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FOURTH GRADE / MATHEMATICS / MULTIPLICATION of NATURAL NUMBERS 1.2

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" RIGHT FOR YOU.
 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  INTE-  GER  NAMED again a MULTIPLICAND.

 IN CASE BOTH MULTIPLICANDS EQUAL, IT IS JUST A CHANGE OF UNITS.                     Ref.-1
y
1. Which of the choices is the result of multiplication of 333 by 33 ?

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

RY1 RY2



a) 10999
b) 10989
c) 11989
d) 11999


Please have a look at ry1 and ry2 . ry2 almost gives the solution.
2. 98x67 = ?



a) 6556
b) 5566
c) 5556
d) 6566
Check if the given digits are right ! .
3. 375 x 164 = ?



a) 615500
b) 60550
c) 61500
d) 625660
Check thee given digits; they may be false; this may be done on purpose .
4. Which errors are made in the following multiplication operation ?



a) There are coloring errors.
b) Thousands of the final sum and the shift contain errors.
c) both a and b is true.
d) all choices are true.
The question refers to operation errors .
5. D - C = ?


a) 5
b) 6
c) 11
d) not defined
2xCD = 76 .
6. Which choice gives the correct A, B and C (in this order) ?



a) 1, 8 ve 0
b) 0, 8 ve 1
c) 8, 1 ve 0
d) 1, 0 ve 8
If 5xC = C ise C is either 0 or 5. Since the choices have no 5 C is 0.
B should be an even number.
7. Which of the following multiplications has the greatest result ?

a) 765844 x 755463
b) 775844 x 745463
c) 785844 x 735463
d) 765844 x 735463
If sums are close to each other, look for the differences. The smallest difference ipmlies the greatest result.
8. How many of the following multiplications are wrong ?

I- 7x(8x5) = 5x(8x7) = 280     II- 15x7x9 = 105x9 = 945
III- 24x(3x5) = 12x30 = 360     IV- (6x48)x8 = 36x48 = 2704


a) 4
b) 3
c) 2
d) 1
Check especially IV, There are 3 multiplications in IV, take care.
y
9. Mr. Jetson's pedometer is defective, it skips the digits 8 and goes to 9 instead.
Failure of the electronic calendar is even graver, it skips both 3 and4 and goes over to 5 .
Within the week 1-7 May he walked the same distance every day and seeing the number 5780 on the display he got surprised. He questioned his copmuterized calendar for the average number of steps for the week and his surprise increased.
What should be the total number of his steps for the week really be and what should he has seen as the average number outputted from his calendar ?


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

RY1 RY2



a) 3332x7 ve 4595
b) 4284x7 ve 4495
c) 6120x7 ve 5495
d) 4750x7 ve 5555


Pedometer perceive nines as tens so the real value of his pedometer's 5780 is 5x9x9x9 + 7x9x9 + 8x9 + 0 .
Calendar counts 9 instead of seven so it gets 7 times 5780 and divides this by 9.
y
10. What is the product of A and B satisfying the following operation ?

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

RY1 RY2



a) 30
b) 6
c) 5
d) 24
There is 10 possible values for A. Take A=9 and evaluate AxB.
If the result is not proper, make A=8 and subtract 40 from the previous AxB product.
11.  46438754 x 889 = ?

a)  4128405236
b)  41284052306
c)  412840526
d)  41288052306
1000 x 46438754 - 111 x 46438754 may be easier to calculate !
12. Which is the easiest method of calculating  5544 x 24 =  ?

a) direct multiplication.
b) calculate 2x5544; multiply by 11 ; add the first.
c) calculate 2x5544 and twice this; add a 0 to the end of the first number; sum.
d) multiplication of 5544 by 100, division by 4 and subtraction of 5544.
a: 5544x24=22176+110880=133056
b: 110880+22176=133056
c: 11088+11088+110880=133056 .
13. A natural number is 4 times another and the sum of these is 625
What should be the product of these two numbers ?

a) 6250
b) 62500
c) 6500
d) 65000
They should be 125 and 500 .
14. The farmer Smith feeds his sheep in groups of 8.
If he gives from a sack 4 kg of fodder to each group there remains 11 kg. and if he gives 5 kg, to each group there remains 4 kg of fodder.
How many sheep should Mr. Smith have ?

a) 54
b) 55
c) 53
d) 56
Find first how many groups of sheep he has .
If he has 7 groups and the sack is 39 kg. the conditions are satisfied .
15. The equation 12x196xA = 196x10xB is valid.
If in addition A and B both are less than 100, what can be the maximum value of AxB ?

a) 7680
b) 96 x 96
c) 96 x 75
d) 8849
196 drops and the minimals of A and B are 10 and 12. .
16. John and Kent have a total of 45 walnuts.
If they share these 3 for John and 2 for Kent at a time, how many walnuts will John eventually have ?

a) 18
b) 27
c) 30
d) 40
nine shares will be made.
17. The result of a multiplication with one multiplicand being 7 and the other having an error, an exchange of ones and tens, is calculated as 896.
What would the error free result be ?

a) 812
b) 869
c) 182
d) 1274
7 x 128 = 896 .
18. What is the average of all natural numbers that are the sum of 3 natural numbers having a product of 36.?

a) 18
b) 34
c) 17
d) 10
You can easily guess that the average should be about 17-18 by having a look at samples.
1, 6, 6 and 2, 2, 9 are such having a sum of 13 and 13 will be used twice in forming the total.
First find all 3 numbers having a product of 36.
Then find the sums of these three numbers.
Then find the grand sum of cases.
Divide this grand sum by the number of the cases.
19. How many times the product of natural numbers from 1 to 5 gives the product of the natural numbers from 1 to 10 ?

a) 60240
b) 100240
c) 30240
d) 80240
6x7x8x9x10=... .
20. How many times the sum of natural numbers from 1 to 7 gives the product of the natural numbers from 1 to 7 ?

a) 180
b) 90
c) 108
d) 120
1+2+3+4+5+6+7=28
1x2x3x4x5x6x7=(2x6)x(3x4)x35 .
21. Erdal and his friends made a race etween Ankata and Istanbul and each completed the race with average velocities (km/hour) given in the figure below.
What is the average total distance Erdal's friends has made in an hour ?



a) 949
b) 948
c) 810
d) 809
The question refers to Erdal's friends; take care .
22. An hybrid race of Holstein cows gives just after birth milk according to the table given in the figure:

* within the first month (30 days) the average daily yield is 25 kg./day.
* for the next eight months the yield shows a decrease of 1 kg/day for each month.
* the last 3 months of the year the cow is not milked because a new offspring is expected.

How many kg.s of milk will the yearly yield of this race be ?



a) 5470
b) 5670
c) 1300
d) 930
1. Find first monthly yield by multiplying the given averages by 30 for each month.
2. For yearly yield find the sum of numbers from 1 to 25 and subtract the sum of from 1 to 16 .
23. A 150 m. long rope is divided into 5 pices each consequent one being 10 m. longer than its previous.
What will the total length of number of 50 of the longest piece be ?



a) 2300
b) 500
c) 1000
d) 2500
Remember that the sum of first 5 naturals gives 15 .
24. Referring to the figure below, which of the following statements is/are true ?

1. In the right part of figure the multiplication 172x896 is calculated.
2. All the figures are about a method of multiplication.
3. Numbers ( results of digit multiplications) are placed (into small squares left/right) based on their place values
4. Summations are done transversally.



a) 1 , 2 , 3 ve 4
b) 2 ve 3
c) 3 ve 4
d) 1 , 3 ve 4
The method is called cage (lattice) method and may be useful depending on the case.
172x896 = 154112.
The summation upper left is vertical.
25. Given the digits A and B with A21 x B11 = 109 931 . What should the sum "A + B" be ?



a) 4
b) 5
c) 13
d) 7
This is a case where the cage method is of some use. The tarnsverse yellow region has a sum A+B+2 = 9 ...
This is the feedback!

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© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
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