SUGGESTED FORMATTING OF STUDENT ASSIGNMENTS…



MAT 115 CP4 ASSIGNMENT

Instructions

Complete the following exercises. Show your work without using a calculator. Checking

your answer on a calculator is a best practice.

|Section Of “Basic Mathematical Skills with Geometry “(6th ed.) |Page Numbers |Exercises |

|Section 4.1 |287-291 |2,4,24,34,72 |

|Section 4.2 | 301-308 |20,36,48,58,72 |

|Section 4.3 | 317-320 |32, 68, 70 |

|Section 4.4 |329-333 |4, 10, 20, 26, 30, 38, 44 |

|Section 4.5 |345-348 |24, 52, 74 |

|Section 4.6 |356-358 |20, 36 |

|Activity 12 : Terminate or Repeat? |359 |ALL |

|Section 4.7 |362-363 |28, 30, 34 |

Instructor Suggestions;

Insert your work in the spaces between problems. When done, save your file with a name like;

“joe students mat 115 cp4.doc”

Attach your file to a note to your instructor in your Individual Forum.

SECTION 4.1

2: For the decimal 8.57932, what is the place value of 5?

Tenths

4: For the decimal 8.57932, what is the place value of 2?

Hundred thousandths

24: Write each of the following as a common fraction or mixed number.

4.0171

[pic][pic]

34: Arrange in order from smallest to largest.

2.05,25/10,2.0513,2.059,251/100,2.0515,2.052,2.051

We Convert All to decimal, they become

2.05, 2.5, 2.0513, 2.059, 2.51, 2.0515, 2.052, 2.051

Now arranging them in order, we get

2.05, 2.051, 2.0513, 2.0515, 2.052, 2.059, 2.5, 2.51

Hence the order is :

2.05, 2.051, 2.0513, 2.0515, 2.052, 2.059, 25/10, 251/100

72: Lula wants to round 76.24491 to the nearest hundredth. She first rounds 76.24491 to 76.245 and then rounds 76.245 to 76.25 and claims that this is the final answer. What is wrong with this approach?.

Since Lula wants to round to nearest hundredth, she should only consider decimal places till the third place. Since the 3rd decimal place is less than 5, she should round it to 76.24.

SECTION 4.2

20: ADD.

[pic]

27.4

+213.321

+ 39.38

= 280.101

20: SUBTRACT.

[pic]

[pic]

= 36.85

48: Add thirty-eight and nine tenths, five and fifty-eight hundredths, seven, and fifteen and eight tenths.

[pic]

= [pic]

Taking LCM of 10, 100,1 and 10

[pic]

= [pic]

= [pic]

Ans = [pic]

58: Geometry. Find the perimeter of the figure given below.

[pic]

Perimeter = 10.5ft + 6.3ft + 3.2 ft +7.4ft + 5.8ft = 33.2ft

72: Business and finance. Alem’s restaurant bill is pictured below. Estimate his total by rounding to the nearest dollar.

[pic]

Total = $18.25 + $8.75 + $6.80+ $7.40+ $1.70 = $42.90

Rounding to nearest dollar, that is units place, it becomes $43 since 9 is more than 5

Ans = $43

SECTION 4.3

32: Business and finance. Claudia earns $6.40 per hour (h). For overtime (each hour over 40 h) she earns $9.60. If she works 48.5 h in a week, what pay should she receive?

For first 40 hours she will earn = 40×6.4 = $256

For rest of hours, it will be overtime, so earnings = 8.5×9.6 = $81.6

Total earnings =256+81.6=$337.60

68: Business and finance. To find the simple interest on a loan for 1 year at 12.5%, multiply the amount of the loan by 0.125. What simple interest will you pay on a loan of $1,458 at 12.5% for 1 year?

Simple interest = 1458×0.125=$182.25

70: Business and finance. In a bottling company, a machine can fill a 2-liter (L)

bottle in 0.5 second (s) and move the next bottle into place in 0.1 s. How many

2-L bottles can be filled by the machine in 2 h?

A machine can fill a 2-liter (L) bottle in 0.5 second (s) and move the next bottle into place in 0.1 s .So it takes 0.5 + 0.1 = 0.6s from the start of 1 bottle to the start of the next bottle.

Now in 2 hours, as there are 60×60 seconds in 1 hour, so there are 2×60×60=7200 seconds in 2 hours.

So, number of bottles that can be filled in 7200 secs = 7200/0.6 = 12,000 bottles

SECTION 4.4

4: Find the circumference of each figure. Use 3.14 for π and round your answer to one decimal place.

[pic]

Circumference = 2 π r = 2 × 3.14× 3.75 = 23.55ft

Rounding to one decimal place, it is 23.6ft

10: Find the perimeter of each figure. (The curves are semicircles.) Round answers to one decimal place

[pic]

Perimeter of the figure = Perimeter of 2 sides of the square +Perimeter of the curve

= 2×10 inches + 1/4 of a circle with radius of 10 inches

= 20 inches + 1/4 × 2 × π × r

= 20 + 1/2 × 3.14 × 10

= 35.7 inches

20: Find the area of each figure

[pic]

Area of figure = Area of parallelogram = b×h

= 7 × 5 sq yards

= 35 sq yards

26: Find the area of each figure

[pic]

Area of figure = Area of square + Area of triangle = l × b + ½ b×h

= 6 × 7 + 1/2 × 2 × 6

= 42 + 6 sq yards

= 48 sq yards

30: Crafts. A circular coffee table has a diameter of 5 ft. What will it cost to have the top refinished if the company charges $3 per square foot for the refinishing?

Area of circle = π r2 = 3.14(5/2) 2 (Since r =diameter/2)

= 19.625 sq ft

So, total cost will be Area × Cost per square foot

= 19.625 × 3

= $58.875

38: Construction. An A-frame cabin has a triangular front with a base of 30 ft and a height of 20 ft. If the front is to be glass that costs $3 per square foot, what will the glass cost?

Area of triangle = 1/2 b × h

= 1/2 × 30 × 20

= 300 sq ft

So, total cost will be Area × Cost per square foot

= 300 × 3

= $900

44: The distance from Philadelphia to Sea Isle City is 100 mi. A car was driven this

distance using tires with a radius of 14 in. How many revolutions of each tire

occurred on the trip?

First we need to find the circumference of the tire, so that we can see how far it travels during one revolution.

Circumference = 2 π r   = 2 × 3.14 × 14 inches = 87.92 inches

Dividing it by 12 to get feet, because 12 inches is a foot, we get 7.327 feet per revolution. Now, A mile is 5280 feet, so

Number of revolutions = 5280 feet / 7.327 feet = 720.62 revolutions

SECTION 4.5

24: DIVIDE

[pic]

0.52) 3.2318 , We can write it as

52) 323.18 ,

So,

6.215

__________

52)323.18

312

________

111

104

_____

78

52

______

260

260

_______

0

 52: Business and finance. Seven employees of an office donated a total of $172.06 during a charity drive. What was the average donation?

The average donation is $172.06 / 7 = $24,58

74: Four brands of soap are available in a local store. Compute the unit price and decide which brand is the best buy.

[pic]

Unit price = Total price / Weight

Unit price of Squeaky Clean = 0.36/5.5 = $0.0655

Unit price of Smell Fresh = 0.41/7.5 = $ 0.0547

Unit price of Feel Nice = 0.31/4.5 = $0.0689

Unit price of Look Bright = 0.44/6.5 = $ 0.0677

 

The lowest is the best so Brand Smell Fresh is best buy.

SECTION 4.6

20: Find the decimal equivalents for each of the following mixed numbers.

[pic]

[pic]

= 7 + ¾

= 7 + .75

= 7.75

36: Statistics. The following table gives the free throws attempted (FTA) and the free throws made (FTM) for the top five players in the NBA for a recent season. Calculate the free throw percentage for each player by writing the FTM over the FTA and converting this fraction to a decimal.

[pic]

Free throw percentage = FTM / FTA. So

Free throw percentage for Allan Houston: 363/395 = 0.9189

Free throw percentage for Ray Allen: 316/345 = 0.9136

Free throw percentage for Steve Nash: 308/339 = 0.9085

Free throw percentage for Troy Hudson: 208/231 = 0.9004

Free throw percentage for Reggie Miller: 207/230 = 0.90

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| |ACTIVITY 12: TERMINATE OR REPEAT |

Every fraction has a decimal equivalent that either terminates (for example, ¼=.25) or repeats (for example, 2/9=.2222222). Work with a group to discover which fractions have terminating decimals and which have repeating decimals. You may assume that the numerator of each fraction you consider is 1 and focus your attention on the denominator. As you complete the table below, you will find that the key to this question lies with the prime factorization of the denominator.

|FRACTION |DECIMAL FORM |TERMINATE? |PRIME FACTORIZATION OF DENOMINATOR |

|½ |0.5 |YES |2 |

|1/3 |0.33333...... |NO |3 |

|¼ |0.25 |YES |2 x 2 |

|1/5 |0.2 |YES |5 |

|1/6 |0.16666… |NO |2 x 3 |

|1/7 |0.1428571428571...... |NO |7 |

|1/8 |0.125 |YES |2 x 2x 2 |

|1/9 |0.111111111111....... |NO |3 x 3 |

|1/10 |0.1 |YES |2 x 5 |

|1/11 |0.090909......... |NO |11 |

|1/12 |0.08333333….. |NO |2x 2 x 3 |

State a general rule describing which fractions have decimal forms that terminate and

which have decimal forms that repeat.

We see that for terminating fractions, denominators are 2, 4, 5, 8, and 10.

We see that their prime factorization has 2 or 5 only.

We see that for repeating fractions, denominators are 3, 6, 7, 9, and 11.

These fractions have at least one prime factor other than 2 or 5.

So we can make a rule that the denominator of fraction which has 2 or 5 as prime factors only turn to terminating decimals. The denominator of fractions which has at least one prime factor other than 2 or 5 turn to repeating decimals.

Now test your rule on at least three new fractions. That is, be able to predict whether a fraction such as 1/25 or 1/30 has a terminating decimal or a repeating decimal. Then confirm your prediction.

Let us take fractions 1/25, 1/30, 1/19

 

1/25

Prime factorization of 25 = 5 x 5 

It has only 2 or 5 as factors so its decimal form is terminating decimal.

 

1/30

Prime factorization of 30 = 2 x 3 x 5 

It has 3 as a factor other than 2 or 5 so its decimal form is repeating decimal.

 

1/19 

Prime factorization of 19 = 19 

It has 19 as a factor other than 2 or 5 so its decimal form is repeating decimal.

SECTION 4.7

28: Write each of the following as a common fraction or mixed number. Write your answer in lowest terms.

15.35

We leave the 15 alone and work with the 0.35.

35/100

Divide denominator and numerator by 5 , we get

[pic]

So the answer is:

[pic]

30: Complete each of the following statements, using the symbol < or >.

[pic]

Converting 5/16 into decimal , we get 0.3125, so

Now, we see that 0.3125 < 0.313, so 5/16 < 0.313

34: Statistics. The following table gives the winning percentages of the top five coaches in NFL history. What fraction of his games has each coach won?

[pic]

We convert all the decimals to fractions

Coach Percentage

Don Shula 0.676 = 676/1000

Dividing numerator and denominator by 4, we get = 169/250

George Halas 0.672 = 672/1000

Dividing numerator and denominator by 8, we get = 84/125

Tom Landry 0.606 = 606/1000

Dividing numerator and denominator by 2, we get = 303/500

Curly Lambeau 0.624 = 624/1000

Dividing numerator and denominator by 8, we get = 78/125

Paul Brown 0.667 = 667/1000

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