Transcript Percent of a Number

6-4 Percent of a Number
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
6-4 Percent of a Number
Warm Up
Multiply.
1. 0.05

20
1
2. 0.32

15
4.8
3. 0.06

25
1.5
4. 0.75

18
13.5
5. 0.34

76
25.84
6-4 Percent of a Number
Problem of the Day
In a group of 60 triangular and square
tiles, 25% are red, and 75% are blue.
The ratio of triangles to squares is 1:2.
Seventy percent of the squares are blue.
Find the number of each kind of tile (red
or blue squares or triangles).
3 red triangles, 17 blue triangles,
12 red squares, 28 blue squares
6-4 Percent of a Number
Sunshine State Standards
MA.7.A.1.2 Solve percent problems, including
problems involving discounts…[and] taxes…
6-4 Percent of a Number
The human body is made up mostly of water. In
fact, about 67% of a person’s total (100%) body
weight is water. If Cameron weighs 90 pounds,
about how much of his weight is water?
Recall that a percent is a part of 100. Since you
want to know the part of Cameron’s body that is
water, you can set up and solve a proportion to
find the answer.
Part
Whole
n
67
=
100 90
Part
Whole
6-4 Percent of a Number
Additional Example 1A: Using Proportions to Find
Percents of Numbers
Find the percent of each number.
30% of 50
30 = n
100
50
30 · 50 = 100 · n
Write a proportion.
Set the cross products equal.
1,500 = 100n
Multiply.
1,500 = 100n
100
100
15 = n
Divide each side by 100 to isolate
the variable.
30% of 50 is 15.
6-4 Percent of a Number
Helpful Hint
When solving a problem with a percent
greater than 100%, the part will be
greater than the whole.
6-4 Percent of a Number
Additional Example 1B: Using Proportions to Find
Percents of Numbers
Find the percent of each number.
200% of 24
200 = n
Write a proportion.
100
24
200 · 24 = 100 · n Set the cross products equal.
4,800 = 100n
Multiply.
4,800 = 100n
100
100
48 = n
Divide each side by 100 to isolate
the variable.
200% of 24 is 48.
6-4 Percent of a Number
Check It Out: Example 1A
Use proportional reasoning to find the percent
of each number.
40% of 18
40 = n
100
18
40 18 = 100n
720
= 100n
100
100
7.2 = n
6-4 Percent of a Number
Check It Out: Example 1B
Use proportional reasoning to find the percent
of each number.
120% of 400
120 = n
100
400
120 400 = 100n
48,000 100n
=
100
100
480 = n
6-4 Percent of a Number
In addition to using proportions, you can
find the percent of a number by using
decimal equivalents.
6-4 Percent of a Number
Additional Example 2A: Using Decimal Equivalents
to Find Percents of Numbers
Find the percent of the number. Check
whether your answer is reasonable.
9% of 80
9% of 80 = 0.09 · 80 Write the percent as a
decimal and multiply.
= 7.2
Model
Since 10% of 80 = 8, a reasonable answer for
9% of 80 is 7.2.
9%
0
0
40%
20%
20
7.2
60%
40
80%
60
100%
80
6-4 Percent of a Number
Additional Example 2B: Using Decimal Equivalents
to Find Percents of Numbers
Find the percent of the number. Estimate
to check whether your answer is reasonable.
0.6% of 270
0.6% of 270 = 0.006 · 270
= 1.62
Write the percent as a
decimal and multiply.
6-4 Percent of a Number
Check It Out: Example 2
Use decimal equivalents to find the percent of
each number.
A. 6% of 18
6% of 18 = 0.06 18
= 1.08
B. 0.8% of 2000
0.8% of 2000 = 0.008 · 2000
= 16
6-4 Percent of a Number
Additional Example 3: Geography Application
The estimated world population in 2001 was
6,157 million. About 40% of the people were
19 or younger. What was the approximate
number of people 19 or younger, to the
nearest million?
Find 40% of 6,157 million.
0.40 · 6,157
Write the percent as a decimal.
2,462.8
Multiply.
The number of people 19 or younger was about
2,463 million.
6-4 Percent of a Number
Check It Out: Example 3A
The estimated world population in 2001 was
6,157 million. About 60% of the people were
above 19 years of age. What was the
approximate number of people 19 or older, to
the nearest million?
60% of 6,157 million = 0.60 · 6,157
= 3694.2
The number of people 19 or older was about
3,694 million.
6-4 Percent of a Number
Check It Out: Example 3B
A bookstore finds that 55% of its total income
in March came from online orders. The total
income for March was $3,150. What was the
income from online orders?
55% of 3,150 = 0.55 · 3,150
= 1,732.50
The income from online orders was $1,732.50.
6-4 Percent of a Number
Check It Out: Example 3C
There are 43,578 students in the public
schools of a city. About 38% of these students
are enrolled in middle school. About how
many students are enrolled in middle school?
38% of 43,578 = 0.38 · 43,578
= 16,559.64
About 16,560 students are enrolled in middle
school.
6-4 Percent of a Number
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
6-4 Percent of a Number
Lesson Quiz
Find the percent of each number.
1. 25% of 8
2
2. 40% of 110 44
Find the percent of each number. Check whether
your answer is reasonable.
3. 150% of 96 144
4. 0.3% of 120 0.36
5. Whitmer Middle School has 850 students. If 42% of
the students bought lunch on Monday, how many
students bought lunch on Monday? 357
6-4 Percent of a Number
Lesson Quiz for Student Response Systems
1. Identify 75% of 4.
A. 1
B. 2
C. 3
D. 4
6-4 Percent of a Number
Lesson Quiz for Student Response Systems
2. Identify 30% of 120.
A. 36
B. 38
C. 40
D. 42
6-4 Percent of a Number
Lesson Quiz for Student Response Systems
3. Identify 140% of 85.
A. 125
B. 120
C. 119
D. 109
6-4 Percent of a Number
Lesson Quiz for Student Response Systems
4. Identify 0.6% of 130.
A. 0.78
B. 0.80
C. 0.82
D. 0.86
6-4 Percent of a Number
Lesson Quiz for Student Response Systems
5. A school has 250 students. If 56% of the
students went on a hiking trip, how many
students went on a hiking trip?
A. 194 students
B. 166 students
C. 154 students
D. 140 students