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FOURTH GRADE / MATHEMATICS /SUBTRACTION of FRACTIONS 1.1

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

   WITH INCLUSION of FRACTIONS
 ♦ 
COUNTING BACKWARDS TENDS TO BE  ADDING END-TO-END, THE NEGATIVE ONE POINTING BACKWARDS, SUBTRACTION.
 ♦ HOWEVER BIG/SMALL THEY ARE, WE SHOULD BE ABLE TO SUM & SUBTRACT.

THERE ARE TWO GOLDEN RULES:
1. DENOMINATORS SHOULD BE EQUAL, OR EXPANDED/REDUCED AND MADE EQUAL.
2. THE MOST EFFICIENT WAY GOES THROUGH THE LEAST COMMON DENOMINATOR (LCD).
y
1. 1/3 - 1/5 = ?

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RY1 RY2



a) 2/5
b) 3/5
c) 2/15
d) 3/15


Just reminded you of the necessity of equal denominators, rest is known (the operations on numerator are already mastered ???).
y
2. 1/5 - 1/15 + 1/25 - 1/35 = ?

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

RY1 RY2



a) 105/525
b) 76/525
c) 51/525
d) 66/525
First make the additions, adding terms with positive and negative signs separately (and without mixing). Then subtract the second sum from the first.
If there are some cancelling, let them cancel; be carefull by the way !
3. What will be the positive difference of two fractions both having 1 at numerator and the greater and the smaller ones having respectively the greatest 2-digit even number and the least 3-digit number at denominators ?

a) 1/980
b) 9/4900
c) 2/4955
d) 9/4900
5/98 - 5/100 is being asked .
4. 1/2 - 1/3 + 1/4 - 1/5 + 1/6 = ?

a) 11/30
b) 5/12
c) 1/3
d) 23/60
Apply the method given in question 2..
5. Considering the the result of "1/2 - 2/3 + 3/4 - 4/5 = ?" , which of the followings is true ?

a) it is an odd number
b) it is an integer
c) it is less than zero
d) it is greater than zero
a and b are not likely .
6. 1 - 1/4 + 1/9 - 1/16 = ?

a) 115/16
b) 115/144
c) 11/12
d) 7/12
the common denominator is 144 .
7. Of a sack of sugar having 50 kg. first sold 1/20 ths and then an additional 3 kg. What will be the amount staying after these sales, in kg. ?

a) 44
b) 44 1/2
c) 45 1/4
d) 40 3/4
The first sale will be 2 1/2 kg .
8. A customer bought a pants off a fabric which should not shrink even a mm. according to the salesman, washed it and he observed that it shrinked by 1/10 ths. Then he brought the pants to a tailor and the tailor made an additional cut of 1/25 ths for hemming. Thus was an appropriate panths having a lenghth of 125 cm for the customer has been prepared.
What was the original length of the pants in cm.
Note: Do not use by the solution to this problem any of decimal fractions, please round not to have anything after the comma.

a) 144
b) 80
c) 150
d) 127
Only he choices a and c are plausible. Use trial and error method.
Before tailor pants should be 130 cm. (1/25 ths of it makes 5.2 cm but rounding makes 5 cm. )
If hte original length is 144 cm. it will shrink 14.4 cm but rounding will give 14 cm.
9. A long-distance heavy goods vehicle driver is to drive from Italy to Sweden and then to Spain. The first day of the trip he drove 1000 km.
He has driven to Spain, reducing his daily range by 1/25 ths each and every day due to tiredness, in 5 days.
How much was the subtotal distance he traveled during the 3rd day ?

a) 900
b) 915
c) 950
d) 922


The second day he drives 960 km. 960/25 = 192/5 = 384/10 .
10. What is the total distance traveled by the driver in question 9 ?

a) 4757
b) 4620
c) 3945
d) 5338
The first day he took 1000 km, the second day 960 km. , the third day 921.6 , the fourth day 884.736 and the fifth day 849.346 km.
Rounding we get respectively : 1000 , 960 , 923, 886 and 851 (or 1000 , 860 , 922 , 885 and 849) depending on the way we round) with a total of ... .
11. Which of the followings can be the graphics showing travel of question 9 ?

!
a) I
b) III
c) II
d) IV
If you solved the previous question explicitly, rounding or not rounding ... .
12. Which of the following figures may be the time-distance graphics of a biycler traveling 2000 km. in twenty days, reducing daily distance by 1/40 each and every day ?

!
a) II
b) III
c) I
d) IV
This is just like the previous question, to have fresh breathe .
13. Which of the following statements are true ?

I: Subtraction is like addition, denominators must be same.
II: The result of a subtrction may be a negative number .
III: By addition we can change the places of the operands without changing the places of their signs.
IV: By subtracttion we can change the places of the operands without changing the places of their signs.


a) I , II ve III
b) tümü
c) II ve III
d) II ve IV
By subtraction signs are an integral part of the operands.
14. Milk, if the temperature is 4 degrees C, is a food rapidly reproducing bacteria.
A definite quantity of milk is held at a temperature below 4 degrees C and meanwhile the amount of bacteria was reduced by 1/10 ths per hour for ten hours. Then it is held in ambient temperature above 4 degrees C for ten hours reproducing 1/10 ths of new bacteria in an hour .
What can be said about the number of bactereia in this sample of milk after this period of 20 hours ?

a) it as much as the original .
b) the number is reduced.
c) the number increases.
d) milk gets sour.
I have $ 100 and spend 1/10 ths. There stays $ 90. I gain 1/10 ths and I have $ 99 .
15. Which of the choices may represent the graphics of reduction mentioned in the previous question ?

!
a) IV
b) I
c) II
d) III
First decreasing for ten hours and then increasing and staying a little bit below ... .
16. Which of the following operations gives the minimal result ?

I :11/12 - 5/11 =?     II : 18/45 - 16/46=?      III : 4/6 - 2/7=?       IV : 16/23 - 8/24=?

a) I
b) II
c) IV
d) III
In which case are the operands nearest to each other ?
17. A car traveling with 100 km/h brakes and reduces its speed by a rate of 1/10 ths per milliseconds till it stops.
What should be the car's speed in km/hours, 2 ms. after braking ?

!
a) 90
b) 910/10
c) 819/10
d) 847/9
After the first ms. the speed is 90 km./hours which is reduced by 91/10 km./hours in the second ms.
18. The bus had an accident and 2/5 ths of the pasengers took a cab and went their workplace. 1/3 rds of the remaining passengers preferred traveling further by metro and 1/3 rds of the rest then called their buddies to take them.
What is the fraction of passengers still waiting around the bus ?

!
a) 8/17
b) 22/59
c) 8/15
d) 4/15
The normal way of solving is prone to errors if not done with care.
60 is really a good number which is evenly divisible by many of its preliminaries, try using it as the denominator.
If tere originally were 60 passengers 24 got a cab, there remained 36.
12 got metro and there remained 24.
8 of them made a call and ... and the fraction of remainings is 16/60
Reduce 16/60 to simplest form and ... .
19. 95/65 - 12/130 = ?

a) 89/65
b) 49/65
c) 77/65
d) 17/47
First reduce the subtrahend, only the subtrahend .
20. 2 27/18 - 1 17/9 = ?

a) 17/18
b) 1/2
c) 11/18
d) 4/9
It is equal to 1+27/18-17/9 = 1+(27-34)/18 .
21. Which of the followings should be true if 10/150 = A/30 - 5/30 is valid ?

a) A=2
b) A=7
c) A=5
d) A=9
10/150 is equivalent to 1/15 .
y
22. An analog of Zeno's Paradox (the original paradox has been expressed first by a Greek philosopher named Zeno, around 400 B.C.):
Rabbit and Turtle are to compete, the rabbit has ten times the speed of the turtle and the distance of the race is 1000 m.
The turtle demands an head start and gets 900 m. of it because the rabbit is extremely self confident. Guns explode and the race begins:
When the rabbit runs the 900 m. head start, the turtle is 90 m. ahead; when rabbit runs this 90 m. the turtle is 9 m. ahead; when rabbit runs this 9 m. the turtle is 90 cm. ahead an so on when rabbit runs the distance between them the turtle is 1/10 ths of this distance ahead and the rabbit can never catch up.

What is faulty with the thinking above ?


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

RY1 RY2



a) The distance between turtle and the rabbit is not always positive during the race.
b) Thinking is pretty fast but faulty infinite loops take time whereas events continue with their pace.
c) The reality that the rabbit is ten times as swift is ignored .
d) The race did not begin simultaneously.


Time does not stop as we are in infinite loops.
23. Which of the followings gives the minimal result ?

a) 25/110 - 15/105
b) 22/157 - 13/110
c) 23/159 - 11/145
d) 10/39 - 1/100
Choice d must be around 0.25 .
24. What should A be if A - A/2 = 105 is valid ?

a) 25
b) 105
c) 55
d) 52 1/2
Naturally the other half .
25. 1/999 - 1/1000 = ?

a) 1/999000
b) 1/9990000
c) 1/90009
d) 1/900009
(1000 - 999)/... .
This is the feedback!

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