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FIFTH GRADE / ADDITION 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.

FRACTION'S 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) 22
b) 10 1/10
c) 10 1/2
d) 11 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. (3 2/10 + 3/100 + 2/1000)/(2/100 + 30 3/10 + 2) = ?

!
a) 10
b) 1 1/10
c) 1/10
d) 1
The first paranthesis is 3200/1000 + 30/1000 + 2/1000 . The second is 20/1000 + 30300/1000 + 2000 . They are then 3232/1000 and 32320/1000 .
As you see in the figure, if the numerator and denominator of a fraction are fractions with a common denominator, common denominators may be dropped .
3. What will be inverse of A, inverted form of A (w.r.t. multiplication) if A = 1/5 + 1/7 ?

a) 35/12
b) 12/35
c) 33/9
d) 9/33
Find A and then write its denominator as numerator and vice versa .
4. How long is the daytime if it is 2/3 hours longer than the night on a certain date ?

!


a) 12 1/4
b) 12 1/2
c) 12 2/3 h
d) 12 1/3 h
Daytime gets longer if night gets shorte, take care .
5. How long is the daytime if it is 2/3 hours shorter than the night on a certain date ?

a) 11 1/3 h
b) 11 2/3 h
c) 11 1/4
d) 11 2/5
Take care .
y
6. A and B are digits. If the numerator of the sum of the fractions 28A/9B and 1/100 is divided by 9, the remainder is 7 and if it is divided by 5 the remainder is 1 .
A-B = ?


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



a) 2
b) 6
c) 3
d) 4


The sum is (100x28A + 9B)/100x9B and its numerator is 28A9B . For the rest have a look at ry1.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. To a wire consecutive multiples of 2/3 rds of its original length is added n times. When length gets 30 times its original, it will be possible to build the wire lady on bike shown in the figure. What is the minimal n that permits ?

!


a) 11
b) 9
c) 7
d) 10
Let the original length of the wire be 1 . Then , 1 + 2/3 + 4/3 + 6/3 + 8/3 + 10/3 + 12/3 + 14/3 + 16/3 + 18/3 + ...
1+2+4+6 + (2+4+8+10+14+16)/3 = 13+18 is the result of first 9 additions .
8. 1/5 + 2/3 + 2 3/15 = ?

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

a) 10 1/2
b) 10 8/9
c) 11 1/11
d) 11


2+1+2+3 +1/4 + 2/4 + 3/4 + 2/3 + 5/6 = 8 + 3/2 + 4/6 + 5/6 = 8+3/2+3/2 = ? .
10. 1/47 + 2/58 + 4/11 = ?

a) 6288/14993
b) 3588/7643
c) 1355/2144
d) 3066/5146
It should be around a half due to 3rd term .
11. 7/15 + 1/14 + 3/5 + 2/25 + 4/7 = ?

a) 1 829/1050
b) 2 641/717
c) 1 954/998
d) 2 34/ 89
7/15 + 9/15 + 2/25 + 1/14 + 8/14 = 1 1/15 + 2/25 + 9/14 = 1 + 5/75 + 6/75 + 9/14 = 1 + 11/75 + 9/14 = .
y
12. A swimmer training for London 2012 Olympics has a weekly program; each week he increases his training periods by 1/20 ths of the previous week. How long will his 5th week training periods (h) be if he trained 2 hours every day in the first week ?

!


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

RY1 RY2



a) 1.55
b) 2.44
c) 2.08
d) 2.66
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) 18.7
b) 20.2
c) 19.41
d) 21.63
Just set A=1 and B=2 and try .
14. Half of the 20 g of salt brine with 4/10 salt, 1/4 ths of 40 g of salt brine with 3/10 salt and 30 g of salt brine with 2/10 salt are emptied in a bowl. What is the fraction of the salt in the new mixture of salt ?

!


a) 26/100
b) 1/4
c) 1/3
d) 25/99
From first brine : 6 g. water, 4 g salt ; from second 7 g water, 3 g salt and from 3rd : 24 g water, 6 g salt. A total of 50 g. brine containing ...
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 average time of production of a toy by these 3 machines ?

a) 3/47
b) 1/15
c) 2/33
d) 3/73
1/3 rd of the sum 1/20 + 1/15 + 1/12 gives 1/15 and this result is not correct.
In a minute a total of 20+15+12=47 toys are produced and the average time of production is 3/47 minutes.
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 second machine produced 180 000 toys.
b) The first machine produced 240 000 toys.
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) 754/1000
b) 341/717
c) 1417/2000
d) 1566/1990
(1000+300+90+27)/2000 = 1417/2000 .
y
18. 7/10 of the students of a class got satisfactory (passing) grades from math. and 4/10 of the class got passing grades from physics. The number of students succeded in both courses is 12. 2/100 of the class succeded in neither of the courses. What (how many students) is the size of the class ?

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


a) 90
b) 100
c) 95
d) 87
Have a look at ry1 . Just to get acquainted with set theory .
Try it with the simplest possible common denominator 100. 70 passed math. 40 passed physics 12 of which have already been taken into account. 2 failed with a total of 100.
19. 437/35 + 943/105 + 144/7 + 19/42 + 61/21 + 3/5 ?

a) 8847/199
b) 9659/210
c) 7634/187
d) 10551/203
437/35+943/105+3/5 + 144/7+19/42+61/21 = (1311+943+63)/105 + (864+19+122)/42 = 2317/105 + 1005/42 = ... (LCM = 210) It should be something around 45 !
20. There are 24 hours in a day and scientists tell us that we should sleep for 1/3 of the day. About 1/4 ths of our sleep is REM (deep) sleep. How much time (h) are we likely to spend in deep sleep ?

a) 2 1/2
b) 3
c) 2
d) 4
You may not know division of fractions, just find the hours spent in sleep and then get a quarter of it .
21. Skateboards cost $63 each in our local store. The shopkeeper says if I buy one I can buy another for 7/9 and a third for only 5/9 of the normal price. How much would these three skateboards cost then per board (in average) ?

!


a) 56 1/2
b) 53 3/5
c) 53 1/3
d) 53 2/3
(1+7/9+5/9)x63 will be the price of all three. So,(1+7/9+5/9)x21=?
y
22. =(1+1/A)/(1-1/(AxA)= ?

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

RY1 RY2



a) (AxA-A)/(AxA-1)
b) (AxA+A)/(AxA+1)
c) (AxA+A)/(AxA-1)
d) (AxA+A)/(AxA-A)


Without having a look at ry1, try to force the upper and lower fractions to have a common denominator AxA .
23. Which addition below has the greatest result ?

a) 5/11 + 1/10
b) 2/15 + 3/11
c) 3/9 + 11/15
d) 10/9 + 1/10
The last two are around 1 whereas the first two are around a half .
24. 21/3 + 32/4 + 43/5 + 54/6 + 63/7 = ?

a) 51 2/3
b) 41 3/5
c) 45 1/6
d) 47 1/7
7+8+43/5+9+9=?
25. How many many natural numbers A less than 20 make 5/(A+5) + 1/2 a proper fraction ?

a) 14
b) 18
c) 15
d) 16
5/(A+5) < 1/2 .
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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