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FIFTH GRADE / SUBTRACTION of FRACTIONS / TEST 1.3

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

(FAST) DAS SELBE AUF DEUTSCH
   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. (5555/10)/(5555/100) - (5555/1000)/(5555/100) = ?

a) 9 9/10
b) 10 1/10
c) 10 1/2
d) 9 1/2
Left of - sign we have a fraction whose numerator is 10 timest its denominator because the same number is divided by 10 in the numerator and by 100 in the denominator .
2. A certain amount of hazelnuts are shared equally among 9 children. Each of the three boys in the first group who do not like hazelnuts much, gave half of their shares to the other children equally such that each boy in the other groups got 5 hazelnuts more.
How many hazelnuts did each boy of first group get from this share and what was the original amount of the hazelnuts ?

!


a) 10 and 180
b) 8 and 160
c) 11 and 160
d) 10 and 210
Each boy of the first group should have given 10 hazelnuts after equal share .
3. Ali Haktan German did 1/3 rds of his homework yesterday. Today he did 1/4 ths of the homework in 3 hours. How much more time does he normally need to complete the work ?

a) 3 h
b) 6 h
c) 5 h
d) 4 h
1 - 1/3 - 1/4 of the work is done. There remains ... of the work . For 1/12 ths of the work he needs 1 hour.
4. Muhammet Daghan German did 1/3 rds of his homework yesterday. Today he did 1/4 ths of the rest in 3 hours. How much more time does he normally need to complete the work ?

a) 7 h
b) 9 h
c) 6 h
d) 5 h
Today he did 1/4 ths of 2/3 rds which means he did 1/6 ths of the whole in 3 hours (1/18 in an hour). This time there remains ... of the work.
5. 1/3 rds of a 75 cm. long wire is marked and then 15 cm. of the wire is cut from right. 1/3 rds of the cut wire is again marked.
How many cm. is the difference between two marks ?

a) 10
b) 7 1/2
c) 5 7/9
d) 5
The difference should be ... of the cut part .
y
6. I have a certain amount of dimes. If I divide them into 7 equal groups and then into 10 equal groups I observe that each group by the first division has 9 elements more than each group by the second.
How much money do I have ?


!


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



a) $33
b) $21
c) $27
d) $24


Please have a look at ry1.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. What should be the value of A if (A/3 + A/4) - (A/5+A/6) = 13 is valid ?

a) 65
b) 45
c) 55
d) 60
7xA/12 - 11xA/30 = 13
8. 1/5 - 2/3 + 2 3/15 = ?

a) 2 1/7
b) 1 11/15
c) 1 12/19
d) 2 4/11
2 + 1/5 + 1/5 - 2/3 = 1 + 1/3 + 2/3 + 1/5 + 1/5 - 2/3 = ?
9. 2 + 2/3 - 1/4 + 1 1/2 + 2 3/4 - 3 5/6 = ?

a) 2 5/6
b) 2 3/4
c) 1 7/9
d) 3 4/9


2+1+2-3 - 1/4 + 2/4 + 3/4 + 2/3 - 5/6 = 2 + 1 -1/6 = ?
10. 1/47 - 2/58 + 4/11 = ?

a) 4051/9574
b) 4794/13467
c) 3555/10551
d) 5254/14993
It should be around a half due to 3rd term .
11. 7/15 - 1/14 + 3/5 - 2/25 + 4/7 = ?

a) 1 73/150
b) 1 1/2
c) 1 1/3
d) 2 1/3
7/15 + 9/15 - 2/25 - 1/14 + 8/14 = 1 1/15 - 2/25 + 7/14 = 1 + 5/75 - 6/75 + 1/2 = 1 + 1/2 - 1/75 = 3/2 - 1/75 = ?
y
12. A/2A is a fraction where A is a digit. When we get 5 from the denominator of this fraction and add this to the numerator the new fraction happens to be equivalent to 1/2.
1 - A/2A = ?


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

RY1 RY2



a) 4/7
b) 5/7
c) 4/5
d) 6/7
Have please a look at ry1 .
13. D=0 and A,B,C are digits different from 0. Using these digits 4-digit numbers are constructed. What will be the result of ABAB/ABD - BABA/BAD ?

a) 11
b) 0
c) 22
d) 2
Just set A=1 and B=2. You now have 1212/120 - 2121/210. Write it in the form 1200/120 + 12/120 - (2100/210 + 21/210) .
14. According to the source reachable by clicking at the picture below, in the USA roughly 4 million acres of active farmland (roughly the same size as Massachusetts) were transformed for development and commercial use between 2002 and 2007.
What will be the difference of fractions having in numerators the number given above and in denominators data from Note 1 and Note 2 ?

Note 1: The United States had almost 60 million acres (23.8 million hectares) of irrigated farmland in 1991.
Note 2: As of the last census of agriculture in 2007, there were 2.2 million farms, covering an area of 922 million acres.

!


a) 551/4077
b) 461/5094
c) 431/6915
d) 477/4321
4/60 - 4/922 = ?
15. A plastic toy is produced by the 1st machine in 1/20 minutes, by the 2nd machine in 1/15 minutes and by the third machine in 1/12 minutes. What is the difference of average production times of a toy for the cases that all three and only machine 1 and machine 2 are working ?

a) 13/1475
b) 11/1645
c) 17/987
d) 15/1356
For all 3 working : In a minute a total of 20+15+12=47 toys are produced and the average time of production is 3/47 minutes.
For M 1 and M2 working : In a minute a total of 20+15=35 toys are produced and the average time of production is 2/35 minutes. So the question is 3/47 - 2/35 = ?
16. The three machines of the previous question began to work simultaneously and the production has been stopped after 564 000 toys . Accordingly, which of the followings is false ?

a) The difference of toys produced by first and second machines is 60 000.
b) The difference of toys produced by first and third machines is 36 000.
c) The third machine produced 72 000 toys.
d) The production continued for 200 hours.
Look at the numbers and just guess, you need to be quick .
17. 1/2 - 3/20 + 9/200 - 27/2000 = ?

a) 1347/3043
b) 544/977
c) 441/100
d) 763/2000
(1000-300+90-27)/2000 = .../2000 .
y
18. My digital watch shows hours and minutes only and it is programmed to 24-hours. The answers to for what fraction of a complete day is there at least one "1" showing on the hours and the minutes part part of the display are respectively to be F1 and F2 .
What will be the answer to the question in the figure below ?


!


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


a) 5 5/6
b) 6 1/6
c) 4 3/7
d) 3 5/9
In 24 hours 1 , ..., 10,11,12,13,14,15,16,17,18,19,.,21 have 1 in display . Fraction is: 12/24
24 hours are 24x60 = 1440 minutes. 01,...,10,11,12,13,14,15,16,17,18,19,.,21,...,31, ...,41,...,51. The fraction is 15/60.
19. 437/35 - 943/105 + 144/7 - 19/42 + 61/21 - 3/5 ?

a) 363/14
b) 521/79
c) 447/34
d) 1041/107
437/35-943/105-3/5 + 144/7-19/42+61/21 = 61/21 + 144/7-19/42+61/21 = 61/21 + 967/42 = ... It should be something around 45 !
20. One pipe fills a tank in 1 hour while another pipe can empty the same tank in 2 hours. How long will it take to fill the tank if both pipes are used from the beginning on ?

a) 1
b) 4
c) 2 h
d) 2 1/2
In one hour the first pipe fils it , the second empties a half; a half remains full .
21. Adam sold 1/3 rds his fishes and 2/3 rds of a fish to his friends and still had 21 fish left. How many fishes did Adam have to start with ?

a) 39
b) 27
c) 22
d) 33
21 + 2/3 should be 2/3 rds of ...
y
22. Janet picked a bad of oranges to give to her friends. To the first of her friends, she gave 1/4 ths of the oranges she had and another three beside. To her second friend she gave 1/3 rds of the remaining oranges and another two beside. To her third friend she gave half of the remaining oranges and another one beside. By this time, she had seven oranges left. How many did she start with ?

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

RY1 RY2



a) 82
b) 27
c) 40
d) 55


The best method to deal in a hurry to substitute the answers. The second is to go in the reverse order .
She hat at the end 7. One extra she gave to her 3rd friend means 8 is the half of remainings after 2nd. To 2nd she gave extra 2 means she had 27 after first friend. 3 extra to first means she had 30 after she gave 1/4 ths.
23. Which subtraction below has the smallest result ?

a) 5/11 - 1/10
b) 3/11 - 2/15
c) 11/15 - 3/9
d) 10/9 - 1/10
The last is greater than 1 .
24. 21/3 - 32/4 + 43/5 - 54/6 + 63/7 = ?

a) 3 5/7
b) 7 3/5
c) 5 3/7
d) 4 5/9
7-8+8+3/5-9+9=?
25. How many many natural numbers A less than 20 make 5/(A-5) - 1/2 a proper fraction ?

a) 4
b) 1
c) 5
d) 3
It should be 5/(A-5) > 3/2 . For A = 5, 6, 7 and 8 the inequality is valid. In case A=5 no fraction is obtained.
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
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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