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FIFTH GRADE / MULTIPLICATION 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. Pam walked 7/3 rds of a mile yesterday and 3/4 ths more than yesterday's distance today. How many miles has Pam walked today ?

a) 2 3/7
b) 49/12
c) 4 3/11
d) 3 3/17
Be careful about "today". 7/3 x(1 + 3/4) = ?
2. Suzanne is preparing for an exam. She studied 7/3 hours on Friday, 1/4 ths more than Friday on Saturday, and 2 2/3 hours on Sunday. How many hours did she study over the weekend ?

!


a) 95/12
b) 89/11
c) 23/3
d) 17/4
7/3x(2 + 1/4) + 8/3 = 7/3 x 9/4 + 32/12 = ?
3. (2 1/2 - 3 2/3) x (3/4 - 1 4/5) = ?

a) 1 11/120
b) 133/120
c) 1 17/120
d) 147/120
Now apply the rule: First paranthesis, the structure is so constructed. Make improper fractions out of mixed numbers, convert them.
4. (1/2 - 2/3)x(3/4 - 4/5)x(2 5/4 - 1 2/3)x(3 1/3 - 10/3) = ?

a) 0
b) 1
c) 10
d) 7/123
Last factor is 0, try to see quickly .
5. A recipe card indicates that a special recipe requires 1/2 teaspoon cayenne pepper, 3/4 ths more than cayenne pepper, black pepper, and 1/4 ths less than black pepper, red pepper. How many teaspoons of pepper does this recipe need ?

!


a) 41/94
b) 65/32
c) 27/17
d) 11/8
1/2 + 1/2 x (1 + 3/4) + 7/8 x (1 - 3/4) = ?
y
6. The most difficult part of multiplication of fractions is calculating the product of two mixed numbers. Two possible methods are to convert them to improper fractions or write them as sum of whole numbers and fractions.
Calculating 5 7/9 x 8 3/7 via the methods mentioned above, a difference of .... between the calculation results is obtained .


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



a) 0
b) 1
c) 1/100
d) 1/1000


The should be no difference but have a look at ry1
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) 2/3
b) 4/9
c) 8/15
d) 7/13
Just place the numbers into their correct places .
We want you to get acquainted with the matrices via this simple operation .
8. 3/4 ths of Martin's friends have a sister. Of whom who have a sister, 3/4 ths do also have a brother. What fraction of the friends have both a sister and a brother ?

a) 7/17
b) 8/11
c) 9/16
d) 4/9
Just 3/4 x 3/4 = ?
9. 7 dolphins at the Newport News Aquarium are fed each 7/8 of a bucket of fish each day. The sea otters are fed each 1/2 as much fish as the dolphins. On a certain date 2 of 7 sea otters have been transported and their share was given to the rest. How many buckets of fish the sea otters fed on that day ?

!


a) 81/77
b) 1 27/49
c) 2 47/51
d) 1 67/80


The sea otters normally had 3/2 x 7/8 = 21/16 buckets but on that special date ... .
10. 12 1/5 x (17 3/4 - 10 1/5) = ?

a) 128 17/100
b) 92 11/100
c) 101 77/100
d) 81 94/100
61/5 x (7 + 3/4 - 1/5) = 61/5 x (7 + 11/20) = 61/5 x 151/20 = ?
11. At Fatih Ataturk Primary School, 1/3 of the students play an instrument. Of the students who play an instrument, 1/4 play a string instrument whose 1/8 play also a wind instrument. What fraction of the students at Fatih Ataturk Primary School play both a string and a wind instrument?

!


a) 1/96
b) 1/48
c) 3/121
d) 5/444
1/3 x 1/4 x 1/8 = ?
y
12. To the gridded red region a spherical body enters from left which is scattered at each and every node. After being scattered it has a probabilty of 2/5 of traveling in each perpendicular direction and of 1/5 continuing in the same direction. The body takes the distances between nodes in equal amounts of time which is given as tN. What will be the probabilty of finding the particle in the near vicinity of point A as the elapsed time after entrance approaches 3xtN ?

!


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

RY1 RY2



a) 2/25
b) 1/23
c) 1/17
d) 2/19
The three possible ways and their probabilities are in ry1.
The total probability is 2/125 + 4/125 + 4/125 .
13. Which of the following statements are true ?

I: Fractions can not be multiplied because multiplication is short way of summation.
II: The first statement above is wrong, a fraction in a unit system may be a whole number in another for whcih multiplication is defined.
III: The second statement above is true, 1 cm. is about 2/5 '' .
IV: As the mixed numbers are multiplied, whole numbers, numerators and denominators are multiplied among themselves and multiplication is done.


a) I , II and III
b) all
c) II and III
d) II and IV
IV is wrong, either they should be converted to improper fractions or be explicitely written as sum of whole numbers and fractions.
14. An amount of milk has stayed under certain conditions for an hour which resulted a decrease of bacteria by 1/10 and then under diffrent conditions for an hour which resulted an increase by 1/10. A bacteriologist has the taken 1/100 ths of this milk for examining it. Which fraction of original amount of bacteria are taken ?

a) 1/100
b) 99/10000
c) 1/10
d) 9/1000
Let the original number of bacteria be 100 . After an hour there will be 90 and after two 99 .
15. 1/3 rds of the students in our class have a family car and 1/5 ths of these go to vacation by car. 2/7 ths of these further go to seaside. What is the fraction ?

!
a) 2/105
b) 1/35
c) 2/71
d) 3/151
1/3 x 1/5 x 2/7 is being asked.
16. Which multiplication among the followings has the least product ?

I :11/12 x 5/11 =?     II : 18/45 x 16/46=?      III : 4/6 x 2/7=?       IV : 16/23 x 8/24=?

a) II
b) I
c) IV
d) III
II is relatively harder to reduce. For the others, after reductions 5/12 , 4/21 and 16/69 are obtained .
17. Two cars made an accident (collision) though they both braked. Both cars have reduced their speeds by 3/10 in the first brake stage and by 2/5 in the second. What will be the ratio of their collision speed to their original speed ?

!
a) 18/25
b) 1/2
c) 21/50
d) 81/100
Let the original speeds be 100 km/hour. After the first stage these will reduce to 70 and then ... .
y
18. Per capita agricultural land in the U.S. is about 7/2 acres. It decreases, due to several reasons, by 1/250 each year. The population on the other hand has a yearly increase rate of about 3/200.
What is likely to be per capita agricultural land after 20 years from now on ?


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


a) 3 1/27
b) 2 31/65
c) 1 17/47
d) 4 1/21
The population, depending on years, will be : 1+3/200, (1+3/200)x(1+3/200), (1+3/200)x(1+3/200)x(1+3/200), ... . The population increase and land decrease are calculated approximately in ry1 and 2 .
For the population increase we found per capita 1+3/10 and land decrease per unit area we found 1-2/25. Per capita land will be (23/25):(13/10)= 46/65 which is of course to be multiplied by 7/2 acres of today. 7/2 x 46/65 = 7 x 23/65 = 161/65 = 2 31/65 .
19. A and B are natural numbers and A/2 x B/3 is supposed to be a proper fraction attainable under these conditions. How many possible A values may there be ?

a) 9
b) 7
c) 6
d) 5
AxB is supposed to be ≤5 . If B=1, there are 5 possibilities, all others are also covered.
20. What will be the product of a, b and c if a=5/6 , b=7/12 and c=24/11 ?

a) 49/21
b) 35/33
c) 751/792
d) 377/792
(5x7x24)/(6x12x11) = ?
21. Which value is A supposed to take if 10/150 x 50/30 = A/30 ?

a) 10/3
b) 7/3
c) 5/3
d) 9/7
It may be written in the form 10/3 x 1/30 = A x 1/30 .
y
22. A and B are nonzero digits and 5/(A-1) x 7/(B-3) is desired to be an improper fraction. How many A,B couples are possible ?

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

RY1 RY2



a) 16
b) 60
c) 81
d) 48


(A-1) x (B-3) should be ≤ 35; negative fractions are permitted .
23. Which product is minimal ?

a) 25/110 x 15/105
b) 22/157 x 13/110
c) 23/159 x 11/145
d) 10/39 x 1/100
Choice d has a dominant factor like 1/100 .
24. (2 - 1/3) x (4 + 1/5) = ?

a) 27/4
b) 21
c) 7
d) 9
5/3 x 21/5 = ?
25. Which is the maximal A that makes 25/(A+10) x 3 a proper fraction ?

a) 44
b) 24
c) 65
d) 74
In case A=65 it is equivalent to unity.
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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