Transcript Powerpoint of Notes

PRE-ALGEBRA
Lesson 6-5 Warm-Up
PRE-ALGEBRA
Proportions and Percents
(6-5)
How do you find the
percent of a number
using a proportion??
You can use a proportion to solve any percent problem. To solve a
percent problem using a proportion, first create a proportion table.
Instead of using “known” and “unknown” on the side, it is suggested that
you use “part” and “whole”. Since percent is always out of 100, the
whole percent is always 100. The whole number is always the
number after the word “of”.
Example: What is 22% of 250?
#
%
Part (Known)
x
22
Whole (Unknown)
250
100
x
22
=
250
100
100 • x = 250 • 22
100x = 5500
1
Proportion
.
Cross products are equal.
Simplify.
55
100x
100
=
5500
100
1
Divide both sides by 100.
.
1
x = 55
Simplify.
So 22% of 250 is 55
PRE-ALGEBRA
Proportions and Percents
(6-5)
How can you check the To check whether the answer to a percent problem is reasonable,
answer to a percent
break up the percent into a smaller compatibles percents, like 1% or
problem??
10%, and use estimation to see whether multiples of those smaller
numbers are close to your answer.
Example: Is 22% of 250 equals 55 reasonable?
Check: 10% of 250 is 25 (move the decimal over 1 place to the left to
find 10%) and 1% of 250 is 2.5 (move the decimal over 2 place to the
left to find 1%). 22% = 10% + 10% + 1% + 1% = 25 + 25 + 2.5 + 2.5 =
55.
The answer is reasonable.
PRE-ALGEBRA
Proportions and Percents
LESSON 6-5
Additional Examples
Find 23% of 158.
#
%
Part
(Known)
n
23
Whole
(Unknown)
158
100
n
23
=
158
100
100 • n = 158(23)
100n = 3634
1
100n
100
Use the table or model to
write a proportion.
Write cross products.
Simplify.
36.34
3684
= 100
1
Divide each side by 100.
1
n = 36.34
Simplify.
23% of 158 is 36.34.
Check. Is the answer reasonable? 10% of 158 is 15.8 16 and 1% of 158 is 1.58
 2. 23% = 10%+10%+1%+1%+1%  16 + 16 +2 + 2 + 2  38, which is close to
36, so the answer is reasonable.
PRE-ALGEBRA
Proportions and Percents
LESSON 6-5
Additional Examples
What percent of 34 is 28? Round to the nearest tenth
of a percent.
#
%
Part
(Known)
28
p
Whole
(Unknown)
34
100
28 = p
34
100
34 • p = 100 • 28
34p = 2800
Use the table or model to
write a proportion. Hint: The
word after “of” is the whole
number.
Write cross products.
Simplify.
1
34p
34
2800
= 34
Divide each side by 34.
1
p  82.35
Simplify.
28 is approximately 82.4% of 34.
Check. Is the answer reasonable? 10% of 34 is 3.4, and 80% is 10% • 8 =
3.4 • 8  27, which is close to 28, so the answer is reasonable.
PRE-ALGEBRA
Proportions and Percents
LESSON 6-5
Additional Examples
216 is 72% of what number?
#
%
Part
(Known)
216
72
Whole
(Unknown)
n
100
216 = 72
n
100
72 • n = 100 • 216
72n = 21,600
1
72n
72
Use the table or model to
write a proportion. Hint: The
word after “of” is the whole
number.
Write cross products.
Simplify.
216
21,600
= 72
1
Divide each side by 72.
1
n = 300
Simplify.
216 is 72% of 300.
Check. Is the answer reasonable? 10% of 300 is 30 and 1% of 300 is 3. 70% = 10%
+10%+10%+10%+10%+10%+10%+1%+1% = 30 + 30 + 30 + 30 + 30 + 30 + 30 + 3
+ 3 = 216. The answer is reasonable.
PRE-ALGEBRA
Proportions and Percents
LESSON 6-5
Additional Examples
A tile floor has 90 blue tiles, which is 15% of all the
tiles in the floor. How many tiles are in the floor in all?
#
%
Part
90
15
Whole
n
100
15
90
= 100
n
Write a proportion.
15n = 100(90)
15n
=
1 15
1
9000)
15
x = 600
Make a proportion table or a model. Hint: 90 is
smaller than the total, so it is the “part” number.
Write cross products.
600
Divide each side by 15.
1
Simplify.
The floor has 600 tiles in all.
Check. Is the answer reasonable? The problem says the number of
blue tiles is 15%. 10% of 600 is 60 and 5% of 600 is 30, so
15% is 60 + 30 = 90. The answer is reasonable.
PRE-ALGEBRA
Proportions and Percents
LESSON 6-5
Lesson Quiz
Solve.
1. Find 47% of 2,400.
1,128
2. What percent of 700 is 1,498?
214%
3. 6 is 3% of what number?
200
4. On Saturday, 1,150 people ate at a restaurant. The previous day,
only 68% of that number ate there. About how many people ate
at the restaurant on Friday?
782
PRE-ALGEBRA