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?
Solution:
Radius = 5/2 = 2.5 ft
Area of table = πr^2 = (3.14)*(2.5)^2 = 19.625 square foot
Cost of refinishing = 19.625*3 = $58.875
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?
Solution:
Area of triangular plate = (1/2)*base*height = (1/2)*30*20 = 300 square feet
Glass cost = 300*3 = $900
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?
Solution:
Circumference of tire = 2 πr = 2*(22/7)*14 = 88 in
1 miles = 63360 inch
100mi = XXXXXXX inch
Number of revolutions = XXXXXXX/88 = 72000 revolutions
Divide.
_______
0.52) 3.2318
We can write it as
6.215
___________
52)323.18
312
_________
111
104
_____
78
52
______
260
260
_______
0
Business and finance. Seven employees of an office donated a total of $172.06
during a charity drive. What was the average donation?
Solution:
Average donation = 172.06/7 = $24.58
Four brands of soap are available in a local store.
BRAND OUNCES TOTAL PRICE UNIT PRICE
Squeaky Clean 5.5 $0.36
Smell Fresh 7.5 0.41
Feel Nice 4.5 0.31
Look Bright 6.5 0.44
Compute the unit price and decide which brand is the best buy.
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
Brand Smell Fresh is best buy.
Statistics. The following table gives the wins and losses of all the teams in the
Western Division of the National Football Conference for a recent season. Determine the ratio of wins to total games played for every team, rounding to three decimal
points for each of the teams.
Team Wins Losses
San Francisco 10 6
St. Louis 7 9
Seattle 7 9
Arizona 5 11
The ratio of wins to total games played for San Francisco = 10/16 = 0.625
The ratio of wins to total games played for St. Louis = 7/16 = 0.4375 = 0.438(round to three decimal places)
The ratio of wins to total games played for Seattle = 7/16 = 0.4375 = 0.438(round to three decimal places)
The ratio of wins to total games played for Arizona = 5/16 = 0.3125 = 0.313(round to three decimal places)
Every fraction has a decimal equivalent that either terminates (for example, ) or
repeats (for example, ). 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 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 prime factorization of the denominator.
fraction | Decimal form | Terminating | prime factorization of the denominator |
1/2 | 0.5 | yes | 2 |
1/3 | 0.33333...... | No | 3 |
1/4 | 0.25 | yes | 2 x 2 |
1/5 | 0.2 | yes | 5 |
1/6 | 0.1666666666666666..... | No | 2 x 3 |
1/7 | 0.1428571428571...... | No | 7 |
1/8 | 0.125 | yes | 2 x 2 x 2 |
1/9 | 0.111111111111........ | No | 3 x 3 |
1/10 | 0.1 | Yes | 2 x 5 |
1/11 | 0.090909......... | No | 11 |
State a general rule describing which fractions have decimal forms that terminate and which have decimal forms that repeat.
The denominators of the fractions above whose decimal form terminates are 2, 4, 5, 8, and 10. Prime factorization of their denominators has 2 or 5 only. The denominators of the fractions above whose decimal form is repeating are 3, 6, 7, 9, and 11. These fractions have at least one prime factor other than 2 or 5. General rule: 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 or1/30 has a terminating decimal or a repeating decimal. Then confirm your prediction.
Let us take fractions 1/30, 1/20, 1/17
1/30
Prime factorization of 30 = 3 x 2 x 5
It has 3 as a factor other than 2 or 5 so its decimal form is repeating decimal.
1/20
Prime factorization of 20 = 2 x 2 x 5
It has only 2 or 5 as factors so its decimal form is terminating decimal.
1/17
Prime factorization of 17 = 17
It has 17 as a factor other than 2 or 5 so its decimal form is repeating decimal.
Write each of the following as a common fraction or mixed number. Write your answer in lowest terms.
15.35 = 15 and 35/100 = 15 and 7/20 OR 15 7/20
Complete each of the following statements, using the symbol < or >.
_ 0.313 INCOMPLETE QUESTION
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?
Convert all the decimals to fractions as shown below.
Coach Percentage
Don Shula 0.676 = 676/1000 = 169/250
George Halas 0.672 = 672/1000 = 84/125
Tom Landry 0.606 = 606/1000 = 303/500
Curly Lambeau 0.624 = 624/1000 = 78/125
XXXX XXXXX 0.667 = 667/1000
Please click ACCEPT. In case of any doubts please do ask.
Edited by Sandhya on January 8 2009 at 11:03 PM