5
5
5
5
5 5
Write the answer as a
mulitplication.
5
5
5
5
5
5
5
5 5
Page - 19
Percent Practice and Review
1)
100% of 160
Write the answer as a
mulitplication.
2)
40% of 90
Write the answer as a
mulitplication.
3)
40% of 70
Write the answer as a
mulitplication.
4)
80% of 120
Write the answer as a
mulitplication.
5)
50% of 180
Write the answer as a
mulitplication.
6)
___ % of ___
Write the answer as a
mulitplication.
7 7
7
7
7
___ % of ___
7)
2
2
2
2
2
2
9)
___ % of ___
8)
2
2
2
Write the answer as a
mulitplication.
2
2 2
___ % of ___
22 22 22
22
22
22
22
22
22 22
5
5
5
5
2
2
10)
5
5
5
5
5
5
Write the answer as a
mulitplication.
7 7
5
5
5
5
5
5
5
5 5
___ % of ___
1
Write the answer as a
mulitplication.
5 5
5
5
5
5
5 5
Write the answer as a
mulitplication.
1
1
1
22
© S. Mercer - Using Multiples to Introduce Percents
1
1 1
Page - 20
Problem:
What is 80% of 120?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 21
Problem:
What is 20% of 60?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 22
Problem:
What is 150% of 40?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 23
Problem:
11 is 10% of what number?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 24
Problem:
160 is what percent of 80?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 25
Problem:
24 is what percent of 30?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 26
Problem:
A Middle School has 300 girls. 40% of the girls play an instrument.
How many girls play an instrument?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 27
Problem:
A Middle School has 250 boys. 60% of the boys play soccer. How
many boys play soccer?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 28
Problem:
Sabrina gets an allowance of $20 a week. She saves 30%. How
much does she save each week?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 29
Problem:
Sean has $70. He used $49 to buy a CD player. What percent of his
money did he spend?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 30
Problem:
A $1200 computer is on sale for $840. What is the percent of discount?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 31
Problem:
Sabrina’s restaurant bill is $50. She leaves a 15% tip. How much is
the tip?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 32
Problem:
The retail price of a TV is $400. The discount is 25%. How many
dollars is the discount?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 33
Problem:
What is 260% of 120?
What is the whole? _____
What is the part? ______
What is the percent? _____
Solve the problem using multiples
0%
%
%
%
%
%
%
Solve the problem using
proportions
part
%
whole
100
%
%
% 100 %
Steps to solve the
proportion
1.
1.
2.
2.
3.
3.
4.
4.
© S. Mercer - Using Multiples to Introduce Percents
Page - 34
Summary
Discovering Shortcuts
Throughout this unit you have used multiples to solve percent problems. Review all the
problems to discover “easy ways” to calculate the specific percents without having to write the
multiples or setup a proportion. For each percent, explain how you can calculate it quickly without
setting up a proportion and give an example:
Percent
Shortcut or easy way to calculate it
Example
10%
50%
100%
200%
20%
5%
© S. Mercer - Using Multiples to Introduce Percents
Page - 35