Common fraction or mixed number of the following
Common fraction or mixed number of the following
4.0171
Solution:
As a fraction
[pic]
As a mixed number
[pic]
Arrange in order from smallest to largest.
2.05, 25/10, 2.0513, 2.059, 251/100, 2.0515, 2.052, 2.051
Solution:
25/10 = 2.5
251/100 = 2.51
Now arrange from smallest to largest
2.05, 2.051, 2.0513, 2.0515, 2.052, 2.059, 25/10, 251/100
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?
Solution:
The correct answer is 76.24 because we should directly round off to nearest hundredth place instead of using Lula’s approach. She rounded twice to get the answer.
Add thirty-eight and nine tenths, five and fifty-eight hundredths, seven, and fifteen
and eight tenths.
Solution:
38.9 + 5.58 + 7 + 15.8 = 67.28 = [pic]
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?
Solution:
Pay received = 40*6.4 + 8.5*9.6 = $337.60
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?
Solution:
Interest = 1458*0.125 = $182.25
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?
Solution:
Total time for one bottle = 0.5 + 0.1 = 0.6
2h = 2*60*60 = 7200
Number of bottles filled = 7200/0.6 = 12000 bottles
Answer: 12000 bottles
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:
Area = [pic] square foot
Total cost = 19.625*3 = $58.875
Crafts. Andy is carpeting a recreation room 18 ft long and 12 ft wide. If the
carpeting costs $15 per square yard, what will be the total cost of the carpet?
Solution:
Convert feet to yards
18 ft = 6 yards
12 ft = 4 yards
Area of room = 6*4 = 24 square yards
Total cost = 24*15 = $360
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:
First we will find the circumference of the tire
Circumference = 2πr = 2*(22/7)*14 = 88 inches
This means that distance travelled by car in one revolution is 88 inches.
Now, Convert miles to inches by multiplying by 63360.
100 miles = 6336,000 feet
Number of revolutions = 6336,000 /88 = 72000 revolutions
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.
Player FTM FTA
Allan Houston 363 395
Ray Allen 316 345
Steve Nash 308 339
Troy Hudson 208 231
Reggie Miller 207 230
Solution:
Allan Houston: 363/395 = 0.919
Ray Allen: 316/345 = 0.916
Steve Nash: 308/339 = 0.909
Troy Hudson: 208/231 = 0.900
Reggie miller: 207/230 = 0.900
Every fraction has a decimal equivalent that either terminates (for example,1/4 = 0.25 ) or
repeats (for example,2/9 =0.2 ). 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.
Fraction Decimal Form Terminate? Prime Factorization of the Denominator
½ 0.5 yes 2
1/3 0.3333… No 3
¼ 0.25 Yes 2*2
1/5 0.20 Yes 5
1/6 0.1666… No 2*3
1/7 0.142857142857... No 7
1/8 0.125 YES 2*2*2
1/9 0.111…… No 3*3
1/10 0.1 Yes 2*5
1/11 0.09090…. No 11
1/12 0.08333…. No 2*2*3
State a general rule describing which fractions have decimal forms that terminate and
which have decimal forms that repeat.
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.
Solution:
General rule:
The fractions having any number other than 2 and 5 in the prime factorization of denominator does not terminate.
Let us take 1/13, 1/20 and 1/15
My prediction is:
1/13 will not terminate.
1/20 will terminate.
1/15 will not terminate.
Let us divide 1/13 = 0.0769230…………., 1/20 = 0.05, 1/15 = 0.066….
Thus, my prediction was correct.
A common fraction or mixed number. Write your answer in
lowest terms.
15.35 = [pic]
Complete each of the following statements, using the symbol < or >
30. 5/16 symbol square in the middle 0.313
5/16 < 0.313
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?
Coach Percentage
Don Shula 0.676
George Halas 0.672
Tom Landry 0.606
Curly Lambeau 0.624
Paul Brown 0.667
Solution:
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
Paul Brown 0.667 = 667/1000
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