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?. ?. ?. ?. ?. ?. ?. Fractions, Decimals, and Percents. LESSON 5-1. Problem of the Day. Replace the question marks with the correct digits. a. 8 9 + 6. = 15.96 b. 13. 0 – . 4 2 = 4.122. 9, 9, 7. 6, 4, 9, 8. 5-1. 90 100. 80 100. 35 100. 25 - PowerPoint PPT Presentation
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FeatureLesson
Course 3Course 3
LessonMain
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
Replace the question marks with the correct digits.
a. 8 9 + 6. = 15.96
b. 13. 0 – . 4 2 = 4.122
? ? ?
? ? ? ?
9, 9, 7
6, 4, 9, 8
Problem of the Day
5-1
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-1LESSON 5-1
Fractions, Decimals, and PercentsFractions, Decimals, and Percents
(For help, go to Lesson 2-2.)
1. Vocabulary Review A rational number is a number that can be written in the form ? .
Write each fraction in simplest form.
2. 3.
4. 5.
90100
80100
35100
25100
Check Skills You’ll Need
Check Skills You’ll Need
5-1
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. , b 0 2. =
3. = 4. =
5. =
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
35 ÷ 5100 ÷ 5
720
14
25 ÷ 25100 ÷ 25
90 ÷ 10100 ÷ 10
910
45
80 ÷ 20100 ÷ 20
ab
Check Skills You’ll Need
5-1
FeatureLesson
Course 3Course 3
LessonMain
Use mental math to write as a percent.
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
325
What you think
I can write as an equivalent fraction with a denominator of 100.
325
12100
= I can rewrite as 12%.12
100
4
4
Why it works
325
3 • 425 • 4
= Multiply the numerator and denominator by 4.
12100
= Simplify.
= 12% Write the fraction as a percent.
325
Quick Check
Additional Examples
5-1
FeatureLesson
Course 3Course 3
LessonMain
Write each decimal as a percent.
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
a. 2.5
b. 0.003
2.5 = 2510
Write the decimal as a fraction.
= 25 • 1010 • 10
=250100
Write as an equivalent fraction with a denominator of 100.
= 250% Write the fraction as a percent.
0.003 =3
1,000 Write the decimal as a fraction.
=3 ÷ 10
1,000 ÷ 10 =0.3100
Write as an equivalent fraction with a denominator of 100.
= 0.3% Write the fraction as a percent.Quick Check
Additional Examples
5-1
FeatureLesson
Course 3Course 3
LessonMain
A brand of cereal supplied 7 % of the RDA of
sodium. Write this portion of the RDA as a fraction.
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
Rewrite the fraction as division.Write the mixed number as animproper fraction.
= 152
÷ 100
Quick Check
12
Simplify.= 340
= 1
100 Multiply by the reciprocal of 100.152
x
Additional Examples
5-1
Write the percent as a fraction with adenominator of 100.7 % =
7 100
12
12
FeatureLesson
Course 3Course 3
LessonMain
Order 27%, 0.24, and from least to greatest.
Fractions, Decimals, and PercentsFractions, Decimals, and PercentsLESSON 5-1LESSON 5-1
15
27% = 0.27 0.24=0.24 =0.20 15
15
Answer: < 0.24 < 27%
Quick Check
Additional Examples
5-1
FeatureLesson
Course 3Course 3
LessonMain
Fractions, Decimals, and PercentsFractions, Decimals, and Percents
1. A cereal supplies 1 % of the RDA for calcium. Write 1 % as a fraction.
2. Write as a percent.
3. Write 1.5 as a percent.
4. Order 60%, 0.58, and .
LESSON 5-1LESSON 5-1
14
14
14
720
58
180
35%
150%
0.58 < 60% < 58
Lesson Quiz
5-1
FeatureLesson
Course 3Course 3
LessonMain
Estimating With PercentsEstimating With Percents
The Jackson Country Bird Sanctuary has three times as many owls as hawks. It has 40 hawks and owls in all. How many of each are in the sanctuary?
LESSON 5-2LESSON 5-2
30 owls, 10 hawks
Problem of the Day
5-2
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-2LESSON 5-2
Estimating With PercentsEstimating With Percents
(For help, go to Lesson 2-5.)
1. Vocabulary Review The multiplicative inverse of is
Find each product.
2. 36 • 3. • 12
4. • 60 5. 81 • 910
23
59
34
37
Check Skills You’ll Need
Check Skills You’ll Need
5-2
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. 2. • = = = 27
3. • = = = 8 4. • = = = 54
5. • = = = 45
Estimating With PercentsEstimating With PercentsLESSON 5-2LESSON 5-2
1
73
23
121
2 • 123 • 1
2 • 123 • 1
9361
34
36 • 3 1 • 4
36 • 3 1 • 4 1
1
49
10601
9 • 6010 • 1
9 • 6010 • 11
6
811
59
81 • 5 1 • 9
81 • 5 1 • 9
9
Check Skills You’ll Need
5-2
FeatureLesson
Course 3Course 3
LessonMain
Estimate 74% of 158 using decimals.
Estimating With PercentsEstimating With PercentsLESSON 5-2LESSON 5-2
74% of 158 0.75 of 160
74% 0.75 Use a decimal that is close to 74%.
158 160Round 158 to a number that is compatible with 0.75.
= 0.75 • 160 Multiply to find 0.75 of 160.
= 120 Simplify.
Quick Check
Additional Examples
5-2
FeatureLesson
Course 3Course 3
LessonMain
A video store rented 297 videos. The customers
returned 19% of the videos late. Estimate, using fractions,
how many videos were returned late.
Estimating With PercentsEstimating With PercentsLESSON 5-2LESSON 5-2
19%15 Use a fraction that is close to 19%.
297 300 Round to a number that is compatible with 5.
19% of 29715 of 300
15 = 60= •
3001 Multiply to find of 300.
1
6015
About 60 videos were returned late. Quick Check
Additional Examples
5-2
FeatureLesson
Course 3Course 3
LessonMain
Dion is saving for a coat that costs $59.95. She
has saved 45% of the cost. Estimate how much she has
saved.
Estimating With PercentsEstimating With PercentsLESSON 5-2LESSON 5-2
What you think
The coat costs about $60.
I know 50% of 60 equals of 60, or 30. Since 5% is one-tenth of 50%, then 5% of 60 is one-tenth of 30, which is 3. So, the amount Dion has saved is about $30 minus $3, which is $27.
12
Additional Examples
5-2
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Estimating With PercentsEstimating With PercentsLESSON 5-2LESSON 5-2
Why it works
50% of 60 = 0.5 • 60To find 50% of a number, multiply the number by 0.5.
= 30 Simplify.
5% of 60 = (50% of 60)5% of a number is one-tenth of 50% of that number.
110
= (30)1
10 Substitute.
= 3 Simplify.
So, 45% of $59.95 is about $27.
45% of 60 = 30 – 3 45% = 50% – 5%
= 27 Simplify.Quick Check
Additional Examples
5-2
FeatureLesson
Course 3Course 3
LessonMain
Estimating With PercentsEstimating With Percents
Show the numbers you use to estimate. Numbers used may vary,
Samples are given.
1. Use decimals to estimate 54% of 29.
2. Use fractions to estimate 74% of 38.
3. Estimate a 15% tip on $8.15.
4. About 60% of 27 students are in the play.
0.5 • 30 = 15
LESSON 5-2LESSON 5-2
• 40 = 3034
0.1(8) + 0.1(4) = 0.8 + 0.4 = $1.20
(30) = 18 students or 0.6 • 30 = 1835
Lesson Quiz
5-2
FeatureLesson
Course 3Course 3
LessonMain
Percents and ProportionsPercents and Proportions
Use graph paper. Design and draw a diagram to determine which has the greater area—a square with sides of 10 cm or a circle with a diameter of 10 cm.
LESSON 5-3LESSON 5-3
Draw a circle within the square to prove that the square has the greater area.
Problem of the Day
5-3
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-3LESSON 5-3
Percents and ProportionsPercents and Proportions
(For help, go to Lesson 4-3.)
1. Vocabulary Review Two equal ratios form a
Solve each proportion.
2. = 3. = 4. =
5. = 6. =
240n
125
6y
24100
s4
75100
4b
20100
812
e100
Check Skills You’ll Need
Check Skills You’ll Need
5-3
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. proportion 2. 20b = 400; b = 20
3. 12e = 800; e = 66 4. 12n = 1,200; n = 100
5. 100s = 300; s = 3 6. 24y = 600; y = 25
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
23
Check Skills You’ll Need
5-3
FeatureLesson
Course 3Course 3
LessonMain
Find 32% of 240.
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
n240
=32
100Write a proportion.
100n = 240 • 32 Write the cross products.
100n = 7,680 Simplify.
=100n100
7,680100
Divide each side by 100.
n = 76.8 Simplify.
Quick Check
Additional Examples
5-3
FeatureLesson
Course 3Course 3
LessonMain
Brenda saw a blender for $24 in a bargain store. In a second store, the same blender was 160% of the cost of the blender in the bargain store. Find 160% of $24.
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
A diagram can help you understand the problem.
n24
=160100
Write a proportion.
100n = 24 • 160 Write the cross products.
100n = 3,840 Simplify.
Additional Examples
5-3
FeatureLesson
Course 3Course 3
LessonMain
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
=100n100
3,840100
Divide each side by 100.
n = 38.4 Simplify.
The price of the blender in the second store was $38.40.
(continued)
Quick Check
Additional Examples
5-3
FeatureLesson
Course 3Course 3
LessonMain
Suppose 11,550 elementary students make up
14% of a city’s population. What is the population of the
city?
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
A diagram can help you understand the problem.
11,500w
14100
= Write a proportion.
11,550 • 100 = 14w Write the cross products.
1,155,000 = 14w Simplify.
= Divide each side by 14.1,155,000
1414w14
82,500 = w Use a calculator.
Additional Examples
5-3
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
The population of the city is 82,500 people.
Check for Reasonableness 82,500 is about 80,000. Since 14% of 80,000 is 11,200, which is close to 11,155, the answer is reasonable.
Quick Check
Additional Examples
5-3
FeatureLesson
Course 3Course 3
LessonMain
26 is what percent of 80?
Percents and ProportionsPercents and ProportionsLESSON 5-3LESSON 5-3
2680
p100
= Write a proportion.
26 • 100 = 80p Write the cross products.
2,600 = 80p Simplify.
= Divide each side by 80.2,600
8080p80
32.5% = p Simplify and insert a percent sign.
Additional Examples
5-3
A diagram can help you understand the problem.
FeatureLesson
Course 3Course 3
LessonMain
Percents and ProportionsPercents and Proportions
1. Find 25% of 160.
2. The price of a music CD is $12. If the store raises the price to 125% of its current price, what will be the new price of the CD?
3. So far, the sixth grade class has sold 32 tickets to their play. The
number represents 20% of the tickets that are available. How many
tickets are available?
4. 98 is what percent of 56?
40
LESSON 5-3LESSON 5-3
$15
160
175%
Lesson Quiz
5-3
FeatureLesson
Course 3Course 3
LessonMain
Percents and EquationsPercents and Equations
Write the prime factorization of 364.
LESSON 5-4LESSON 5-4
22 7 13
Problem of the Day
5-4
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-4LESSON 5-4
Percents and EquationsPercents and Equations
(For help, go to Lesson 1-7.)
1. Vocabulary Review Is 2 • 8 = 16 an equation or an expression? Explain.
Solve each equation.
2. 0.25p = 10
3. 12.25 = 9.8x
4. 24 = 1.6s
5. 0.64k = 0.02
Check Skills You’ll Need
Check Skills You’ll Need
5-4
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. Equation; it contains an = sign. 2. = ; p = 40
3. = ; x = 1.25 4. = ; s =15
5. = ; k = 0.03125
Percents and EquationsPercents and EquationsLESSON 5-4LESSON 5-4
100.25
241.6
0.020.64
1.6s1.6
0.64k0.64
0.25p0.25
9.8x9.8
12.259.8
Check Skills You’ll Need
5-4
FeatureLesson
Course 3Course 3
LessonMain
Misha got 84% correct on a 25 problem test. How
many did he answer correctly?
Percents and EquationsPercents and EquationsLESSON 5-4LESSON 5-4
c = 0.84 • 25
c = 21 Simplify.
Check for Reasonableness 84% of 25 80% of 25. Since 80% of 25 is 20, which is close to 21, the answer is reasonable.
Quick Check
number of problems correct is 84% of 25Words
Equation
Let = the number of problems correct.
c 84% of 25=
c
Additional Examples
5-4
FeatureLesson
Course 3Course 3
LessonMain
Use an equation. 12 is 8% of what number?
Percents and EquationsPercents and EquationsLESSON 5-4LESSON 5-4
12 = 0.08 • w Write a percent equation.
=12
0.080.08w0.08
Divide each side by 0.08.
Simplify.150 = w
Quick Check
Additional Examples
5-4
FeatureLesson
Course 3Course 3
LessonMain
Percents and EquationsPercents and Equations
1. Find 81% of 110.
2. You buy a book for $17.80. Sales tax is 8%. What is the sales tax cost of the book?
3. 45 is 75% of what number?
4. Find what percent 68 is of 80.
89.1
LESSON 5-4LESSON 5-4
$1.42
60
85%
Lesson Quiz
5-4
FeatureLesson
Course 3Course 3
LessonMain
Percent of ChangePercent of Change
Dan, Susan, Monica, and Jose want to talk on the phone once to each of the others. How many telephone calls will be made?
LESSON 5-5LESSON 5-5
6 calls
Problem of the Day
5-5
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-5LESSON 5-5
Percent of ChangePercent of Change
(For help, go to Lesson 5-1.)
1. Vocabulary Review A is a ratio that compares a number to 100.
Write each fraction as a percent. Round to the nearest tenth of a percent.
2. 3.
4. 5.
622
415
113
98
Check Skills You’ll Need
Check Skills You’ll Need
5-5
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. percent 2. = 1.125; 112.5% 3. = 0.27; 27.3%
4. = 0.26; 26.7% 5. = 3.6; 366.7%
Percent of ChangePercent of ChangeLESSON 5-5LESSON 5-5
98
622
113
415
Check Skills You’ll Need
5-5
FeatureLesson
Course 3Course 3
LessonMain
Ten years ago, Max’s comic book was worth
$2.50. Now it is worth $13. Find the percent of increase in
value.
Percent of ChangePercent of ChangeLESSON 5-5LESSON 5-5
amount of change = 13 – 2.50 = 10.50
P =10.502.50
amount of changeoriginal amount
Check for Reasonableness 420% of 2.5 400% of 3. Since 400% of 3 = 12, which is close to 13, the answer is reasonable.
10.50 2.50 4.2 Use a calculator to divide.
= 420% Write the decimal as a percent.
The percent of increase in value is 420%.
Quick Check
Additional Examples
5-5
FeatureLesson
Course 3Course 3
LessonMain
Andre changed the height of his basketball hoop
from 8 ft 4 in. to 9 ft 2 in. Find the percent of increase.
Percent of ChangePercent of ChangeLESSON 5-5LESSON 5-5
amount of change = 110 – 100 = 10
8 ft 4 in. = 8 • 12 + 4 = 100 in.9 ft 2 in. = 9 • 12 + 2 = 110 in.
Write measures in the same units.
P =10
100amount of changeoriginal amount
= 0.1 Simplify.
= 10% Write the decimal as a percent.
The height of the basketball hoop increased by 10%. Quick Check
Additional Examples
5-5
FeatureLesson
Course 3Course 3
LessonMain
In 1980, the population of a city was 557,927.In 1990, its population was 496,938. Find the percentof decrease. Round to the nearest tenth.
Percent of ChangePercent of ChangeLESSON 5-5LESSON 5-5
amount of change = 557,927 – 496,938 = 60,989
P =60,989
557,927amount of changeoriginal amount
The population decreased by about 11%.
= 0.109313584 Use a calculator.
11%Write the decimal as a percent. Round to thenearest tenth.
Quick Check
Additional Examples
5-5
FeatureLesson
Course 3Course 3
LessonMain
Percent of ChangePercent of Change
Round to the nearest whole percent.
1. 81 people attended last year’s annual picnic, and 93 people attended this year’s picnic. What is the percent of increase?
2. The speed limit on a highway was 55 miles per hour last year. This year the speed limit was increased to 65 miles per hour. What is the percent increase in the speed limit?
3. The population in Arthur County, Nebraska dropped from 462 in 1990 to 444 in 2000. What was the percent of decrease?
about 15%
LESSON 5-5LESSON 5-5
about 18%
about 4%
Lesson Quiz
5-5
FeatureLesson
Course 3Course 3
LessonMain
Markup and DiscountMarkup and Discount
Round to the underlined place.
a. 0.09972 b. 0.109 c. 17.51 d. 0.998
LESSON 5-6LESSON 5-6
0.0997 0.1 18 1.00
Problem of the Day
5-6
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-6LESSON 5-6
Markup and DiscountMarkup and Discount
(For help, go to Lesson 5-4.)
1. Vocabulary Review A relates a part to the whole.
Use an equation to solve each problem.
2. What number is 16% of 25?
3. Find 80% of 250.
4. 33 is 3% of what number?
5. 0.55% of what number is 77? Check Skills You’ll Need
Check Skills You’ll Need
5-6
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. percent 2. 0.16 • 25 = n; n = 4
3. 0.80 • 250 = n; n = 200 4. 0.03 • w = 33; w = 1,100
5. 0.0055 • w = 77; w = 14,000
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
Check Skills You’ll Need
5-6
FeatureLesson
Course 3Course 3
LessonMain
Find the percent of markup for a stapler costing the
school store $2.10 and selling for $3.36.
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
markup = selling price – store’s cost
= $3.36 – $2.10 Substitute.
= $1.26 Subtract.
percent of markup =1.262.10
markupstore’s cost
= 0.6 Write the fraction as a decimal.
= 60% Write the decimal as a percent.
Quick Check
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
A store sells a skirt that costs the store $40 and
marks up the price 25%. What is the selling price for this
skirt?
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
Method 1 Find the markup first. Then find the selling price.
25% of $40 equals the markup.
= $10
$40 + 10 = $50
The store sells the skirt for $50.
0.25 • 40 = 10 Multiply to find the markup.
store’s cost + markup = selling price
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
Method 2 Find the selling price directly.
The selling price equals 100% of the store’s cost plus a markup of 25% of the store’s cost.
The store sells the skirt for $50.
So, the selling price of the skirt is 100% + 25%, or 125%, of $40.
= $50
Multiply to find the selling price.
125% of $40 equals the selling price.
1.25 • 40 = 50
Quick Check
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
A shoe store advertises a 35%-off sale. What is
the sale price of shoes that regularly cost $94.99?
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
Method 1 Find the discount first. Then find the sale price.
35% of $94.99 equals the discount.
The sale price is $61.74.
= $33.25
94.99 – 33.25 = 61.74
0.35 • 94.99 = 33.2465 Multiply to find the discount.
regular price – discount = sale price
Round to the nearest cent.
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
Method 2 Find the sale price directly.
The sale price equals 100% of the regular price minus a discount of 35% of the regular price.
The sale price is $61.74.
The sale price is 100% – 35%, or 65%, of $94.99.
= $61.74
Multiply to find the sale price.
65% of $94.99 equals the sale price.
0.65 • 94.99 = 61.744
Round to the nearest cent.
Quick Check
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
You buy a CD at the sale price of $6. This is 25%
off the regular price. Find the regular price of the CD.
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
regular price – 25% of regular price = sale price
The regular price of the CD is $8.
r – (0.25 • r ) = 6 Substitute. Write the percent as a decimal.
Let r = the regular price.
0.75r = 6 Combine like terms: r – 0.25r = 0.75r.
= Divide each side by 0.75.0.75r0.75
60.75
r = 8 Simplify.
Quick Check
Additional Examples
5-6
FeatureLesson
Course 3Course 3
LessonMain
Markup and DiscountMarkup and DiscountLESSON 5-6LESSON 5-6
1. A pair of shoes costs the store $40. The store sells them for $65.What is the percent markup?
62.5%
2. A school service club sells calendars. Each calendar costs the club $5.50. The club marks up the price 80%. What is the selling price of each calendar? $9.90
3. A sweater regularly sells for $49. It is on sale for 20% off. What is the sale price? $39.20
4. You buy a baseball cap for $13. This price is 35% off the regular price. Find the regular price. $20.00
Lesson Quiz
5-6
FeatureLesson
Course 3Course 3
LessonMain
Simple InterestSimple Interest
Luis’s mother has two older sisters who are twins and 6 yr older than she is. She has a brother who is half her age. The sum of all their combined ages is 145 yr. How old is each?
LESSON 5-7LESSON 5-7
mother 38, older twins 44, brother 19
Problem of the Day
5-7
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-7LESSON 5-7
Simple InterestSimple Interest
(For help, go to Lesson 2-6.)
1. Vocabulary Review A is a rule that shows a relationship between quantities.
Solve each formula for the underlined variable.
2. V = lwh 3. d = rt
4. y = x + b 5. V = Bh13
Check Skills You’ll Need
Check Skills You’ll Need
5-7
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. formula 2. w =
3. r = 4. b = y – x
5. B =
Simple InterestSimple InterestLESSON 5-7LESSON 5-7
Vlh
3V h
d t
Check Skills You’ll Need
5-7
FeatureLesson
Course 3Course 3
LessonMain
A student deposits $150 into a bank that pays 6%
simple interest. Find the interest earned in 4 years.
Simple InterestSimple InterestLESSON 5-7LESSON 5-7
l = p • r • t Use the simple interest formula.
= 150 • 0.006 • 4 Substitute: p = 150, r = 6% = 0.06, t = 4.
= 36 Multiply.
In 4 years, the interest earned is $36.
Quick Check
Additional Examples
5-7
FeatureLesson
Course 3Course 3
LessonMain
Use the information from Example 1. Find thefinal balance in the account after 5 years.
Simple InterestSimple InterestLESSON 5-7LESSON 5-7
l = p • r • t= 150 • 0.06 • 5 Substitute into the simple interest formula.
= 45 Multiply.
In 5 years, the interest earned is $45.
First, find the interest earned.
Next, find the final balance in the account.
The final balance in the account is $195.
principal + earned interest = balance
= balance45+150
= 195
Substitution.
Add.Quick Check
Additional Examples
5-7
FeatureLesson
Course 3Course 3
LessonMain
Simple InterestSimple Interest
1. You deposit $80 into an account that earns 6% simple interest. Find the amount of interest earned in 3 years.
2. You deposit $180 into an account that earns 6% simple interest. How much will be in the account after 3 years?
LESSON 5-7LESSON 5-7
$14.40
$212.40
Lesson Quiz
5-7
FeatureLesson
Course 3Course 3
LessonMain
Ratios and ProbabilityRatios and Probability
Which of the following numbers would give the smallest product?
4.9, 75.12, 15.02, 21.275, 8.61, 0.942, 47.38, 3.824
LESSON 5-8LESSON 5-8
0.942, 3.824
Problem of the Day
5-8
FeatureLesson
Course 3Course 3
LessonMain
LESSON 5-8LESSON 5-8
Ratios and ProbabilityRatios and Probability
(For help, go to Lesson 4-1.)1. Vocabulary Review A is a comparison of two quantities by
division.
Write each ratio in simplest form.
2. 3 : 6
3.
4.
5.
6. 17 to 68
8 h100 h
90 s270 s
20 cm36 cm
Check Skills You’ll Need
Check Skills You’ll Need
5-8
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. ratio 2. = = = , = or 1:2
3. = = = 4. = = =
5. = = 6. = = , = or 1 to
4
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
8 h100 h
8100
8 ÷ 4100 ÷ 4
225
1768
17 ÷ 1768 ÷ 17
14
90 s270 s
90270
90 ÷ 90270 ÷ 90
13
20 cm36 cm
2036
20 ÷ 436 ÷ 4
59
3 ÷ 36 ÷ 3
12
36
36
Check Skills You’ll Need
5-8
FeatureLesson
Course 3Course 3
LessonMain
There are 3 red, 2 green, 5 yellow, and 1 blue
marker pens in a box. Suppose you choose one at random.
Find these probabilities.
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
P (yellow) =5
115 favorable outcomes11 possible outcomes
P (brown) =0
110 favorable outcomes11 possible outcomes
The probability of choosing a yellow marker pen is .5
11
= 0 Write the fraction in simplest form.
The probability of choosing a brown marker pen is 0.
b. P (brown)
a. P (yellow)
Quick Check
Additional Examples
5-8
FeatureLesson
Course 3Course 3
LessonMain
In a survey of the class, 13% of the students prefer
vanilla, 27% prefer chocolate, 10% prefer strawberry, and
the rest chose other flavors of ice cream. What is the
probability that a student randomly selected from the class
chose vanilla or chocolate?
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
13% of the students chose vanilla, and 27% of the students chose chocolate.
P(vanilla or chocolate) = P(vanilla) + P(chocolate)
= 13% + 27% Substitute.
= 40% Simplify.
The probability that the student chose vanilla or chocolate is 40%.
Quick Check
Additional Examples
5-8
FeatureLesson
Course 3Course 3
LessonMain
Express as a fraction the probability that the
outcome for rolling two number cubes has a sum less than 7.
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
Make a table to find the sample space for rolling two number cubes.
1 2 3 4 5 61 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1)2 (1,2) (2,2) (3,2) (4,2) (5,2) (6,2)3 (1,3) (2,3) (3,3) (4,3) (5,3) (6,3)4 (1,4) (2,4) (3,4) (4,4) (5,4) (6,4)5 (1,5) (2,5) (3,5) (4,5) (5,5) (6,5)6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
So, P(sum less than 7) = , or .1536
512 Quick Check
1 (1,1) (2,1) (3,1) (4,1) (5,1) (6,1)2 (1,2) (2,2) (3,2) (4,2) (5,2) (6,2)3 (1,3) (2,3) (3,3) (4,3) (5,3) (6,3)4 (1,4) (2,4) (3,4) (4,4) (5,4) (6,4)5 (1,5) (2,5) (3,5) (4,5) (5,5) (6,5)6 (1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
Out of the 36 possible outcomes, the 15 outcomes shown in red have a sum less than 7.
Additional Examples
5-8
FeatureLesson
Course 3Course 3
LessonMain
What is the probability (as a fraction) of there being at least 1 male kitten in a litter of 4 kittens? Drawthe sample space. Express the probability as a fraction.
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
Additional Examples
5-8
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Ratios and ProbabilityRatios and ProbabilityLESSON 5-8LESSON 5-8
P(at least one male) = number of outcomes with at least one male kittentotal number of possible outcomes with four kittens
1516
= Substitute.
Quick Check
Additional Examples
5-8
FeatureLesson
Course 3Course 3
LessonMain
Ratios and ProbabilityRatios and Probability
1. A 6-sided number cube has the numbers 1, 2, 3, 4, 5, and 6 on its faces. What is the probability of rolling a number less than 5? Write your answer as a fraction.
2. A survey shows that 24% of people get their news from the internet, 48% percent from TV, 22% from newspapers, and 6% from news magazines. If you interviewed at random one person who answered the survey, what is the probability that you would select someone who gets news from TV or the internet?
3. A spinner has two equal sections, one yellow and one green. You spin 3 times in a row. Make an organized list to show the sample space for spinning the spinner 3 times. What is the probability of spinning green at least twice in a row?
LESSON 5-8LESSON 5-8
72%
23
Sample space: YYY YYG YGY YGG GYY GYG GGY GGGProbability of spinning green at least twice in a row is .3
8
Lesson Quiz
5-8