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FIFTH GRADE /MULTIPLICATION / 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.

 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. How many of the following multiplications are wrong ?

390944x728=284607233   321x436=139956
  555x660=366310   770x111=85470


a) 1
b) 2
c) 3
d) 4
If both multiplicands even, multiplication should also be ... .
555x660 = 111 x 110 x 5 x 6 = 111x110x30 should have double 0's at the end.
2. What will 6xA be if [(1+9)x(1+9) + (Ax6-25)] = 120 - (1+12) + 10 ?

a) 6
b) 42
c) 7
d) 24
The simplified form is 75 + 6xA = 117
3. What should the digit A be, if 1421 = 2A x 4A ?

a) 1
b) 5
c) 8
d) 9
A x A = 1 , 11 , 21 , 31 , 41 ... if A is equal to 1 and 9. Looking at the numbers the problem is solved at this point. But have a look at the 2nd "y" for future convenience .
1421 has a digit sum of 8 . The digit sum the product is (2+A)x(4+A) = 8 + 6xA + AxA. This means A should be a multiple of 9.
4. Which figure may be a (correctly applied) check for 1286 x 304 = 390944 ?

!


a) upper left
b) upper right
c) lower left
d) lower right
Multiplication is repeated summation in a sense. By summation we know the digit sum of the summands must be equal to the digit sum of the sum if no carry is done. In case of carry mod 9 summation (casting out nines) should work because the change then is a multiple of 9 (i.e. carrying a ten from ones' is putting a 1 to tens' which is an effective change of 9 in digits' sum). So casting out nines we may chack our multiplications up to a multiple of 9:
a- mod 9 sum of the digits of one of the multiplicands is put into say right of the cross.
b- mod 9 sum of the digits of the other multiplicand is written into left then.
c- These two are multiplied and mod 9 sum of the digits of the result is written into the top.
d- Mod 9 sum of the digits of the result of the original multiplication is written into the bottom.
Check is OK if the digits in top and and bottom are equal.
5. If casting out nines as a check is done correctly, which further check is of no use ?

a) checking "if one multiplicand is a multiple of 5, the result of multiplication is a multiple of 5."
b) checking "if one multiplicand is a multiple of 4, the result of multiplication is a multiple of 4."
c) checking "if one multiplicand is even, the result of multiplication is even."
d) checking "if one multiplicand is a multiple of 3, the result of multiplication is a multiple of 3."
Checking "if one multiplicand is a multiple of 5, the result of multiplication is a multiple of 5." is of no further use because any possible error is a multiple of 9 .
y
6. One or both factors of multiplication may be negative. 5x(-5) must be -25 and this is understandable because it means 5 consecutive summation of negative five.
It is a little bir harder to understand (-5)x(-5)=+25. Which of the following statements describes best the reason of this positive sign ?

I : Positives and negatives are subjective and relative. The signs should be symmetrical.
II : (-5)*(-5)= -[(5)*(-5)] proves already that the sign is positive .
III : Multiplied "-" signs do naturally give "+" sign as a result.
IV : 25 = 5x5 = (7-2)x(7-2)= 49 - 14 - 14 ? 4 = 21 ? 4 requires a "+" sign instead of "?" to be consistent.
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) IV
b) II
c) III
d) I


Have a look at ry1 also .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. How many of the following statements are correct ?

  I : For the result to be odd, both multiplicands need to be odd.
  II : If 20 multiplications are performed one after another, the probability of an odd result is fifty-fifty.
  III : If one multiplicand has a 5 at ones', the result should also have.
  IV : "The most probable error to be done during multiplication is forgetting a carry." is an objective judgement.
  V : There is only a unique method of obtaining the result of a multiplication.
  VI : Ones' of the result can be a one only if both multiplicands have 1 at ones' .

a) 5
b) 1
c) 4
d) 3
I is certainly ... .
8. What can be the maximum sum of two natural numbers whose product is 36 ?

a) 13
b) 20
c) 37
d) 120
The factors (multiplicands) of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 . Constant product gives max. sum if facors differ as much as possible.
9. How can ve evaluate multiplication of 33333333 x 405307984 with a calculator whose keypad has a corrupted "3", without any division operation ?

a) by multiplying the second by 44444444 and 11111111, and finding the diference of results.
b) by multiplying the second by 44444444 and 22222222, and finding the diference of results.
c) by multiplying the second by 44444444 and 11111111, and subtracting the smaller from the bigger.
d) by multiplying the second by 44444444 and 11111111, and adding the smaller to the bigger.


Subtraction is necessary and it should be done the right way .
10. Which is the best method of calculating the multiplication of the previous question by hand ?

a) 405307984 x 3 x 11
b) 405307984 x 33 x 11
c) 405307984 x 3 x 33
d) 405307984 x 3 and shifted sum
Multiplication of the second nu. by 3 once, is enough.
11. (2500 x 5 + 28) x ( 88 x 44 + 1) = ?

a) 48520944
b) 4852094
c) 8520944
d) 485209441
First are multiplications due: 2500x5 =12500 , 88x44 = 352 x 11 = ... .
y
12. The to a definite degree abstracted operations of mathematics may often have corresponding situations in real life. Which of the following figures may geometrically correspond to the arithmetic operation (7-2)x(7-2)=25 ?


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

RY1 RY2



a) I
b) II
c) III
d) IV
Have please a look at ry1 .
13. Per capita GNP (Gross National product of Mandinia is $4500. How big should its GNP be if it has a population of 35 000 000 ?

!


a) $175 500 000 000
b) $177 500 000 000
c) $157 500 000 000
d) $57 700 000 000
Just multiply the given numbers.
14. The highest waterfall on Earth is Angle Falls in southeastern Venezuella with an approximate height of 1000 m. The potential energy of 1 kg. (mass) of water at any/this height is given by the formula P = massx10xheight in terms of Joules. Find please this potential energy .

!


a) 1 000 J
b) 10 000 J
c) 9 000 J
d) 11 000 J
1x10x1000 = ?
15. Joule/second is called Watt, from James Watt. If a 10 Watt lamp burns for 10 seconds the energy used by this lamp (in this amount of time) is 10 W x 10 s. = 100 J.
What is the energy used by this lamp in 2 minutes ?

!


a) 120 J
b) 600 J
c) 1 200 J
d) 2 400 J
2 minutes are 120 seconds. Just multiply 120 by 10 .
16. A dry bulk cargo barge is designed to carry 440 t. of freight. 500 containers each having 750 kg. have been loaded. How much load can still be loaded ?

!


a) 75 t.
b) 65 t.
c) 120 t.
d) 85 t.
500x750 = 750 000 / 2 but tons are in question .
17. The map is about human history. The numbers in red regions are dates of human arrival to respective points. "k" means 1000, 60k means humans began to live in the neighborhood about 60 000 years ago.
The blue numbers are practically distances. They, with accompanying factors like climate, should somehow be correlated with the dates of arrival.
What is obtained if the dates and distances are multiplied and the average is calculated ?

Note : The distance from 65k point to 60k point is unity.

!


a) 162.5
b) 175
c) 87.5
d) 155
(60x1+40x2.5+50x3.5+45x6+16x10+15x14)/6 = ? .
y
18. The average height of Turkey may be taken to be 1000 m. , the average rainfall may be taken as .1 m. and the surface area as 750 000 000 000 m2. What amount of potential energy corresponds to these values ?

Note: For each square meter there is 100 kg. of water.

!


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


a) 75 000 000 000 000 000 J
b) 75 000 000 000 000 J
c) 7 500 000 000 000 000 J
d) 7 500 000 000 000 J
Just multiply the numbers: 1000 x 100 x 750 000 000 000 = ?
19. The product of Archimedes' mass (100 kg.) and the length of long enough lever ( 60 000 000 000 000 000 000 000 m.) gives the mass of the Earth as kg . In which choice is it given ?

!


a) 6 000 000 000 000 000 000 000 000 kg.
b) 6 000 000 000 000 000 000 000 kg.
c) 60 000 000 000 000 000 000 000 kg.
d) 600 000 000 000 000 000 000 000 kg.
It is a matter of counting 0's carefully. The right answer should have 22+2 = 24 zeros.
20. A 4-digit number having a digits sum of 8 is supposed to be symmetrical. What will be the product of all possible numbers with the cited properties ?

a) 11 941 757 928
b) 11 841 757 928
c) 11 841 777 928
d) 11 841 757 908
The number should have the form ABBA with A+B=4. Cases are : 4004, 3113 and 2222 .
Masters are supposed to calculate the product of these 3 numbers via the most efficient way. 4004x2222=8008x1111=8888000+8888=8896808. You only need to multiply this number by 3 and ... .
21. What will be the value of the right side of the equation in the figure if A=375, B=1375, C=10553 and D=553 ?

!


a) 4 777 750
b) 4 717 770
c) 4 717 950
d) 4 717 750
AxC+BxD=375x10553+1375x553 .
y
22. A single turbine may have an power producing capacity of 150 MW. What power can be produced by 250 turbines of this capacity ?

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

!
RY1 RY2



a) 75 GW
b) 37.5 GW
c) 137.5 GW
d) 175 GW


M stands for mega and means 1 million and G stands for giga and means 1 billion . ry1 is just for knowledge, helps not.
23. What is the following figure trying to tell ?

!


a) 10x(10+8) = 10x10 + 10x8
b) 10x(10+9) = 10x10 + 10x8
c) 10x(10+9) = 10x10 + 10x9
d) 9x(10+8) = 10x10 + 10x8
The distribution of "x" over "+".
24. The building in the figure below is a 26-storey building; there corresponds to every storey a letter of the english alphabet. So sind the storeys also coded, the first storey is coded with A and the last is with Z, all others in between within the right order.
The janitor has been in early morning to 5 storeys, four of them make the word "TRAP" and the fifth is unkown but the product of corresponding numbers of storeys is recorded and later found out to be 5760.
Which of the choices may be the code of the 5th storey ?

!


a) A
b) T
c) W
d) F
A corresponds to 1, P to 16, R to 18 and T to 20.
25. What is the product of the 3 (Fibonacci?) numbers shown in the figure below ?

!


a) 124 629 568 802 729 635 160
b) 114 629 568 802 729 635 160
c) 114 629 568 802 729 635 360
d) 114 629 568 852 729 635 160
832040x5702887x24157817 = ? Make check(s) and find !
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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