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FIFTH GRADE /MULTIPLICATION / 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 MULTIPLICATION of INTEGERS is (are)

   ♦ 
METHOD(s) of DETERMINING the RESULT of
   ♦ COUNTING FORWARD from ZERO by BLOCKS containing so many NATURAL NUMBERS called a MULTIPLICAND

   ♦ by an AMOUNT of ANOTHER GIVEN INTEGER NAMED again a MULTIPLICAND.

    Ref.-1
 * There are diff. methods all doing the same .
1. One of the numbers of the following clock is wrong. Which choice gives the correct one ?

!
a) 9!/99
b) 4!x3/2-9/9
c) 9!/9999
d) 99
5 is wrong. √(9!) is approximately 602 . 4!=1x2x3x4 .
9!/9999=6.0242
2. Bernd has been punished for not completing his creative writing homework. He has been given a choice of writing "creative" once every day for 5 months or writing 17 times "writing" every day for 2 weeks. How many letters will he write less if he choses the option of writing minimal amount of letters ?

!
a) 386
b) 322
c) 466
d) 416
creative has 8 letters and writing has 7. 1 month is 30 days will be assumed .
3. Fibonacci Numbers have the following properties:
♦ The first two of them are 0 and 1.
♦ Any consecutive is calculated as the sum of two numbers prior to it.
♦ They increase rapidly as seen in the figure.

What will the the product of first 9 Fibonacci Numbers be ?

!


a) 0
b) 65 520
c) 32 400
d) 550
The first 9 are 0, 1, 1, 2, 3, 5, 8, 13, 21, ... .
4. What will the product of the first 9 elements of the pattern be, if each element is obtained by subtracting the respective Fibonacci Number from the respective triangular number ?

!
a) 203 489
b) 489 280
c) 203 489 280
d) 203 489 280 489
The first 9 elements of the pattern : 1-0 , 3-1 , 6-1 , 10-2 , 15-3 , 21-5 , 28-8 , 36-13 , 45-21.
The multiplication is 1x2x5x8x12x16x24x23x24 = 10 x 2x3x4x(4x4x4) x 23x(6x6)x(4x4) which means it should be a multiple of 10.
5. For how many 2-digit numbers is the number equal to seven times the sum of the digits ?

a) 4
b) 8
c) 2
d) 6
10xA + B = 7xA + 7xB => 3xA = 6xB . So the first digit must be twice the second .
y
6. Pangonia has 12 major cities each of which is connected to each other via a flight line. How many different 2 consecutive flights are possible in this country among major cities ?

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



a) 110
b) 220
c) 78
d) 156


The first flight may have 11 paths.
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7. The average adult inhales and exhales something like 9 liters of air per minute. How many liters of air does this total in a day ?

a) 9 600
b) 12 960
c) 10 850
d) 8 840
A day is 24x60 minutes . 24x60x9 = 24x6x9x10 = 24x54x10 = 12x108x10 = (1080+216)x10 = ...
8. The air that is inhaled is about 20/100 oxygen, and the air that is exhaled is about 15/100 oxygen, so about 5/100 of the volume of air is consumed in each breath and converted to carbon dioxide. Therefore, a human being uses about 12960x5/100 = A liters of pure oxygen per day. Which choice is A ?

a) 868
b) 454
c) 648
d) 1246
= 12960 = 12900 + 60 => A = 5x129 + 3
9. We get about 0.5 liters of air when we inhale and there are about 300 000 oxygen molecules. How many oxygen molecules then we use per day ?

a) 22 660 000
b) 14 220 000
c) 16 880 000
d) 19 440 000


The answer of the previous question says we inhale 648 liters which means we inhale 648x600 000 = ... molecules 1/20 of which we use .
10. A cigarette needs about 10 inhales and an adult smoking 20 cigarettes/day inhales 200 cigarette smokes each containing 1.2 mg of nicotine.
What will the total daily dose of nicotine of this adult be ?

!
a) 110 mg.
b) 240 mg.
c) 300 mg.
d) 180 mg.
Really tooo much, would kill in a couple of minutes if injected directly into blodstream.
11. 2500 - 500 + 800 x (880-440+200) = ?

a) 212 000
b) 514 000
c) 344 000
d) 454 000
First is the multiplication due, that needs the evaluation of the paranthesis. It gives 640 and the multiplication is 8x64x1000. 8x64 you may remember ...
y
12. Tonight is an election. One of the 11 players of the team playing into the screen will be the captain and one the deputy. How many possible cases can you see ?


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

RY1 RY2



a) 220
b) 65
c) 180
d) 110
The captain can not also be the deputy .
13. Which of the following statements are true ?

I: If one of the multiplicands' last digit is 4, the last two digit of the multiplication happens to be a multiple of 4.
II: The multiplication of 10551 by 9 is obtained by adding a zero to the end of 10551 and adding 10551 to the result.
III: If one of the multiplicands' last digit is 8, the last three digit of the multiplication happens to be a multiple of 8.
IV: The multiplication of 169367 by 11 is obtained by adding a zero to the end of 169367 and subtracting 169367 from the result.

a) II and IV
b) I and III
c) all
d) I , III and IV
9 and 11 are interchanged.
14. If a number is multiplied by 11, we add a zero at the end and add tis to the number. Let the number for example be a 5-digit number which may be written as ax10000 + bx1000 + cx100 + dx10 + e . Multiplied by 10 (put a 0 at the end) it happens to be : ax100000 + bx10000 + cx1000 + dx100 + ex10 + 0 .
The addition of these two gives : ax100000 + (a+b)x10000 + (b+c)x1000 + (c+d)x100 + (d+e)x10 + e
What result do we get if we sum the coefficients of the places ones'place with plus sign, tens' with minus sign and then changing the sign at each consecutive place ?

a) 11
b) 1
c) 0
d) 111
+e -(d+e) +(c+d) -(b+c) +(a+b) - a = ?
15. Ali's age is a multiple of 11. Muhammet is a year younger brother of Ali and Muhammet's age is a multiple of both 2 and 5 .
What should the product of these two ages be ?

a) 91
b) 241
c) 110
d) 220
11 is a multiple of 11. Among multiples of 10 and 11 there is 10 and 11, 121 and 120, ... , etc. with a difference of 1 ?
16. Which of the following multiplication operations are wrong ?

I :1221x111 = 135531    II : 6094x11 = 5454   
III : 2709x44 = 6661    IV : 3050x122 = 372100

a) only II
b) I and IV
c) all
d) II and III
If a number is multiplied by 10, its number of places increases by 1.
17. The building in the figure below has dimensions 121 m. , 35 m. and 21 m. How big should its volume be in m3 ?

!


a) 88935
b) 88985
c) 88835
d) 89935
Finding the volume is generally a multiplication of the 3 dimensions i.e. 121x35x21 is being asked .
y
18. What can be said about the statement "In real use multiplication is more than a short way of addition." ?

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


a) it is correct
b) it is incorrect
c) it is indefinite
d) it can not be said
Addition is one dimensional whreas multiplication is multidimensional: 1 mm. x 1 mm. is 1 mm.2 , 1mm. x 1 mm. x 1 mm. is 1 mm.3 etc.
19. What will be the product of 5 consecutive numbers whose sum is 90 ?

a) 186048
b) 1860480
c) 1866480
d) 860480
First we have to find the numbers, the middle one is 90/5 = 18 .
20. Which natural number gives 130 if it is multiplied by 4 and 18 is added ?

a) 23
b) 26
c) 28
d) 112
Four times the number should be 112 .
21. The difference of a 3-digit number and its digits reversed form is 198. What will their product be if the number is the smallest of its kind ?

a) 55 009
b) 44 666
c) 66 008
d) 31 003
The difference is about 200 means the greater may have 3 at tens'. And of course 1 at ones'. The smallest of these numbers is 301.
Ax100+Bx10+C -Cx100-Bx10-A = 99x(A-C) gives that A-C =2 . If we get C = 0 we have contradiction. Taking C = 1 gives A=3 . The smallest of such numbers is 301 and its digits reversed form is 103 which satisfy the restriction.
y
22. What should the result of the following multiplication be ?

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

!
RY1 RY2



a) 6325
b) 6481
c) 3696
d) 9936


The rectangle may be 5 or 6 .
23. A 3-digit number and its digits written in reverse order form have a sum of 888. What should the maximal product of these numbers be ?

a) 343 234
b) 234 343
c) 136 197
d) 197 136
That the difference is a multiple of 99 we already know. Candidates of difference are 0 , 99, 198, 297, 396, 495, 594, 693, 792 and 891.
If the difference is 0, there are 9 possibilities:111, 222, 333, ..., 999. 444 satisfies the sum.
Odd differences does not give a natural number when the summation condition is also considered. Difference 198 gives 543 and 345. Difference 396 gives 642 and 246. Difference 594 gives 741 and 147. Here we have to remember that, among the numbers with a definite sum, the nearer the numbers the greater the product as in the case of the area of a square.
24. (100 000 - 1000)x(100 000 + 1000) = ?

a) 999900000
b) 9999000000
c) 99999000000
d) 5999000000
The first multiplicand is 1000x(100-1)=1000 x 99 . The product should be around 100 000 x 100 000 i.e. 10 billions.
1000x1000(100-1)x(100+1) = ? as (100-1)x(100+1) = 1002 - 12 = 9999.
25. What is the product of 10. and 15. triangular numbers ?

!


a) 5500
b) 3300
c) 6600
d) 7700
Being questioned is the product of the sum of integers from 1 to 10 and from 1 to 15 .
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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