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FIFTH GRADE /DIVISION / 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.

 Method(s) of DIVISION of INTEGERS   is  (are)
 ♦ 
METHOD(s) of DETERMINING the RESULT  (QUOTIENT) of
 ♦ HOW MANY TIMES A NATURAL NUMBER  CALLED a  DIVISOR

 ♦ CAN BE SUBTRACTED FROM / IS CONTAIN-  ED IN ANOTHER NATURAL NUMBER CALLED
 a DIVIDEND


 and WHICH NATURAL NUMBER (REMAINDER,  LESS THAN DIVISOR) STAYS BEHIND.
  Ref.-1
1. As the Ataturk Primary School's students visited the Darica Zoo there were 3 times as many boys as girls. If 54 more girls showed up, the number of both boys and girls would be equal.
How many students then should have visited the zoo ?

!


a) 54
b) 27
c) 108
d) 128
G+B=N where G is the number of girl visitors, B is of boy visitors and N is of G total visitors. 4xG=N . G+54=B .
This all say : G+54+G = 4xG i.e. G = 54/2
2. Ali Haktan German, Muhammet Daghan German and a friend of them emptied their piggy banks. It turned out that Ali had thrice as many dimes as the friend and Muhammet had twice as many. The sum was 324 dimes.
What amount of dimes had then Muhammet in his piggy ?

!


a) 162
b) 154
c) 99
d) 108
324/6 = 54 and 2x54 = ?
3. The divisor and remainder of a division operation are respectively 5 and 3. Digits sum of the 2-digit dividend is 17 whereas the digit at its tens' is equal to the digit at the ones' in the quotient.
Which choice should be the quotient ?

a) 19
b) 29
c) 33
d) 42
Let the dividend be AB (A&B are digits) and the quotient CA. AB=5xCA + 3 should be valid .
10xA + B = 50xC + 5xA + 3 and 5xA + B = 50xC + 3 . C must then be 1 otherwise A and B can not cope with. This means 5xA + B = 53 . Not many choices !
4. Mr. Harris began to build a brick wall. The Gossip Girl knows he began with 857 brick 17 of which is broken in a way not to be used anymore. She can see that the wall is 34 to 36 bricks long but the exact legth she can not see.
How many bricks high may the wall Mr. Harris built be ?

!


a) 22
b) 18
c) 24
d) 12
840/35 = 24. If 25 bricks high, then 25x34 = 850 for which not enough bricks.
5. The dividend is supposed to be 7750 if the divisor and the quotient respectively are ... and 62 .

a) 125
b) 250
c) 175
d) 225
7750/62 = ? but we know 60x125=6x1250=3x2500=7500 .
y
6. The quotient of a division operation is 5 . The 3-digit dividend and the 2-digit divisor have the same digits at their ones' which is also equal to the remainder.
Which choice should be the minimal dividend that satisfies the conditions cited ?

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



a) 155
b) 172
c) 112
d) 202


Have please a look at ry1 .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. The World's Gross Domestic Product in the year 2010 is given as $63 trillion. Assuming an approximate population of 7 billion in the same year, what was per capita GDP in the World in 2010 ?

!


a) $6 000
b) $9 000
c) $7 000
d) $5 000
63 000 000 000 000 / 7 000 000 000 = 63 000 / 7 = ?
8. (600+1200+7200+9600)/(320+280) = ?

a) 33
b) 31
c) 27
d) 21
The denominator should always be, also working with complex numbers, as simple as possible. Evaluate 320+280 first. It is 600 and all numbers in the numerator are divisible by 600 .
9. 1, 4, 9, 16, 25, 36, ... and 1, 2, 6, 8, 10, ... are two different patterns. Which number will be obtained if the sum of elements of each pattern up to the tenth element are seperately obtained and then these sums are divided ?

a) 6.07
b) 7.45
c) 11.66
d) 12.83


The pattern at the denominator should be ...2xn ... Its sum will be 30.
385/30 = 77/6 = 72/6 + 5/6 = 12+ ...
10. Which number is obtained if 281 291 010 is divided by the the product of the first 8 prime numbers?

a) 29
b) 31
c) 35
d) 42
The first 8 primes are 2,3,5,7,11,13,17 and 19. First divide the number by 2x3x5=30 to get 9 376 367. If you can not this way, then divide first by 2, then by 3, by 5 etc.
11. About 300 Asiatic lions live in a 1,412 km2 sanctuary in the state of Gujarat, which covers most of the forest. How many m2 is then per capita living area of these lions ?

!


a) 2 966 555.555
b) 4 706 666.666...
c) 4 306 333.333
d) 3 739 444.444
The area is 1 412 000 000 m2 and this should be divided by 300
y
12. What is he least number that leaves always a remainder of 1 when divided by all the natural numbers 2 to 7 ?


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

RY1 RY2



a) 341
b) 421
c) 437
d) 377
In general 2x3x4x5x6x7 + 1 satisfies the conditions with the exception of being the least .
13. Which of the following statements are true ?

I: A natural number is divisible by 9 if the digit sum is a multiple of 9 .
II: If the number 10551 is divided by 9 the remainder will be 2 .
III: To check the divisibility by 11, put a + sign in front of ones, - in ftront of tens, + ... etc. and see if this sum iz zero .
IV: 169367 is divisible by 11 .


a) II and IV
b) I and II
c) all
d) I , III and IV
Check given in III applied to 169 367 : -7+6-3+9-6+1 = 0 .
14. Which of the following figures gives a simple proof of division by 11 for 5 and less digit numbers whose digits are also less than 5 ?

a)   
!


b)   
!


c)   
!


d)   
!
The result should be zero !
15. Ali's age is divisible by 11 .
His a year younger brother Muhammet's age is divisible by both 2 and 5 .
What should be the sum of their ages ?

a) 41
b) 241
c) 121
d) 22
Some may live 130 years, though rare.
16. Which of the following divisions are/is wrong ?

I :1221/111 = 11    II : 6094/11 = 545
  III : 2709/44 = 61    IV : 3050/122 = 25


a) I , II and IV
b) II and III
c) II and IV
d) all
IV is obviously not wrong .
17. The operation 2711/44 = 61 is certainly wrong. In order to be divisible by 44 is divisibilty by 11 a prerequisite which is not satisfied.
If we think checking via the inverse operation we need to check 61x44=2711 and check, as seen in the figure below, implies correct result.
Which choice explains the reason behind this ?

!


a) check indicates correct result beacuse error is too great.
b) check indicates correct result because error is a multiple of 9.
c) check indicates false result.
d) check indicates false operation since the error is too big.
mod 9 count is blind to errors of multiples of 9.
y
18. The number 3A54A where A is a digit, is supposed to be divisible by 2,3 and 5. What must A be for a digit ?

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


a) 9
b) 5
c) 0
d) 8
Please have a look at ry1.
19. The monthly income of our family is $2200 .
Fixed expenses like rent and utility bills requires $750.
Which choice should we prefer if we want to give an approximate answer to the question "How much daily money in average do we have to spend for the other expenses ?" ?

a) 70
b) 50
c) 90
d) 110
We have $1459 for 30 days for the other expenses .
20. Which sign should replace the question mark in "305407 / 7 ? 41365" ?

a) =
b) <
c) >
d) approximately equal .
305407 > 7 x 42000 .
21. Which choice should replace A in "3009/5 > A > 5050/11" ?

a) 551
b) 703
c) 457
d) none
3009/5 is approximately 602 whereas 5050/11 is nearly 459 .
y
22. An Ottoman archives expert has seen the following division as he investigated. Which choice may give this division in an understandable modern format ?

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

RY1 RY2



a) 20025/35 = 779
b) 19725/25 = 789
c) 19775/15 = 799
d) 30320/30 = 305


The quotient does not have 1 at ones, many facts indicate this .
23. Which one of the following divisions has the least quotient ?

a) 251 : 110
b) 222 : 1570
c) 239 : 159
d) 100 : 39
220 < 1570 .
24. Which choice is the best approximate answer to "9999 + 100/99 - 10000 = ?" ?

a) 1.1
b) 10
c) 1
d) 0.1
100/99 is approximately 1.01 .
25. Zeynep has read 100 pages from the book "Karanlık Algısı" which has 382 pages. How many pages per day should she read if she desires to have completely read the rest in 6 days ?

!


a) 39
b) 53
c) 41
d) 47
282/6 = ?
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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