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FIFTH GRADE / SUBTRACTION of FRACTIONS / 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.

FRACTIONS' UTILITIES
   WITH INCLUSION of FRACTIONS
 ♦ 
COUNTING FORWARD TENDS TO BE  ADDING END-TO-END, SUMMING.
 ♦ HOWEVER BIG/SMALL THEY ARE, WE SHOULD BE ABLE TO SUM.

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).
1. 76/525 + 1/45 - 1/55 = ?

a) 2578/17325
b) 5521/17325
c) 184/17325
d) 7641/17325
Common denominator of last 2 is 495; find first the difference of these.
LCM of 495 and 525 is 17325. Use Fractions' Utilities if you wish .
33x76=2508 .
2. (1/3 + 3/4) - 1/3 = ?

a) 3/4
b) 4/3
c) 1/5
d) 4/9
Paranthesis are normally to be calculated first but here is no need for any calculation. Paranthesis are to make sight harder .
3. (1/2 - 2/3) - (3/4 - 4/5) = ?

a) 7/60
b) -7/60
c) 14/41
d) -14/41
Now apply the rule: First paranthesis, the structure is so constructed.
4. (1/2 - 2/3) + (3/4 - 4/5) = ?

a) -13/60
b) 13/60
c) 7/50
d) -7/50
First paranth... That is why we use them.
5. A cycler traveling from Lausanne to Paris traveled 2/17, 2/15 and 1/7 of the way in the first three days. What is the remaining fractional part ?

!
a) 987/1785
b) 1082/1785
c) 647/1795
d) 1111/1785
1 - 2/17 - 2/15 - 1/7 = ?
y
6. 1/48 - 12/720 = ?

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



a) 1/120
b) 1/60
c) 1/240
d) 1/30


12/720 has even numbers in num. and denom. It should be reduced.
The most efficient way of reducing fractions is to find GCD.
How is GCD to be found is shown in ry1. After you get experienced, you may use fractions' utilities. In this case it is 12.
The second step is to get equal denominators in all fractions taking part in addition/subtraction. To this end LCM is needed.
How is LCM to be found is shown in ry2.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which result is obtained if the operation defined below in the figure is performed with the numbers given in the figure ?

!


a) -21/89
b) 21/89
c) -7/60
d) 7/60
Just place the numbers into their correct places .
We want you to get acquainted with the matrices via this simple operation .
8. The graphics below indicates per capita water usage in London between 2000-2005 .
Green lines are actual usage and black line indicates trend.
What is the fractional change of usage between 2000 and 2005 ?

!


a) 5/65
b) 3/65
c) 7/85
d) 1/65
(260 - 248)/260 = ?
9. What will be the fractional difference of greeen regions of III and II ?

!


a) 1/16
b) 1/8
c) 3/22
d) 5/17


Neglect the upper half and divide the result you obtained by 2 .
10. 12 1/5 - (17 3/4 - 10 1/5) = ?

a) 83/20
b) 87/20
c) 93/20
d) 97/20
Sum of positive terms: 22 2/5 .
11. The employees of a residential moving firm in the final stage of transporting a home gave a break after doing 1/4 ths of the final work. Then they finished 5/9 ths of the work till noon and they left for meal. What fractional part of the work do they still have to do after noon ?

!
a) 5/36
b) 7/36
c) 7/18
d) 5/18
1 - 1/4 - 5/9 = ?
y
12. 2/945 - 7/1680 = ?

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

RY1 RY2



a) 37/15120
b) -17/15120
c) 21/15120
d) -31/15120
It is not posssible to reduce 2/945; try if 1680 = 700 + 700 + 280 is divisible by 7 .
Finding the GCD of 7 and 1680 is in ry1 and finding LCM is in ry2. Just as an exmple .
13. A seat multiplex is divided into 3 theatres. The 27/80 of the seats are in Theatre 1, and there are as many as 15/80 of the total number of seats more seats in Theatre 2 than in Theatre 3. What is the fractional difference of the seats in Theatre 2 and Theatre 3 ?

!


a) 31/80
b) 21/80
c) 15/80
d) 17/40
Take the simplest case of 80 seats. In Theatre 2 and 3 there should be 53 seats. 53/2 = 26 1/2 .
There should be 15 more in T-2 which means 26 1/2 - 7 1/2 = 19 seats in T-3. And of course 34 in T-2 .
14. Terry goes to shopping mall with $500. He buys PSP for his son and then he buys a toy for his daughter for half the price of PSP. Then he spends 1/10 ths of money's rest on food, leaving him with $270. How much ($) is the price of PSP more than the toy in comparison to $500 ?

!


a) 3/5
b) 1/5
c) 1 1/3
d) 2/3
Before food he must have $300. Let the price of PSP be P, (1+1/2)xP should be $200
15. The sum of 1 - 36/A is desired to be an integer. How many A (natural number) values are possible ?

a) 9
b) 6
c) 4
d) 3
A-36 should be divisible by A. 1 is an integer which means 36/A should be an integer. 36 is divisible by A if A=1, ...
16. The question is below in the figure .

!


a) 2
b) 4
c) 3
d) 5/3
Each element of the numerator is twice the corresponding element in the denominator .
17. 1/2 - 3/(4x5) + 6/(7x8) - 9/(10x11) = ? ?

a) 323/385
b) 144/175
c) 71/98
d) 289/770
1/2 - 3/20 + 3/28 - 9/110 = (110-33-18)/220 + 3/28 = 59/220 + 3/28...
y
18. The ratio of weights of two children is 3/4 and the difference of weigths is 3 kg. What is the fractional weight of the heavier child ?

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


a) 12/21
b) 11/22
c) 13/23
d) 11/23
Informal solution: Posssbile weights are 3 and 4 , 6 and 8 , 9 and 12 , 12 and 16 ... Third is O.K.
For the formal solution have a look at ry1.
19. From a bucket whose 3/5 is full of water 3 l. is taken. The bucket is then half full. How many liters is the full size of the bucket ?

a) 15
b) 24
c) 30
d) 27
3/5 - 1/2 = 1/10 .
20. Jane's allowance is 5/6 ths of Janet's. Janet saves 1/12 of her allowance and Jane saves 1/C of hers. After a year they see that the difference of their allowances is zero. What should then C be ?

a) 10
b) 12
c) 13
d) 15
Let Janet's allowance be AJ and Janet's AT. AJ/AT = 5/6. What is true for a year should also be valid for a month since the rate is the same over the year. In a month Janet saves AT/12 which should be equal to (5xAT)/6xC . This says 1/12 = 5/6xC ...
21. From a mixture whose half is water 20 l. of water has evaporated. 3/10 ths of the resulting mixture is water. How many liters was the original mixture ?

a) 70
b) 85
c) 57
d) 68
These type of problems are more easily solved by trial and error. Just try the answers .
Let the amount of mixture be B at the beginning and E at the end. We have to find 2 equations:
1. E = B - 20 .
2. (3/10)xE + 20 = B/2.
Putting 1 in 2 we have (3/10)x(B-20) + 20 = B/2 which means B/2 - 3xB/10 = 14
y
22. A certain weight is lifted up by a machine in 16 seconds whereas a man does the same job in 4 minutes. During a lift power failed to the machine after it has worked for 15 seconds and the rest of the way the weight is to be elevated by a man. How long will the duration of this work be ?

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

RY1 RY2



a) 18 s
b) 16 s
c) 21 s
d) 22 s


In a second the machine does 1/16 ths of the whole lifting. After 15 seconds 1/16 ths of the work (w.r.t. the machine) remains.
The man does the work in 240 seconds. What the machine does in a second, he does in 240/16 = ... seconds . See ry1 also.
23. Which addition below has the smallest result ?

a) 5/11 - 1/10
b) 3/11 - 2/15
c) 11/15 - 3/19
d) 10/9 - 1/10
The last two are not very likely .
24. 21/3 - 32/4 + 43/5 = ?

a) 21 2/7
b) 23 3/5
c) 7 3/5
d) 5 7/8
The first two are 7 and 8 and 43/5 is 8 3/5
25. How many many natural numbers, 0 excluded, A make 5/(A+5) - 1/2 an improper fraction ?

a) 4
b) 0
c) 2
d) 3
5/(A+5) ≥ 1 1/2 . The first is certainly less than 1 as long as A is natural number.
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , Ismail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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