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FIFTH GRADE / SUBTRACTION of FRACTIONS / TEST 1.1

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. What is the difference of the lengths of the fishes caught in 1959 (2 1/10 m.) and nowadays (1 m.) ?

!


a) 1 m.
b) 1 1/10 m.
c) 2 1/10 m.
d) 9/10 m.
This is a very simple question whose main aim is to warn you about the possible outcomes of observation/calculation deficiency .
2. 4 equilateral triangles have heights of 1 m. , 1/2 m. , 1/3 m. and 1/4 m. Let the area of the first be taken as the unit area. What will be the difference of the sums of areas of the first and the last couples ?

a) 1 11/144
b) 1 15/144
c) 1 9/133
d) 1 11/141
The areas will be proportional with the squares of the heights. 1+1/4-1/9-1/16 = 5/4 - 25/144 = ?
3. Both figures are squares, the second having 7/10 ths of the side of the first. The whole area of the first square is 1 m2 .
To cover all of the blue areas in both figures is desired and there is 1/2 m2 fabric at hand. How much more (m2) is needed ?

!


a) 1330/3221
b) 1229/3200
c) 1329/3200
d) 1400/3221
The blue areas in the first square are 9/16 m2 . The whole area of the second square is 49/100 m2.
9/16 + 1029/3200 - 1/2 = ?
4. What will be the result of subtracting the smallest fraction from the biggest both shown in the figure below ?

!


a) 1/35
b) 2/49
c) 2/87
d) 1/36
3/40 - 17/360 = ?
5. A training marathon runner decided to run a definite distance in 7 months. The first month he ran 1/10, in the second 1/9, in the third 1/8, in the fourth 1/7, in the fifth 1/6 and in the 6th 1/5 of the distance set. What part of the distance has he to run in the last month ?

!


a) 1/4
b) 389/2520
c) 1/3
d) 385/2521
1 - (1/10+1/9+1/8+1/7+1/6+1/5) = ?
y
6. Mr. Blackberry has a total of 7 ducks and ducklings; all ducks weigh the same and so are the ducklings (among themselves).
If 2/3 of the total weight of ducklings is subtracted from 3/4 of the total weight of the ducks 15 (kg) is obtained. Total weight of both groups make 37 kg.
What is the weight of the half of the ducks ?

!


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



a) 12 kg.
b) 15 kg.
c) 14 kg.
d) 13 kg.


Please have a look at ry1 and make the changes necassary to solve the new situation.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which number gets equal to 119 if 6 is added to (1/7 + 1/9 - 1/11) ths of it ?

a) 693
b) 721
c) 599
d) 633
Find what in the paranthesis first and ... .
8. 1/2 + 2/3 + 3/4 - 4/9 - 5/16 - 6/81 = ?

a) 1 27/432
b) 1 37/432
c) 1 17/337
d) 1 19/337


Change the order to 1/2 + 3/4 - 5/16 + 2/3 - 4/9 - 6/81 = 15/16 + 2/9 - 6/81 = 15/16 + 12/81 = ?
9. 46/0.46 + 23/2.3 - 555/55 = ?

a) 1089/11
b) 1099/11
c) 1112/11
d) 1036/11
In case you have not learned decimals : 46/0.46 = 100 and 23/2.3 = 10 .
Solving 555/55 = 111/11 = (110 + 1)/11 = 10 + 1/11
10. What will (A + B + C)/3 be if 500/ABC - C/ABC = 4 is valid where A, B and C are digits and ABC is a 3-digit number ?

a) 14/3
b) 7
c) 7/3
d) 5
(500-C)/ABC = 4 means 500-C should be divisible by 4. There are 3 candidates: 492, 496 and 500. 496/4 = 124 which means A=1, B=2 and C=4. 496/4 = 124 fits.
11. What will 1/A - 1/B be if A/B = 2/3 and the least common multiple of A and B is 48 ?

a) 1/48
b) 1/43
c) 1/39
d) 1/54
1/16 - 1/24 = ?
y
12. The square has unit area and π is to be taken as 22/7 . What is the area of the orange region 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) 1/4
b) 1/3
c) 4/15
d) 3/14
1 - π/4 = 1 - 22/28 = 3/... .
13. Which of the following statements are correct ?

I: The first step in calculating GCD and LCM is prime factorization.
II: In prime factorization the divisibility of a number by 2,3,4 ... is questioned.
III: In calculating GCD and LCM of very big numbers there is no efficient algorithm.
IV: Calculation of GCD and LCM is very simple independent of the siz of the number(s).


a) I , II and III
b) All
c) II and III
d) II and IV
Think of product of 2 big number like billions. This number is not prime and it has 2 prime factors. Since we do not know what these primes are, we begin by 2 and ask for divisibility. If not , the number next.
For orders of millions this can be done by the machines pretty swiftly. It gets harder and harder and for orders of quadrillions and up, it is a burden even for a machine. It takes too long.
14. If the temperature of milk is below 4 °C, the number of bacteria decreases. How many hours will it take till the number of bacteria decreases to 0 if there are originally 1 billion of them and they decrease by 1/10 each hour ?

a) 100
b) 10000
c) it never gets realized.
d) 91000
Number of bacteria are quantized, they increase and decrease one by one .
Next after 1 it will be 0, but this model can not cope with .
15. 1/4 ths of students of our class plan to have holyday at seaside, 1/5 ths plan to climb mountains, 1/20 ths plan to travel Europe. The rest will stay within State borders.
What will be the number of students that stay within State ?

Note: 20 < class size < 50.

!
a) 25
b) 40
c) 20
d) 50
The class size should be a multiple of 20 .
16. Which of the following subtractions are wrong ?

I :11/12 - 5/11 = 59/132     II : 18/45 - 16/46 = 6/115     III : 4/6 - 2/7 = 8/21?

a) I
b) II and III
c) none
d) III
I is correct .
17. Binary operations do normally have two elements both of which changes after the operation. The identity element is an exception. It leaves other elements unchanged when combined with them.
Which choice may be the identity element in addition and subtraction ?

a) 0
b) 1
c) 10
d) none
Example: 17 - 0 = 17 .
y
18. Which choice gives the (intermediate) result of the subtraction in the figure below ?

Note: 3/4 x 4/3 = 1 . Do not make the multiplications, leave in the form . x .


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


a) 1/2 x 2/5 - 1/3 x 2/5
b) 1/3 x 2/5 - 1/2 x 2/5
c) 1/6 x 3/4 - 3/2 x 4/3
d) 3/2 x 4/3 - 1/6 x 3/4
The main fractions have 3/2 and 1/6 as numerators, whereas the first has 3/4 as denenominator . You probably know multiplication of fractions but for those of you who do not, the problem is to expand the main fractions to have equal denominators.
Just multiply the numeaarator of the first main fraction by 4/3 and the other's by 3/4. The common denominator of the main fractions is then 1 and may be ignored.
19. (3/7 + 134/14) / (32/20 - 36/60) = ?

a) 5
b) 11/2
c) 10
d) 15/4
Just do the operations due; you will see it is simpler than it seems . It is (140/14)/1 .
20. = 2 1/3 - ( 1 1/2 - 1 1/4 x 4) = ?

a) 41/6
b) 35/6
c) 39/7
d) 2//8
(1 1/4) x 4 = (5/4) x 4 = 5 .
21. (16 - 14/20) + (4 1/3 - 3 1/2) = ?

a) 16 2/15
b) 15 4/9
c) 13 5/8
d) 11 3/2
Önce 16 - 7/10 = 153/10 and then the 2nd paranthesis .
y
22. Graphics below indicates World's water consumption as billion m3 vs. years.
If World's population amounts to 10 billions in 2050, by which amount per capita water consumption is expected to increase ?


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

RY1 RY2



a) 173/449
b) 5/6
c) 7/5
d) 3/2


Per capita consumption in 2050 = 300000000000/10000000000 m3/year.
Per capita consumption in 2000 = 175000000000/6000000000 m3/year.
23. Which subtraction below has the smallest result ?

a) 25/110 - 15/10
b) 22/157 - 13/110
c) 23/159 - 11/145
d) 100/39 - 1/100
not a and d, seek btween the others .
24. (2 1/3 - 1/3) - (2 - 1/5) = ?

a) 1/3
b) 1/15
c) 2/15
d) 1/5
First paranthesis gives 2 ... .
25. Which property should the integer A have in order to make 1/(A+1) - 1 a mixed number ?

a) A < -1
b) A ≠ 1
c) A < 0
d) A > 0
If A=-3 it is -1/2 -1; if A=-2 it is -1-1; in case A=-1 it explodes; if A=0 it is 0; if A=1 it is 1/2 - 1.
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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