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FOURTH GRADE / MATHEMATICS / MULTIPLICATION of NATURAL NUMBERS 1.1

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" RIGHT FOR YOU.
 Methods 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
1. 17+17+17+17+17+17+17+17+17 = ?

a) 153
b) 163
c) 157
d) 172
9x17 is being asked and to find 10x17 and to subtract 17 from it is the easiest way.
2. 54x5 = ?

a) 170
b) 264
c) 270
d) 360
Multiply by 10 (add a 9 to right) and get half of this result .
3. Which multiplication gives the greatest result ?

1: 17387 x 49        2: 17387 x 54        3: 17387 x 12        4: 17387 x 15

a) 3
b) 4
c) 2
d) 1
If one of the multiplicands is the same, the greatest result is obtained with the greatest of the other mult.
4. Which multiplication gives the greatest result ?

1: 1052x123        2: 282x156        3: 9x18963        4: 25x16745

a) 1
b) 2
c) 3
d) 4
The result of the last choice is about 500000 .
5. Which multiplication gives the greatest result with the restriction that the sum of the multiplicands is the same.?

a) 1787343 x 312657
b) 1500000 x 500000
c) 1000000 x 1000000
d) 1250000 x 750000
The closer the multiplicands , the greater the result . The square has the greatest area among rectangles having the same circumferences.
6. The elements of a multiplication has the followings:
I- One of the multiplicands is 5 times the other.
II- Sum of the multiplicands is 120.
Which choice gives the result of this multiplication ?

a) 200
b) 2000
c) 1600
d) 2500
If 5xA+A=6xA=120 then A = 20 and ...
7. Evaluating the multiplication "16x250=?" mentally, which is to be preferred ?

a) Take a quarter of 16 and add "000" to the end.
b) Find the quarter of 250 and multiply by 16.
c) Find the half of 250 and multiply by 32.
d) Do regular multiplication.
The addition of "000" to the end means mult. by 1000.
Multiplying one of the multiplicands by a number and dividing the other by the same number does not effect the result of a multiplication.
8. A bus travels with an average speed of 50 km./hour for 4 hours and then 60 km/hour for 5 hours.
What is the total travel distance of the bus ?

a) 480
b) 450
c) 400
d) 500
50 x 4 + 60 x 5 = 50 x 4 + 50 x 5 + 50 = 50 x 10 .
9. What may be the value of b , if in "8b5b" the product of place values of "b"s is 2500 ?

a) 3
b) 4
c) 5
d) 6
Trial and error is a plausible way of solving .
10. A driver driving with an average speed of 70 km/hour sees the plate "Wellington 60 km" after a drive of 7 hours.
How long should the distance between the starting point of the car and Wellington via the path of this driver be ?

a) 550
b) 450
c) 490
d) 560
Depending on the specific way, the distance may cahnge .
11. 248163264 x 27 = ?

a) 6700808128
b) 6700408128
c) 6700406464
d) 6700806464
Think as 200000000x27 + 40000000x27 + 8x000000x27 + 160000x27 + 3200x27 + 64x27 .
12. 888888 x 44 = ?

a) 39121072
b) 39211072
c) 38111072
d) 39111072
Treat as 111111 x (11 x 32) .
13. Claus wants to check his result in a relatively easy way after he has multiplied two relatively big numbers. Which of the followings would you advice him to do ?



a) Only the method given left.
b) The methods given right.
c) All of the 3 checks given.
d) None.
İkinci yöntemin nasıl çalıştığını anlamak kolaydır, uygulanabilir ve oldukça iyi bir denetim olur.
14. Which method must have Claus used to check the multiplication given in the figure and is this use well applied ?



a) drop multiples of nine, yes
b) drop multiples of nine, no
c) drop multiples three, yes
d) drop multiples of three, yes
All multiples of nine including nine itself, should be dropped.
The use of rules should be done strictly.
15. A school-boy used 7x9=63 instead of 6x9=54 and miscalculated 1426 x 1329 as 1895163. Please answer the followings :

1. What result is obtained if dropping the multiples of 9 is applied ?
2. Why ?
3. Which additional check can be applied ?

a) result is OK , the error is a multiple of 9 .
b) result is OK , the error is a multiple of 9 , one of multiplicands even-result even.
c) result is OK .
d) result is OK , the error is a multiple of 9 , dropping multiples of 3.
Dropping multiples of three is of no use because 9=3x3 .
16. Which relation should be valid between the digits A and B if ABxA = 11xAxA ?

a) A=B
b) A=2xB
c) A=3xB
d) 2xA=B
Since AB = 10xA + B , AB x A = (10xA + B)xA = 10xAxA + BxA . This is given to be 11 x A x A which ipmlies B = ...
Exapmles : For A=B=2 the equation is 22x2 = 11x2 and for A=B=3 it is 33x3 = 11x3x3
17. The non covered tribune of Jaffa Stadium has 47 tiers each having 275 seats. During a game between Jaffa and Tripoli this tribune was quite filled and had only 350 seats empty.
How many viewers should have watched this match from the mentioned tribune ?

a) 7400
b) 13540
c) 15460
d) 12575
275x47 - 350 = ? .
18. The turkish alphabet contains 29 characters. The last ten of them are p , r , s , ş , t , u , ü , v , y and z.
Which 4 of these 29 characters has the max. result in case order numbers are multiplied and what is the result of this multiplication ?

a) ü , v , y ve z ; 21924
b) ü , v , y ve z ; 491400
c) ü , v , y ve z ; 570024
d) u , v , y ve z ; 491400
26x27x28x29 = ? .
19. The new Ataturk Culture center of Istanbul will be a 50 store building with 24 windows at each side of each store.
What will be the total number of windows ?

a) 1200
b) 2400
c) 4800
d) 9600
50x24 will be the number of windows at one side .
20. Which of the choices gives A if 79x17x45 = 237xAx15 ?

a) 17
b) 16
c) 170
d) 15
237 = 79 x 3 ; 45 = 15 x 3 ... .
21. What should the value of the digit A be , if 14A x A4 = 7830 ?

a) 0
b) 5
c) 15
d) 8
According to ones, A is either 5 or 0 .
22. A cheque (check) of value of $ 40 000 is cashed by 4 cents of loss for each $.
What will be the value of cash ?

a) 35000
b) 39000
c) 38400
d) 36000
400x96=?
23. Which one of the following multiplications is incorrect ?

a) 254x7=1788
b) 141x9=1269
c) 387x4=1548
d) 551x8=4408
First apply the check given in Q. 13 .
24. 12-8x4+1535x7=?

a) 10745
b) 10735
c) 10730
d) 10725
Evaluate first the multiplications .
y
25. What should the sum A+B be , if the equality 14A x A4 = 783B is valid ?

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

RY1 RY2



a) 8
b) 7
c) 6
d) 5


Have please a look at ry1 .
This is the feedback!
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