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FIFTH GRADE / ADDITION 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. A worker digs half of a 3mx3mx2m hole in a work day of 9 hours. How long will it take if he works with another man digging a quarter more than him ?

a) 10 hours
b) 8 hours
c) 12 hours
d) 6 hours
First the whole hole fill take 2 days of him. On the other hand the total capacity of both is 1+1+1/4 as much. The work force will amount to 9/4 .
2. 4 equilateral triangles have heights of 1 m. , 1/2 m. , 1/3 m. and 1/4 m. What will be the total area of these triangles if the area of the first is taken as the unit area ?

a) 205/144
b) 103/141
c) 203/141
d) 25/17
The areas will be proportional with the squares of the heights. 1+1/4+1/9+1/16 = ?
3. Both figures are squares, the second having 7/10 ths of the side of the first. How much fabric is needed to cover whole blue areas if 1 m2 is needed to cover the whole area of the first (bigger) square?

!


a) 2434/1713
b) 1654/1041
c) 1834/1927
d) 2829/3200
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 = ?
4. What is the sum of the fractions given in the figure below ?

!


a) 61/47
b) 64/33
c) 65/36
d) 66/37
Find 3/4 + 7/12 + 17/36 and get 1/10 ths.
5. A training marathon runner ran 2100 km in 7 months. Each month he ran 20 km more than the previous month. What fraction of the total should he have ran in the first 3 months ?

!


a) 17/35
b) 13/35
c) 15/37
d) 17/36
First month he should have run 12/105 of the total .
y
6. Mr. Blackberry has a total of 7 ducks and ducklings; all ducks weigh the same and so are the ducklings (among themselves).
3/4 of the total weight of the ducks and 2/3 of the total weight of the ducklings make 24 kg. Total weight of both groups make 33 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) 13 kg.
c) 17 kg.
d) 18 kg.


Please have a look at ry1 .
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7. Which number gets equal to 245 if 6 is added to (1/7 + 1/9 + 1/11) ths of it ?

a) 577
b) 596
c) 693
d) 715
Find what in the paranthesis first and ... .
8. 1/2 + 2/3 + 3/4 + 4/9 + 5/16 + 6/81 = ?

a) 1185/436
b) 1217/427
c) 1187/432
d) 1041/395


Change the order to 1/2 + 3/4 + 5/16 + 2/3 + 4/9 + 6/81 .
9. 46/0.46 + 23/2.3 + 55/5555 = ?

a) 101 + 1/101
b) 110 + 1/101
c) 99 + 1/99
d) 99 + 1/909
In case you have not learned decimals : 46/0.46 = 100 and 23/2.3 = 10 .
Solve 5555/55 and invert the result: 5555/55 = 5500/55 + 55/55 = 100 + 1. And "invert" means write numerator as the denominator ...
10. What will (A + B + C)/3 be if 500/ABC + A/ABC = 3 is valid where A, B and C are digits and ABC is a 3-digit number. ?

a) 14/3
b) 3
c) 16/3
d) 17/3
(500+A)/ABC = 3 means 500+A should be divisible by 3. There are 3 candidates: 501, 504 and 507. 501/3 = 167
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) 4/47
b) 6/49
c) 5/48
d) 7/51
1/16 + 1/24 = ?
y
12. The square has unit area. What is the area of the red 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+π/8
b) 1+π/16
c) 1-π/8
d) 1-π/16
1 - π/4 + 3xπ/16 .
13. Which of the following statements are correct ?

I: Sum of proper fractions are proper .
II: By improper fractions the numerator is always greater than 1 .
III: Sum of equivalent fractions are equivalent to any one of the summands .
IV: Improper fractions may be changed to mixed fractions .


a) I , II and III
b) Only IV
c) II and III
d) II and IV
1/2 is a proper fraction while 1/2 + 1/2 is equivalent to unity and improper .
1/3 + 3/9 = 2/3
14. Which of the following equations is true for A=3 ?

a) (9+A)/2 = (A+7)/5 + 16/4
b) (9+A)/3 = (A+7)/5 + 16/4
c) (9+A)/2 = (A+7)/3 + 16/4
d) (9+A)/2 = (A+7)/5 + 16/5
Put 3 instead of A and calculate .
15. A is the fraction less than 1, formed by the smallest and the biggest natural numbers obtained by using the digits 2, 4 and 0 only once.
B is the fraction less than 1, formed by the smallest and the biggest natural numbers obtained by using the digits 1, 8 and 0 only once.
A+B = ?

a) 27/17
b) 7/9
c) 13/21
d) 347/525
The smallest numbers are 204 and 108 respectively.
After reductions we see we have to find : 17/35 + 2/15 = ?
16. Which of the following additions are wrong ?

I :11/12 + 5/11 = 59/132     II : 18/45 + 16/46 = 6/115     III : 4/6 + 2/7 = 20/21

a) I and II
b) Only I
c) Only II
d) All
In I left side is grater than 1 whereas right side is smaller.
In II left is around 1, right is very small.
17. In the buro in which Mr. Kayle Works there are 3 clocks. One gains 1/2 minutes, one other gains 1/3 minutes and the last gains 1/4 minutes in a day but which specific one gains which amount is not known.
So the workers decide by averaging all three. How many minutes are the mean error of these three clocks per day ?

!


a) 1/3
b) 13/36
c) 1/4
d) 1/2
Find 1/2 + 1/3 + 1/4 and divide by 3 .
y
18. Which choice gives the (intermediate) result of the summations in the figure ?

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) 3/4 x 4/3 + 5/6 x 3/4
b) 3/2 x 5/3 + 1/6 x 3/4
c) 3/2 x 4/3 + 5/6 x 3/4
d) 3/2 x 4/3 + 1/6 x 3/4
The main fractions have 3/2 and 5/6 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. How many kilometers should the total distance between two cities be if the distance the auto of question 8 of test-2 has traveled (11/15 of the total distance between 2 cities) is 105 km. more than the halfway between two cities ?

a) 425
b) 550
c) 450
d) 535
All it means is 7/30 ths of the distance between two cities is 105 km. Have a look at problem of "http://www.test-dr.com/education/5th-Grade-Mathematics/addition-of-fractions-5.1.2.html"
20. = 2 1/3 + [ 1 1/2 + (1 1/4) x 4] = ?

a) 53/6
b) 45/7
c) 17/38
d) 21/7
Just to inform you when to use "[ ... ]" .
First are multiplications and (1 1/4) x 4 = (5/4) x 4 = 5 , i.e. four quarters make one.
21. (16 + 14/20) + (4 1/3 + 3 1/2) = ?

a) 23/6
b) 256/18
c) 144/11
d) 368/15
Önce 16 + 7/10 = ... and then the 2nd paranthesis .
y
22. How many natural numbers (0 excluded) does there exist for which the equation given in the figure below will be valid ?

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

RY1 RY2



a) infinitely many
b) 9
c) 5
d) 2


Have please a look at ry1.
23. Which addition 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
100/39 is almost 3 . Choice a is greater than 1. Choose between b and c .
24. (2 1/3 + 1/3) + (2 + 1/5) = ?

a) 4 7/9
b) 4 13/15
c) 3 8/9
d) 5 1/7
4 + 2/3 + 1/5 = ?
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
For all A > 0 .
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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