Transcript 6-4 - TeacherWeb

6-4 Percent of a Number
Warm Up
Problem of the Day
Lesson Presentation
Course 2
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
Course 2
6-4 Percent of a Number
Learn to find the percent of a number.
Course 2
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.
%
100
Course 2
n
67
=
100 90
Part
Whole
Using a proportion…
PART
PERCENT
% = “IS”
100
“OF”
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
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.
Course 2
Write a proportion.
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.
Course 2
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
Divide each side by 100 to isolate
the variable.
48 = n
200% of 24 is 48.
Course 2
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.
3% of 12
“OF” MEANS MULTIPLY
3% of 12 = 0.03 · 12
= 0.36
Write the percent as a
decimal and multiply.
Estimate
5% · 12 = 0.6, so 3% of 12 is a little less than
0.6. Thus 0.36 is a reasonable answer.
Course 2
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.
Course 2
6-4 Percent
Insert Lesson
of a Number
Title Here
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
student bought lunch on Monday?
357
Course 2
6-5 Solving Percents Problems
Warm Up
Solve.
1. 4x = 90
2. 8x = 96
3. 12x = 180
4. 26x = 182
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22.5
12
15
7
6-5 Solving Percents Problems
Learn to solve problems involving
percents.
Course 2
6-5 Solving Percents Problems
Sloths may seem lazy, but their extremely slow
movement helps to make them almost invisible to
predators. Sloths sleep an average of 16.5 hours
a day.
To find out what percent of a 24-hour day 16.5
hours is, you can use a proportion or an equation.
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6-5 Solving Percents Problems
Proportion Method
Part
Whole
n
= 16.5
24
100
Part
Whole
n · 24 = 100 · 16.5
24n = 1,650
n = 68.75
Sloths spend about 69% of the day sleeping!
Course 2
6-5 Solving Percents Problems
Additional Example 1A: Using Proportions to Solve
Problems with Percents
Solve.
What percent of 40 is 25?
n = 25
Write a proportion.
100
40
n · 40 = 100 · 25
Set the cross products equal.
40n = 2,500
Multiply.
40n = 2,500
40
40
n = 62.5
Divide each side by 40 to isolate
the variable.
25 is 62.5% of 40.
Course 2
6-5 Solving Percents Problems
Additional Example 1B: Using Proportions to Solve
Problems with Percents
Solve.
15 is 25% of what number?
25 = 15
100
n
Write a proportion.
n · 25 = 100 · 15 Set the cross products equal.
25n = 1,500
Multiply.
25n = 1,500
25
25
n = 60
Divide each side by 25 to isolate
the variable.
15 is 25% of 60.
Course 2
6-5 Solving Percents Problems
Check It Out: Example 1A
Solve.
What percent of 50 is 10?
n = 10
Write a proportion.
100
50
n · 50 = 100 · 10
Set the cross products equal.
50n = 1,000
Multiply.
50n = 1,000
50
50
n = 20
Divide each side by 50 to isolate
the variable.
10 is 20% of 50.
Course 2
6-5 Solving Percents Problems
Check It Out: Example 1B
Solve.
8 is 40% of what number?
40 = 8
100
n
n · 40 = 100 · 8
Set the cross products equal.
40n = 800
Multiply.
40n = 800
40
40
n = 20
Divide each side by 40 to isolate
the variable.
8 is 40% of 20.
Course 2
Write a proportion.
6-5 Solving Percents Problems
Additional Example 3: Finding Sales Tax
A portable DVD player costs $225 before tax at
an appliance warehouse. What is the sales tax
rate if the tax is $18?
Restate the question: What percent of $225 is $18?
n = 18
Write a proportion.
100
225
n · 225 = 100 · 18 Set the cross products equal.
225n = 1800
Multiply.
225n = 1800
225
225
Divide each side by 225.
n=8
8% of $225 is $18. The sales tax is 8%.
Course 2
6-5 Solving Percents Problems
Check It Out: Example 3
A new flat screen TV costs $800 before tax at an
appliance warehouse. What is the sales tax rate
if the tax is $56?
Restate the question: What percent of $800 is $56?
n = 56
Write a proportion.
100
800
n · 800 = 100 · 56 Set the cross products equal.
800n = 5600
Multiply.
800n = 5600
800
800
Divide each side by 800.
n=7
7% of $800 is $56. The sales tax is 7%.
Course 2
Problems
6-5 Solving
Insert Percents
Lesson Title
Here
Lesson Quiz
Solve.
1. 21 is 42% of what number?
50
2. What percent of 292 is 73?
25%
3. 112% of what number is 84? 75
4. What percent of 1,340 is 13.4? 1%
5. An ad features a bicycle on sale for $139. If
the total cost of the bike is $147.34, what is
the sales tax rate?
6%
Course 2