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FIFTH GRADE / DECIMAL FRACTIONS, PERCENT and RATIO / TEST 1.2

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

FRACTION'S UTILITIES

FAST DAS SELBE AUF DEUTSCH
  AS WE HAVE NOTED EARLIER
 ♦ 
MULTIPLICATION IS REPEATED SUMMATION  MODELED COMPACTLY IN TWO DIMENSIONS
 ♦ SO IT IS (PSEUDO) TWO DIMENSIONAL.

THERE ARE TWO GOLDEN RULES:
1. NUMERATORS ARE MULTIPLIED, USED AS THE RESULT'S.
2. DENOMINATORS ARE MULTIPLIED, USED AS THE RESULT'S.
1. The ratio sen in the figure below indicates the ratio of width to height of standard-definition television. What is the ratio of this to the Golden Ratio if both are considered up to the 3rd place after the point ?

!


a) 1.003
b) 0.553
c) 0.823
d) 1.107
Take Golden Ratio as 1.618 . So 1.333/1.618 = ? and this may be seen as 1.333/1.618 x 1000/1000 .
2. The Golden Ratio is 1.618. What will be the height of Mona Lisa if width is 10 cm. ?

!


a) 10 cm.
b) 26.18 cm.
c) 16.18 cm.
d) 6.18 cm.
The ratio is Golden Ratio .
3. What is the ratio of the months of a year to the days of a year ?

a) 12/365
b) 16/487
c) 11/135
d) 4/121
Do not forget the leap years.
4. What is the ratio of (n+1)th Fibonacci Number to the (n-1)th if n is greater than 1000 ?

a) 2.739
b) 2.447
c) 2.617
d) 2.501
Around this big an n two consecutive Fibonaccis should give Golden Ratio which is 1.618 .
5. What is the ratio of the Moon-to-Earth distance to the radius of the Earth ?

a) 60.345
b) 60.459
c) 61.728
d) 57.327
384 400/6 370 = ?
y
6. How many cm. is the image height I ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) 1.618
b) 2
c) 1
d) 2.618


Look at ry1 please .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. The so-far unnamed waterway through the Bosphorus would be the world's sixth largest river in terms of the amount of water flowing through it if it were on ground. Dr Parsons from Leeds University found that the Black Sea river is flowing at around four miles per hour with 22,000 cubic metres of water passing through the channel every second.
What is the ratio of Danube's flow to this underwater river's flow ?

!


a) 0.0295
b) 0.2934
c) 2.954
d) 0.2954
6500/22000 = 65/220 = 13/44 = ... .
8. The Black Sea river is flowing at around four miles per hour. A mile is 1.609 kilometers. How many m/s is the speed of the underwater river ?

!


a) 1.051
b) 1.787
c) 1.349
d) 1.877
4 x 1 609 / 3600 = ?
9. If the flow of the underwater river in Bosphorus were completely converted to energy it would be 1/2 x 22 000 000 x 1.797x 1.797 Watts = 11 x 3.193 MWatts where M stays for a million.
If Niagara Falls were used to obtain energy, without any loss at all, they would roughly produce 2 000 000 x 50 x 10 Watts = 1000 MWatts .
What is the smaller to bigger ratio if an accuracy of 3 digits after the point is enough ?

!


a) 0.035
b) 0.0035
c) 0.35
d) 1.35
11 x 3.193 / 1000 .
10. As you see in the previous question the (kinetic) energy of a mass increases proportionally with the the square of velocity. What would be the new to old energies' ratio if the velocity of the underground river were to double ?

a) 8
b) 4
c) 2
d) 1
The flow is steady. Power is the energy per unit time and it is exactly that we calculate. Power and enrgy ratios will not change since flow is steady. If velocity doubles it s square ...
11. The World's largest dam, the Three Gorges Dam is supposed to produce a power of 22 500 MWatts. Assuming that the Bosphorus has a potential capacity of 35 MWatts, what would be the decimal ratio of this power to the power of Three Gorges considered up to the fourth digit after the point ?

!


a) 0.15
b) 0.0015
c) 1.15
d) 1.5
35/22 500 = 7/4 500 . Calculate 7/45 and make two left point shifts.
y
12. Which of the choices may be the height of the dam ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 180 m.
b) 220 m.
c) 195 m.
d) 155 m.
Have please a look at ry1 .
13. The world’s population is now more than 7 billion and continues to grow by 82 million people per year. What is the increase in percent (nowadays) ?

a) 1.221
b) 1.71
c) 1.117
d) 1.171
82 000 000 / 7 000 000 000 = 82 / 7000. Percent means make the denominator 100 by reducing/expanding the fraction and take the numerator. (82 x 1/70)/7000 x 1/70 is equal to (82/70)/100, so 82/70 is the answer to ...
14. During the last half-century, the world’s population more than doubled. Between 1960 and 2010, the world population rose from 3 billion to 6.8 billion. What is the increase in percent ?

a) 126.444
b) 166.666
c) 155.666
d) 116.666


The net increase is 6.8-3.3 = 3.5. To find the in percent increase 3.5/3 = 3.5 x (100/3)/3 x (100/3) which ipmlies the desired number is 3.5 x (100/3).
15. Between 2010 and 2011, the U.S. population increased by 0.7 percent. In other words the United States added just 2.3 million people from 2010 to 2011. What should be the population at the beginning of 2010 ?

a) 318 571 428
b) 328 571 428
c) 328 511 428
d) 336 571 428
(7/1000)x P = (0.007)xP = 2.3 million, i.e. P = 2 300 000/0.007 = 2 300 000 000/7 .
16. A cyclist took 2 000 km. , driving each day the same amount of distance, in 30 days. Which percent of the total should he have driven in a day ?

!
a) 0.222
b) 3.333
c) 3.3
d) 0.444
1/30 = ?/100 should be answered. Try to make the denominator 100 by multiplying both the denominator and numerator by 100/30 .
17. Between 2010 and 2011, the U.S. population increased by 0.7 percent, after averaging 0.9 percent growth each year from 2000 through 2010. What is the in percent increase of population within the first decade of the third millenium ?

Note: 1.009 x 1.009 x 1.008 = 1.027 ; 1.027 x 1.027 x 1.027 = 1.083

a) 9.2
b) 9.8
c) 8.8
d) 8.6
You just need to calculate 1.083 x 1.009, subtract 1 from the result you obtain and ... .
y
18. The world's population has a yearly increase rate of 1.2% . In how many years is it to double with this rate of increase ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 75
b) 57
c) 51
d) 47
Please look at ry1 and then ry2.
19. Every year, circa 11 cubic kilometres of water flow into the Okavango delta in Botswana. Approximately 60% is consumed through transpiration by plants, 36% by evaporation, 2% percolates into the aquifer system; and 2% flows into Lake Ngami. How many liters flow into lake ?

!


a) 2 200 000 000 000
b) 220 000 000 000
c) 22 000 000 000
d) 222 000 000 000
(11 000 000 000 000/100)x2 litres
20. A 2006 estimate by the World Conservation Union puts the number of lions left on the entire African continent at 23 000 to 39 000, down from a 1975 report of 200 000. What is the average in percent decrease ?

a) 83.5
b) 83.9
c) 85.5
d) 86.1
(23 + 39)/2 = 31. Take half of it to make life easy. So every group of 100 lions decreased to 31/2 = 16.5 ...
21. A recent study has stated that large mammals like buffalo and lions in African game parks have decreased by 59 percent from 1970 to 2005. What would be the number of 200 000 lions after such a decrease ?

a) 77 000
b) 80 000
c) 82 000
d) 83 000
Just to remind you of the fact that something is not natural. We always thought the number of prey would increase in case of less hunter . There must be something behind it.
y
22. Population increases in developed countries at a rate of 1.5% and in developing countries at 2.5%. What will be the ratio of two initially equal number groups in 10 years, the in developed to the in developing ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 8/11
b) 8/10
c) 7/10
d) 9/10


Have please a look at ry1. We derived the formula mentioned in:http://www.test-dr.com/education/5th-Grade-Mathematics/multiplication-of-fractions-5.1.2.html Question 18
23. 325 27/108 = ?

a) 325.25
b) 32.25
c) 32.35
d) 335.35
Find the decimal equivalent of 27/108 = 1/4 = ...
24. 1+ 1/2 + 1/3 + 1/4 = ?

a) 2.06
b) 2.083
c) 2.08
d) 2.063
1 + 3/4 + 1/3 = 7/4 + 1/3 = 25/12 =
25. 54.07 x 54.007 = ?

a) 292.15849
b) 298.15849
c) 292.35849
d) 288.15849
(54 + 0.07)x(54 + 0.007) = 54x54 + 0.077x54 + 0.07x0.007 = 2916 + 4.158 + 0.00049 = ?
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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