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8-5
8-5 Estimating
Estimatingwith
withPercents
Percents
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
8-5 Estimating with Percents
Warm Up
Find each percent increase or decrease
to the nearest percent.
1. from 1 to 0.62
2. from 162 to 177
38% decrease
9% increase
3. from 16 to 22
38% increase
4. from 3 to 5
17% decrease
4
Pre-Algebra
8
8-5 Estimating with Percents
Problem of the Day
If you enlarge a picture by 25%, by
what percent do you need to reduce it
to return it to its original size? (Hint: Try
using a simple number for the original
area of the picture.)
20%
Pre-Algebra
8-5 Estimating with Percents
Learn to estimate with percents.
Pre-Algebra
8-5 Estimating with Percents
Vocabulary
estimate
compatible numbers
Pre-Algebra
8-5 Estimating with Percents
Some problems require only an estimate.
Estimates involving percents and fractions
can be found by using compatible
numbers, numbers that go well together
because they have common factors.
not compatible 13  12 compatible
24 24
Pre-Algebra
8-5 Estimating with Percents
Additional Example 1A: Estimating with Percents
Estimate.
A. 21% of 66
Instead of computing the exact answer of
21%  66, estimate.
21% = 21  20 Use compatible numbers, 20 and
100 100 100.
 1
Simplify.
5
1
5

66  65
Use compatible numbers, 65 and 5.
65 = 13
Use mental math: 65 ÷ 5.
So 21% of 66 is about 13.
Pre-Algebra
8-5 Estimating with Percents
Additional Example 1B: Estimating with Percents
Estimate.
B. 36% of 120
Instead of computing the exact answer of
36%  120, estimate.
36%  35%
Round.
 30% + 5%
3
35%

Pre-Algebra

Break down the percent into
smaller parts.
10% + 5%
120 = (3

10% + 5%)

120
Set up an
equation.
8-5 Estimating with Percents
Additional Example 1B Continued
=3

10%
= 36 + 6

120 + 5%

120
Use Distributive Property.
10% of 120 is 12, so 5% of 120 is 6.
= 42
So 36% of 120 is about 42.
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 1A
Estimate.
A. 29% of 86
Instead of computing the exact answer of
29%  86, estimate.
29% = 29  30 Use compatible numbers, 30 and
100 100 100.
 3
10 Simplify.
86  90
3
10 90 = 27
Use compatible numbers, 90 and 10.
Use mental math: 90 ÷ 10.
So 29% of 86 is about 27.
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 1B
Estimate.
B. 44% of 130
Instead of computing the exact answer of
44%  130, estimate.
44%  45%
Round.
 40% + 5%
4
45%

Pre-Algebra

Break down the percent into
smaller parts.
10% + 5%
130 = (4

10% + 5%)

130
Set up an
equation.
8-5 Estimating with Percents
Try This: Example 1B Continued
=4

10%
= 52 + 6.5
= 58.5

130 + 5%

130
10% of 130 is 13,
so 5% of 130 is 6.5.
So 44% of 130 is about 58.5.
Pre-Algebra
Setup an equation.
8-5 Estimating with Percents
Additional Example 2: Problem Solving Application
The diameter of the Moon is about 2160
miles. If the diameter of the Moon is
about 27% of the diameter of Earth,
what is the approximate diameter of
Earth?
Pre-Algebra
8-5 Estimating with Percents
Additional Example 2 Continued
1
Understand the Problem
The answer is the approximate diameter of Earth.
List the important information:
• The diameter of the Moon is about 2160 miles.
• The diameter of the Moon is about 27% of the
diameter of the Earth.
Let e represent the diameter of the Earth.
Diameter of the Moon  27%
2160
Pre-Algebra
 27%

Diameter of Earth

e
8-5 Estimating with Percents
Additional Example 2 Continued
2
Make a Plan
Think: The numbers 2160 and 27% are difficult to
work with.
Use compatible numbers: 2160 is close to 2000;
27% is close to 25%
1
25
25% =
=
Find an equivalent ratio for 25%.
100 4
Pre-Algebra
8-5 Estimating with Percents
Additional Example 2 Continued
3
Solve
Think: 2000 is 1 of what number?
4
4

2000 = e
8000 = e
The diameter of Earth is approximately 8000 miles.
Pre-Algebra
8-5 Estimating with Percents
Additional Example 2 Continued
4
Look Back
25% of 8000 mi is 8000 , or 2000 mi. This is the
4
approximate diameter of the moon.
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 2
The length of a football field is 83% of
the length of a soccer field. If a football
field is 100 yards, what is the
approximate length of a soccer field?
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 2 Continued
1
Understand the Problem
The answer is the approximate length of a soccer
field.
List the important information:
• The length of a football is about 100 yards.
• The length of a football field is 83% of a soccer
field.
Let l represent the length of a soccer field.
Length of football field  83%
100
Pre-Algebra
 83%


Length of soccer field
l
8-5 Estimating with Percents
Try This: Example 2 Continued
2
Make a Plan
Think: The number 83% is difficult to work with.
Use compatible numbers: 83% is close to 80%
4
80
80% =
=
Find an equivalent ratio for 80%.
100 5
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 2 Continued
3
Solve
Think: 100 is 4 of what number?
5
5 
4 100 = l
125 = l
The length of a soccer field is approximately
125 yards.
Pre-Algebra
8-5 Estimating with Percents
Try This: Example 2 Continued
4
Look Back
80% of 125 yards is 4  125 , or 100 yards. This is
5
the length of a football field.
Pre-Algebra
8-5 Estimating with Percents
Lesson Quiz
Estimate. Possible answers:
1. 34% of 12 4
2. 47 out of 236 20%
3. 113% of 80 90
4. 22 out of 51 40%
5. According to the last census, 33,871,648
people live in California, and 3,694,820 of those
people live in Los Angeles. Estimate the percent
of Californians who live in Los Angeles. 10%
Pre-Algebra