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FOURTH GRADE / MATHEMATICS / FRACTIONS 1.3

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. A wholesaler has in the warehouse 480 sacks of sugar each being 50 kg. of weight. On March 3, first 5/480 ths, a while after 1/95 ths of the remainings and till the end of the day 3/47 ths of the rest has been sold.
What will be the gain of this sale in dollars, if the price per kg. is $ 2.00 and the fractional profit is 1/20 ?

a) 250
b) 100
c) 200
d) 115
First sold 5 sacks, then another 5 and then ... .
2. Yaman, Metin, Çetin and Doğan are friends from the eastern Black-Sea coast of Turkey where hazelnuts are grown. They went nutting on August 8, 9 and 10 with some other people and their rate of nutting is given in the figure below .



What is the total rate of Yaman's friends ?

a) 1/2
b) 51/130
c) 145/325
d) 120/420
The rate of Yaman's friends, not including Yaman, is being asked !
3. How will 1/7 , 1/5 , 1/8 , 7/14 and 3/9 be ordered from greatest to least ?

a) 1/5 , 1/7 , 1/8 , 3/9 , 7/14
b) 1/5 , 1/7 , 1/8 , 7/14 , 3/9
c) 7/14 , 1/5 , 1/7 , 1/8 , 3/9
d) 7/14 , 3/9 , 1/5 , 1/7 , 1/8
Reduce 7/14 and 3/9 .
4. It is desired to have a ratio of 1/2 between the green and yellow areas. How many of the white rectangles should in addition be made green ?



a) 5
b) 4
c) 6
d) 3
The number of yellow colored rectangles is 24 .
5. What is the name of multipliying both the numerator and the denominator of a fraction with the same number ?

a) Multiplication
b) Expansion
c) Extension
d) Reduction
Reduction is done via division .
6. Which fraction differs ?

a) 31/64
b) 29/64
c) 62/128
d) 341/704
choose between b and d .
7. What is the sum of the two fractions represented in the figure below ?



a) 19/66
b) 7/55
c) 1/3
d) 27/55
Determine first the two fractions or try to create a common denominator .
8. Which is the simplest, completely reduced, version of 20/60 ?

a) 1/5
b) 2/30
c) 1/3
d) 1/6
A much simpler form is 2/6 .
9. Which of the fractions below are between 1/5 and 1/4 ?

a) 3/10 and 15/80
b) 17/80 and 9/40
c) 7/11 and 15/27
d) 13/14 and 4/9
Try 80 as the common denominator and see the situation for the first two choices. The other choices are all more than a half.
10. 1/6 ths of 5/6 ths of a number is added to 5/6 ths of the same number. What will this sum to the original number ratio be ?

a) 1
b) greater than 1
c) less than 1
d) 9/10
Take 1 as the number . 5/6 + 5/36 = ...
y
11. Blue rectangle in the figure is shifted right such that its first scale line coincided with 15 mm. line of the black figure and so is the red figure created.
How long should the distance between the first line of the black figure and the last of the red be (mm.) ?


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

RY1 RY2



a) 225/9
b) 215/9
c) 230/9
d) 220/9
Calipers and slide rules use the same principle .
12. Which one is the number that will be equal to 1/4 ths of 48 when the number 6 is added to its (original nu.'s) 1/5 ths ?

a) 12
b) 36
c) 24
d) 30
1/4 ths of 48 is 12 .
13. A clock delays 1/2 seconds in 6 hours. How many seconds will its weakly delay be ?

a) 84
b) 82
c) 56
d) 14
A week has 168 hours but use rather that the daily delay will be 2 seconds ... .
14. 2/5 ths of our class get folklore and 5/9 ths get music course as option
What is the fraction of pupils/students in our class getting (at least) one of these courses and how many pupils/students are there in our class ?

a) 43/44 ; 48
b) 43
c) 43/45 , undetermined
d) 43/45 , 45
The number of students of the class can not be determined only with the help of ratios . Depending on the type of the class the number may be 45, 90, 135 etc. Another clue might help us to decide.
15. Seen in the figure below is a vernier caliper that can be used to obtain interpolated measurements to 1/10 mm or better.
These calipers comprise a calibrated scale with a fixed jaw (the region with 12 , 13, 14, 15 cm on), and another jaw (relatively darker lower region with 0, 1, 2, ... mm) with a pointer that slides along the scale.
On relativeley dark region there are 50 equidistant intervals (between 0 and 0) corresponding to .... mm.s of the upper fixed jaw .



a) 15
b) 25
c) 35
d) 49
4 cm. and ... .
16. What will 1/(1/5) ths of the fraction 1/8 be ?

a) 1/8
b) 1/40
c) 1/60
d) 5/8
If 1/5 ths of 1/8 were asked the answer would be 1/40 ! 1/(1/5) is 5 because there are 5 times 1/5 in 1.
17. Which choice gives the number whose 3/5 ths' half makes 189 ?

a) 666
b) 712
c) 630
d) 649
3/5 ths of the number should be 378 .
18. To an appointment Ahmet came 1/3 hours too early and Nesrin came 1/6 hours too late.
How long (in minutes) should Ahmet have waited for Nesrin in this case ?

a) 10
b) 30
c) 20
d) 25
1/3 + 1/6 hours = ? minutes
19. How many guestion answers a student, who answered 30 questions in 3/4 hours, in 15 minutes ?

a) 10
b) 15
c) 8
d) 20
3/4 hours contains 15 thrice .
20. Farmer Smith got a yield of 3.5 tons and sold 1/7 of it for $ 1/2 per kg. , 2/7 of it for $ 0.55 per kg. and 4/7 of it for $ 0.60 per kg. How much money got Mr. Smith for the whole yield (in dollars) ?

a) 200
b) 800
c) 1500
d) 2000
3 sales of resoectively 500 kg. , 1000 kg. ve 2000 kg.
21. What is the ratio of the total green area to the total purple area ?



a) 3/2
b) 2
c) 5/2
d) 4/3
Total green area is obviously greater tahn ... .
22. What should replace the question mark in the figure below ?



a) 1/9
b) 9
c) nothing, it should stay
d) 1/6
The division is defined for numbers not for figures !
23. Mrs. Rosenbaum had $ 2 400 and spent first 1/4 ths of it, then 5/9 ths of the rest. How much money stayed back ?

a) 800
b) 100
c) 600
d) 800
After first expense she still has $ 1800 .
24. A vendor bought 200 eggs for $ 50 and 10 of them got broken during transport. How much a sale price should he set per egg if he wants a total gain of $ 19 ?

a) 33/100
b) 7/20
c) 35
d) 7/15
He must gain 10 cents per egg .
25. The figures are regular hexagons. What is the ratio of the areas of the green and blue regions within the red hexagon ?



a) 3
b) 5/3
c) 7/2
d) 4
There are ... equilateral triangles in the blue region as there are 42 in green.
This is the feedback!
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