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FOURTH GRADE / MATHEMATICS / FRACTIONS 1.1

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

  FRACTIONS are

   ♦ 
OUR GATEWAY FROM DISCRETE TO CONTINIOUS
   ♦ which PERMIT US TO GET ALMOST a FULL NUMBER LINE;


 without which WE WOULD NEED a CHANGE of UNITS EVERY NOW and THEN.

    Ref.-1
 
1. What is the sum of numerators of fractions formed by blue and red regions ?



a) 2
b) 10
c) 2/3
d) 10/15
Numerator is a natural number.
Unit is the great rectangle that is divided into 15 pieces .
Unit fractions are the colored (for differentiation, not disturbing equality) small rectangles.
2. Accepting the totality of all circles on yellow background a unit, what is the fraction formed by the red circles ?



a) 12/37
b) 12/39
c) 12/41
d) 12/42
To determine the denominator we need to count all of the circles ! 4 of the groups contain 7 circles (circular regions).
3. Referring to the figure below, which of the followings is true ?



a) The red numbers below the circles are reductions.
b) Top to bottom script at the right is to conduct that it is not possible to evaluate the sum of fractions unless the denominators are equal. The fractions shold be expanded if necessary.
c) In the middle row the equality 1/2 + 1/3 = 5/6 is right but the figure does not correpond to this equality .
d) In the lowest part it is not possible to see that 1/2 and 3/6 are equivalent fractions .
Reduction is the division of both the numerator and the denominator by the same number .
4. What is the value of p that makes (p/15) hours = 24 minutes a valid equality ?

a) 5
b) 4
c) 6
d) 3
Make the minutes the common units at both sides to get (p/15)x60=24 .
5. The multicolored figure on sky blue background is a square of unit area. Each colered region is attained by division by 2.

What should the area of white region be ?



a) 1/4
b) 1/16
c) 1/128
d) 1/256
The white and purple areas are equal .
6. Referring to the figure in question 5, what will be the remaining area if the total area of purple and blue regions is subtracted from the area of red region ?

a) 31/64
b) 29/64
c) 63/128
d) 61/128
Area of the red region is 64/128 units .
7. By consecutively dividing 1 by 2 the numbers 1/2 , 1/4 , ... , 1/16384 are obtained. Which fraction we could get by adding/subtracting these numbers will be closest to the fraction 7/357 ?

a) 1/256 + 1/16384
b) 1/64 + 1/256
c) 1/256 + 1/32768
d) 1/256
7/357 = 1/51.
8. How closely can we approximate any fraction by using the additions of the elements of the sequence 1 , 1/2 , 1/4 , ... , 1/64256 , ... ?

a) as close as the reductions of 1/2
b) as close as we want
c) 1/1 000 000 close
d) 1/1 000 close
reductions of 1/2 is not well defined.
y
9. What is the ratio of the area of green colored region to the red colored ?

Note: The octagon is regular and the green triangle is isosceles triangle .


In case you need help or tips get the mouse on "y" or click on "ry1/2" .

RY1 RY2



a) 1/3
b) 1/2
c) 2/3
d) 3/5
Look at the page : "http://wiki.zum.de/Mathematik-digital/Bruchteile_bestimmen" !
10. Which of the fractions is the greatest among 3/7 , 5/9 , 7/11 , 9/13 , 11/15 ?

a) 3/7
b) 11/15
c) 7/11
d) 13/14
Usually denominators should be the same for comparison ....
But in this case tthe numerator and the denominator are being increased by the same amount (2) and the one with the greatest numerator will be ... .
11. Which of the followings should replace queastion mark ?



a) >
b) =
c) <
d) = or >
1/3 + 1 = 4/3 and 1/2 + 1 = 3/2
4/3 < 3/2 .
12. What will be the result of (2/3 - 5/12) x (4/7 + 3/21) ?

a) 3/7
b) 7/36
c) 5/28
d) 3/17
2/3 = 8/12 ve 4/7 = 12/21 i.e. 3/12 x 15/21 .
13. A retiree has traveled every day in August to Anadolu Kavagi. He did 12 of his voyages by ship and 19 by bus.
What is the fraction of ship trips in total trips for this case ?

a) 12/19
b) 12/30
c) 12/31
d) 19/12
simple q. .
14. We mostly have 20 baby teeth and 32 normal teeth in our life. 4 of our normal teeth are wisdom teeth or third molars.
What rounded to the nearest ten percentage have our wisdom teeth in our normal teeth ?

a) 12.5
b) 63
c) 12
d) 13
4/32 = x/100 . Should be rounded to the nearest ten !
15. What should be the value of A if A/5 = 3/100 is valid ?

a) 15%
b) %15
c) 15
d) 15/100
Since the denominator is 100 we only need to multiply both sides by 5 .
16. Light from the Sun arrives to the World in 8 minutes whereas the reflected light by the moon arrives in a second.
What should be the ratio of distances ?



a) 1/8
b) 1/360
c) 1/60
d) 1/480
8 minutes are 480 seconds .
17. In case of mixed numbers we can first add the integers and then the (remaining) fractions. As an example calculate 5 + 3/5 + 7 + 4/7 .
Which result have you found ?

a) 13 + 6/35
b) 13 + 1/7
c) 13 + 4/35
d) 13 + 1/5
When we add fractions we get 41/35, an improper fraction. As a mixed number it is 1 + 6/35 .
18. What is the sum of all digits A and B for which A/B = 1/2 is valid ?

a) 10
b) 18
c) 20
d) 30
The sum of the natural numbers from 1 to 4 is 10 .
19. In case of same denominators the numerators can be added and the denominator is written as the denominator of the addition.A similar behavior for the case of numerators being the same may very rarely give the correct result.
What is the reason of this asymmetrical behavior ?

a) If number of divisions were written up and the taken parts were written down, the second would also yield correct results.
b) It is a result of our definitions.
c) The question is not a valid question.
d) For equality of fractions numerators and denominators should both be equal.
Numerator could be defined to be writen below the division sign but both way correct results can not be attained.
20. Half of 7.8 tons of hazelnuts is sold in January. One third of the remaining is sold in March.
What will be the remaining amount after the second sale ?



a) 2.6
b) 5.2
c) 1.3
d) 2.5
There remains 3.9 tons after the first sale.
21. Ali walked half a quarter of the road. The distance she walked is 440 m. less than twice the whole of the road.
How long should the length of the whole road be ?

a) 234 2/3
b) 251.42
c) 251.42 m.
d) 234 2/3 m.
The equality y/8 = 2 . y - 440 is valid .
22. Alper, Ali and Omar brought a pack of nuts with them as they go to scout camp. At night they entered their tents and began to sleep. During the night first Alper got up and ate 1/4 of the nuts; then Ali got up and ate 1/4 of remains. Lastly Omar got up and he ate half of the remains. In the morning they shared the remaining nuts equally and each got 27 hazelnuts.
How many hazelnuts were there in the pack as they brought it to the camp ?



a) 288
b) 162
c) 256
d) 340
Let the original number of nuts be F.
Alper ate F/4 and there remains 3F/4 .
Ali ate 3F/16 .
What is the total amount they ate and what remained ? .
23. One worker finishes a job in 5 hours and another does it in 6 hours.
How long will the job take if they work together ?



a) 3
b) 2.5
c) 18/7
d) 30/11
The image gives clue. If a worker finishes the job in 6 hours, in one hour he makes 1/6 of it .
For two workers add 1/6 and 1/5 which makes 11/39 and this is the part of the job done in an hour.
24. Penny ate 1/3 of its food the first day and ate the 1/6 of the remains the second day. For the third day there remained 420 g. of food.
What was the original weight of the food ?

a) 303
b) 900
c) 800
d) 756
The equation m - m/3 - m/18 = 420 should be valid .
25. A certain amount of money is to be shared among 25 persons. 5 of them wanted no share and the remaining 20 has gotten $ 500 more because of this will.
How many dollars was the original amount of money to be shared ?

a) 50000
b) 90000
c) 18000
d) 30000
1/5 th of the money should be $ 10 000 .
This is the feedback!
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