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• • • • • • • • • • • • • • • • Work with Percents8 How to
Facts to Know
What Is a Percent?
Percent means “per hundred.” The symbol % also means percent or “per hundred.” Percent is abusiness term going back to the Roman times which is still used to measure interest rates, commissionrates, mark-ups, discounts, and tax rates.
Percent is another way of writing a fraction with a denominator of 100. You can see how decimals,fractions, and percents are three ways of saying the same amount:
0.30 say, “thirty hundredths”
30——100
say, “thirty hundredths”
30% say, “thirty percent,” which means “thirty per hundred”
Changing Decimals to Percents
To change a decimal to a percent, move the decimal point two places to the right and write a % sign.
Sample: Change .16 to a percent .16 = .16 = 16%
Sample: No need to put the decimal point to the right of a whole number.
Sample: Change .4 to a percent .4 = .40 = 40%
Sample: You need to add a zero in order to move the decimal point two places.
Sample: Change .015 to a percent. .015 = .01 5 = 1.5%
Sample: Moving the decimal two places puts it in the middle of 15.
Sample: Change .16 2 –
3
to a percent. .16 2 –
3
= .16 2 –
3
= 16 2 –
3
%
Sample: You don’t need to put the decimal point between the whole number and the fraction.
Changing Percents to Decimals
To change percents to decimals, do the reverse of what you did with the decimal point in changingdecimals to percents—move it to the left.
Sample: Change 6% to a decimal.
Step 1 Remove the % sign.
Step 2 Move the decimal point 2 places to the left. If you don’t see a decimal point, there isan imaginary one to the right of the number.
Step 3 Place zeros in front if necessary.
No matter how many places there are in a number, the rule is the same about moving the decimal.
Samples: 300% = 300. or 3 175% = 175. =
6% = .06 = .06
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• • • • • • • • • • • • • • • • Work with Percents8 How to
Facts to Know (cont.)
Fractional Percents
A fractional percent is a number such as 1 –3% or 1 –
5%. First change
the fraction to a decimal (See Unit 7). Then follow the same steps
for changing a percent to a decimal.
Changing Percents to Fractions
To change a percent to a fraction, follow these steps:
Sample: Change 30% to a fraction.
Step 1 Remove the percent sign. 30% 30
Step 2 Make the number the numerator of the fraction. 30 30
Step 3 Write 100 for the denominator. 30—100
Step 4 Simplify the fraction, if possible. 30—100
= 3—10
Changing Fractions to Percents
To change a fraction to a percent, follow these steps:
Sample: Change 5 –8
to a percent.
Step 1 Change the fraction to a decimal. Dividethe numerator 5 by the denominator 8.
Step 2 Follow the rules for changing a decimal
to a percent.
Finding a Percent of a Number
To find a percent of a number, change the percent to a fraction or a decimal and multiply.
Sample: Your teacher says that only 4% of two classes totaling 50 students will be awarded ticketsto a baseball game. How many students will receive tickets?
You want to find 4% or 4———100
of 50.
Step 1 Change 4% to a fraction or to a decimal.
Step 2 Multiply 50 by the fraction 4———100
or thedecimal .04.
The final answer is 2 tickets because 4% of 50 is 2.
.6255 –8
= 8 5.000 – 4 800
200 – 160
40 – 40
= 62.5%
1 –3
% = .3% = .003
1 –
5
% = .20% = .0020
As a fraction 4% = 4—100
(or)
As a decimal 4% = .04
4————100
x50—1
=200———100
= 2 or .04 x 50 = 2
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• • • • • • • • • • • • • • • • Work with Percents8 How to
Facts to Know (cont.)
Finding a Percent of a Number and Rounding
Percent is often used in connection with money, but money in the United States has only two decimalplaces. When a money answer has more than two decimal places, round off the answer to the nearestcent.
Sample: Find 12% of $14.70.
Step 1 Change 12% to a decimal. 12% = .12
Step 2 Multiply $14.70 by .12.
Step 3 Round to the nearest cent.
Since 4 is in the thousandths place and is less than 5, drop it for the final answer. If the number in thethousandths place were 5 or greater than 5, you would raise the number in the hundredths place.
Finding What Percent One Number Is of Another
To find what percent one number is of another, make a fraction by placing the part—usually the smallernumber— over the whole, which is usually the larger number.
Sample: What percent is 15 of 40?
Step 1 Place the part over the whole and reduce. 15—40
= 3 –8
Step 2 Change the fraction to a percent.
$14.70x .12
2940+ 14700$1.7640
Finding a Number When a Percent of It Is Given
Sometimes you know only the percent of a number that is missing. To find the missing number, changethe percent to a fraction or a decimal. Then divide the amount you have by the fraction or decimal.
Sample: The student government of the junior high had a car wash and raised $525. That is 75% of what they need to purchase a sound system for the cafeteria. How much do they need?
Step 1 Change 75% to a fraction or change 75% to a decimal.
Step 2 Divide $525 by the fraction or divide $525 by the decimal.
15—40 = 3 –8 x 100———1 = 300———8 = 75—2 = 37 1 –2 %
$700.
.75 $525.00 – 525.00
0
75% = 75—100
= 3 –4
75% = .75
175
1
= $ 1.76
or$525 ÷ 3 –4
= $525—1
x 4 –3
= $700
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• • • • • • • • • • • • • • Working with Percents8 Practice
1. .07 = _____
2. .75 = _____
3. .035 = _____
4. .33 1 –3
= _____
5. .9 = _____
6. 1.5 = _____
7. .004 = _____
8. .65 = _____
9. .1 = _____
10. .66 2 –3
= _____
Directions: Change the percents to decimals.
11. 9% = _____
12. 35% = _____
13. 4.8% = _____
14. 22 2/9% = _____
15. 60% = _____
16. 125% = _____
17. .3% = _____
18. 95% = _____
19. 20% = _____
20. 33 1/3% = _____
Directions: Change the percents to fractions.
21. 75% = _____
22. 40% = _____
23. 5% = _____
24. 80% = _____
25. 6% = _____
26. 9% = _____
27. 8% = _____
28. 20% = _____
29. 35% = _____
30. 86% = _____
Directions: Change the fractions to percents.
Directions: Find the number when the percentis given.
31. 3 –8
= _____
32. 1 –3
= _____
33. 2 –5
= _____
34. 7 –8
= _____
35. 2 –3
= _____
36. 1 –5
= _____
37. 1 –2
= _____
38. 1 –8
= _____
39. 1—20
= _____
40. 1 –4
= _____
Directions: Find the percent of a number.
41. 17 is what percent of 340? ________
42. 420 is what percent of 70? ________
43. 60 is what percent of 300? ________
44. 25 is what percent of 150? ________
45. 30 is what percent of 120? ________
46. 16 is 20% of what number? ________
47. 63 is 70% of what number? ________
48. 70 is 110% of what number? ________
49. 13 is 10% of what number? ________
50. 12 is 14% of what number? ________
Directions: Change the decimals to percents.
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• • • • • • • • • • • • • • • • • Calculate Percents9 How to
Calculating Interest
To find simple interest, use the formula I = PRT
Sample: How much would a loan of $500 be at 6% interest for 6 months?
Step 1 Use the interest formula. The formula to calculate interest is this:Interest = Principal x Rate of Interest x Time (I = P x R x T)
Step 2 Change the rate, given as a percent, to a fraction and reduce. Set up time as afraction of a year.
R = 6———100
= 3—50
T = 6—12
= 1 –2
Step 3 Multiply principal x rate x time. Cancel where possible.
I = 500—1
x 3—50
x 1 –2
= $15
You can also change the percent to a decimal (6% = .06) and the time to a decimal
(6 months = 6—12
= .5) and then multiply.
I = $500.00 x .06 x .5 = $15
Facts to Know
When money is borrowed, you must pay to use it because someone else is losing an opportunity to useit while you have it. What you pay to use the money is called interest . The rate of interest is a percent.The money you borrow is called the principal. Simple interest is paid only on the principal.
The Interest FormulaTo calculate the amount of simple interest on a loan, use this formula:
Interest = Principal x Rate of Interest x Time (or) I = PRT
Rate of Interest
The rate of interest is always given as a percent. You often see rates of interest on loans andinvestments posted outside of banks.
Time
Time in connection with loans is always expressed in years or parts of a year.
1 month = 1—12
of a year 6 months = 6—12
or 1 –2
year
510
1 1
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• • • • • • • • • • • • • • • • • Calculate Percents9 How to
Facts to Know (cont.)
Calculating Interest (cont.)
Sample: A T-shirt costs $24.99 and a pair
of jeans costs $34.99. Each is on sale for25% off the original price. If Jennabought the T-shirt and jeans while theywere on sale, what was her total pricebefore adding tax? What is the totalamount that Jenna had to pay for her pur-chase after tax was added? (Tax is 8%.)
one-day pass
one-day passtwo-day pass
Discounts and Sales
A discount is used by manufacturers and merchants to mean taking off a certain percentage of the pricegiven in a price list. This price is called the list price. The list price less the discount is known as thenet price. The noun “discount” can be used as a verb, too—“We’re discounting by 15% the list priceon all new cars and trucks during our storewide ‘Get into Spring’ sale!”
You would ask “What’s the discount?” but not, “What’s the sale?” Often you have to figure out yourown savings during a sale, and this is where understanding decimals and percents comes in handy.
Let’s say, for instance, you read that a local amusement park is offering a single, one-day pass to allrides for $12.50, or a special two-day pass for $20.00. You do some quick decimal arithmetic.
$12.50x 2
$25.00
So your savings on a two day pass is the following:
$25.00 – $20.00
$5.00
But, just curious—what percent off is that?
$5.00 = x invert and multiply $5.00 x 100 = 500 or 20% off $25.00 100 $25.00 x 25
Jenna paid $18.74 + $26.24 = $44.98 for the T-shirt and jeans.
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• • • • • • • • • • • • • • • • • • • • • • Answer Key
20. 0.15; 0.51; 5.01;50.1
21. 4
22. 27
23. 21
24. 5.6
25. 0.2
26. 7.6
27. 18.7
28. 304.81
29. 1.06
30. 27.39
31. 356.14
32. $13.02
33. $163.76
34. 4,567.83
Page 27
1. 2.7
2. .14
3. 4.3384. 1825.2
5. 4121
6. 6
7. 150.9
8. 10.625
9. 1.628
10. 31.88
11. .056
12. .00702
13. .084
14. 599.104
15. 161.505
16. 2.16408
17. 56.088
18. 48.708
19. 7.616
20. .18446
21. 1.8
22. 53
23. 145
24. .091
25. 112.34
26. .922
27. 524.75
28. 893,15529. 0.23
30. 1679.45
Page 28
1. $93.96
2. $4.47
3. $105.30
4. $69.93
5. $53.38
6. $420.52
7. $585.39
8. $256.50
9. 2.646
10. 1.872
11. 2.6628
12. 0.00228
13. $6.30
14. 4.78
15. 137.74
16. $1.38
17. $8.37
18. .1218
Page 32
1. 5
2. 0.139
3. 10.80
4. 625
5. 0.013
6. 0.04
7. 0.038. 750
9. 175
10. $81.25
11. 5.7
12. .043
13. 4.9
14. 80
15. 50
16. 7/20
17. 8/125
18. 3 2/5
19. 3 1/820. 18 1/3
21. 4 5/8
22. 21/2500
23. 66 3/4
24. 159/500
25. 1/16
26. 4 1/4
27. 1 1/10
28. .8
29. .37 1/2 or .375
30. .66 2/3
31. .77 7/9
32. .83 1/3
33. .62 1/2 or .625
34. .33 1/3
35. .7
Page 36
1. 7%
2. 75%
3. 3.5%
4. 33 1/3%
5. 90%
6. 150%
7. .4%
8. 65%
9. 10%
10. 66 2/3%
11. .09
12. .35
13. .048
14. .22 2/9
15. .6
16. 1.25
17. .003
18. .95
19. .2
20. .33 1/3
21. 3/4
22. 2/5
23. 1/20
24. 4/525. 3/50
26. 9/100
27. 2/25
28. 1/5
29. 7/20
30. 43/50
31. 37.5%
32. 33 1/3%
33. 40%
34. 87.5%
35. 66 2/3%
36. 20%37. 50%
38. 12.5%
39. 5%
40. 25%
41. 5%
42. 600%
43. 20%
44. 16 2/3%
45. 25%
46. 80
47. 90
48. 63.6
49. 130
50. 85.71
Page 39
1. $45.00
2. $45.42
3. $10.00
4. $30.00
5. $135.00
6. $73.75
7. $19.90
8. $9.12
9. $298
10. $54.08
Page 40
1. $42.29
2. $196
3. $16.20
4. $0.25
5. $1372.70
Pages 41 and 42
1. 24 pieces of pie
2 1/4 yard
3. 4 miles4. 1 1/8 miles
5. 2 1/2 pieces of taffy
6. 3 weeks
7. 75 ounces
8. 66 1/4 inches
9. $287.65
10. $21.79
11. $114.26
12. $81.16
13. $300; $90; $210
14. $26.45
15. 25 students16. 150 children
17. 20 homes
18. 225 cards
19. $0.87
20. $1.50
21. 26 minutes
22. 288 boxes
23. 6 pounds
24. 6.25%
Pages 43 and 44
1. $500 every sixmonths. Take asalary of $10,000for Sample:
1st year: $5,000 +$5,500 = $10,500
vs. $10,0002nd year: $6,000+ $6,500 =$12,500 vs.$12,000
2. about 18,000miles
3. house numbers
4. $0.20
5. 100%
6. Choco-Chunk andNuts to U areequal in value.Goodie Two-
Shoes is the betterbuy.
7. 200 miles a day
8. $4,250.00
9. $1.25 to breakeven; $4.38 tomake $25,000.
10. a. $14.00
b. $42.00
c. $52.50
d. $87.50
e. $49.00
f. $105.00
Yes, he saved$350.00
11. b
12. a
13. a
14. a
15. After 31 years,the system willstill be worth$10!
16. 52 bushels of wheat, 55 bushelsof corn, and 34bushels of oats.
.5 0 1 – 2 5 0 %
Chart
1. 1—10
, .10, 10%
2. 1 –4
, .25, 25%
3. 9—20
, .45, 45%
4. 3—20
, .15, 15%
5. 4—5
, .80, 80%
6. 5—6
, .833, 83.3%
7. 77——100
, .77, 77%
8. 1—20
, .20, 20%
9. 11—50
, .222, 22%
10. 2 –5
, .40, 40%
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Unit 4: Probability, Percent, and Proportion
Name _____________________________________
Percent 1
Directions: Set up each proportion and solve. Write a “therefore statement” for eachsolution.
92
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Unit 4: Probability, Percent, and Proportion
Percent 1 (cont.)
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Appendix B: Answer Keys
Guided Practice Book Answers
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1. 1—10
2. .25
3. 45%
4. 15%
5.
4
—5
6. 5—6
7. .77
8. 1—20
9. .222
10. 40%
• • • • • • Calculating Fractions, Decimals,and Percents
9 Practice
Directions: Some states require that out-of-state businesses pay a shipping tax to send goods to stateresidents. Refer to this table to do the problems below. (Note: The shipping rates do not reflect theactual current rates.)
Some States’ Shipping Taxes
Alabama . . . . . . . . . . . . . . . AL . . . . . . . 8.00%Maryland . . . . . . . . . . . . . . MD . . . . . . . 5.75%
Georgia. . . . . . . . . . . . . . . . GA . . . . . . . 4.00%
Illinois . . . . . . . . . . . . . . . . . IL. . . . . . . . 2.00%
Indiana . . . . . . . . . . . . . . . . IN . . . . . . . 5.00%
Kentucky . . . . . . . . . . . . . . KY . . . . . . . 6.00%
Missouri . . . . . . . . . . . . . . . MO . . . . . . . 5.725%
1. Miguel lives in Maryland and purchased a sweater for $39.99 from a catalog. Add the shippingtax. What’s the total cost of the sweater? __________
2. Mr. and Mrs. Wong paid a total of $200.00 for an entertainment center for their home in Chicago,Illinois. The salesperson said that there was already a 2% shipping tax already added to the finalprice. What was the price of the entertainment center before the tax was added? __________
3. Stuart lives in Alabama and recently joined a book club that will send a book to him every month.The books are $15.00 each. The book club billing will include the shipping tax. What is the totalamount that Stuart will have to pay for each book? __________
4. The Middlebury High School band in Indiana is going to sell holiday ornaments to raise moneyfor uniforms. Each ornament will cost $5.00. How much is the shipping price per ornament?__________
5. The Williams family live in Lexington, Kentucky. They recently purchased a computer for
$1,295.00. What is the total price for the computer after the shipping tax was added? __________Directions: Complete the table below.
Fraction Decimal Percent
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• • • • • • • • • • • • • • • • • • • • • • Answer Key
20. 0.15; 0.51; 5.01;50.1
21. 4
22. 27
23. 21
24. 5.6
25. 0.2
26. 7.6
27. 18.7
28. 304.81
29. 1.06
30. 27.39
31. 356.14
32. $13.02
33. $163.76
34. 4,567.83
Page 27
1. 2.7
2. .14
3. 4.3384. 1825.2
5. 4121
6. 6
7. 150.9
8. 10.625
9. 1.628
10. 31.88
11. .056
12. .00702
13. .084
14. 599.104
15. 161.505
16. 2.16408
17. 56.088
18. 48.708
19. 7.616
20. .18446
21. 1.8
22. 53
23. 145
24. .091
25. 112.34
26. .922
27. 524.75
28. 893,15529. 0.23
30. 1679.45
Page 28
1. $93.96
2. $4.47
3. $105.30
4. $69.93
5. $53.38
6. $420.52
7. $585.39
8. $256.50
9. 2.646
10. 1.872
11. 2.6628
12. 0.00228
13. $6.30
14. 4.78
15. 137.74
16. $1.38
17. $8.37
18. .1218
Page 32
1. 5
2. 0.139
3. 10.80
4. 625
5. 0.013
6. 0.04
7. 0.038. 750
9. 175
10. $81.25
11. 5.7
12. .043
13. 4.9
14. 80
15. 50
16. 7/20
17. 8/125
18. 3 2/5
19. 3 1/820. 18 1/3
21. 4 5/8
22. 21/2500
23. 66 3/4
24. 159/500
25. 1/16
26. 4 1/4
27. 1 1/10
28. .8
29. .37 1/2 or .375
30. .66 2/3
31. .77 7/9
32. .83 1/3
33. .62 1/2 or .625
34. .33 1/3
35. .7
Page 36
1. 7%
2. 75%
3. 3.5%
4. 33 1/3%
5. 90%
6. 150%
7. .4%
8. 65%
9. 10%
10. 66 2/3%
11. .09
12. .35
13. .048
14. .22 2/9
15. .6
16. 1.25
17. .003
18. .95
19. .2
20. .33 1/3
21. 3/4
22. 2/5
23. 1/20
24. 4/525. 3/50
26. 9/100
27. 2/25
28. 1/5
29. 7/20
30. 43/50
31. 37.5%
32. 33 1/3%
33. 40%
34. 87.5%
35. 66 2/3%
36. 20%37. 50%
38. 12.5%
39. 5%
40. 25%
41. 5%
42. 600%
43. 20%
44. 16 2/3%
45. 25%
46. 80
47. 90
48. 63.6
49. 130
50. 85.71
Page 39
1. $45.00
2. $45.42
3. $10.00
4. $30.00
5. $135.00
6. $73.75
7. $19.90
8. $9.12
9. $298
10. $54.08
Page 40
1. $42.29
2. $196
3. $16.20
4. $0.25
5. $1372.70
Pages 41 and 42
1. 24 pieces of pie
2 1/4 yard
3. 4 miles4. 1 1/8 miles
5. 2 1/2 pieces of taffy
6. 3 weeks
7. 75 ounces
8. 66 1/4 inches
9. $287.65
10. $21.79
11. $114.26
12. $81.16
13. $300; $90; $210
14. $26.45
15. 25 students16. 150 children
17. 20 homes
18. 225 cards
19. $0.87
20. $1.50
21. 26 minutes
22. 288 boxes
23. 6 pounds
24. 6.25%
Pages 43 and 44
1. $500 every sixmonths. Take asalary of $10,000for Sample:
1st year: $5,000 +$5,500 = $10,500
vs. $10,0002nd year: $6,000+ $6,500 =$12,500 vs.$12,000
2. about 18,000miles
3. house numbers
4. $0.20
5. 100%
6. Choco-Chunk andNuts to U areequal in value.Goodie Two-
Shoes is the betterbuy.
7. 200 miles a day
8. $4,250.00
9. $1.25 to breakeven; $4.38 tomake $25,000.
10. a. $14.00
b. $42.00
c. $52.50
d. $87.50
e. $49.00
f. $105.00
Yes, he saved$350.00
11. b
12. a
13. a
14. a
15. After 31 years,the system willstill be worth$10!
16. 52 bushels of wheat, 55 bushelsof corn, and 34bushels of oats.
.5 0 1 – 2 5 0 %
Chart
1. 1—10
, .10, 10%
2. 1 –4
, .25, 25%
3. 9—20
, .45, 45%
4. 3—20
, .15, 15%
5. 4—5
, .80, 80%
6. 5—6
, .833, 83.3%
7. 77——100
, .77, 77%
8. 1—20
, .20, 20%
9. 11—50
, .222, 22%
10. 2 –5
, .40, 40%