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FOURTH GRADE / MATHEMATICS / SUBTRACTION of NATURAL NUMBERS 1.1

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

 (METHODS* of) SUBTRACTION of INTEGERS  (are) is

   ♦ 
METHOD(s) of DETERMINING the RESULT of
   ♦ COUNTING BACKWARD from a given INTE-  GER  NAMED as MINUEND

   ♦ by an AMOUNT of  ANOTHER  GIVEN  INTE-  GER  NAMED as SUBTRAHEND.

    Ref.-1
 * There are diff. methods all doing the same .
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1. If we go upstairs from the ground floor of a bulding first by 5 steps and then by 7 steps we find ourselves on the 12th step. By the way, the order does not make any difference; the result will be the same if we go up first by 7 and then by 5.
The same is not true for going up and down. In that case we have some restrictions:
I- We can not go down from the ground floor unless there is at least a basement.
II- The order makes a difference; no problem if we go first 7 steps up and then by 5 down (will be on the 2nd step) but if we change the order we need again a basement.
Making abstarctions from this concrete case, what can be said about the subtraction (binary) operation ?

a) The definition of subtraction contains factual errors.
b) Subtraction is defined for all natural numbers and a natural number is attained as a result.
c) To get the subtraction defined for all members the set of natural numbers needs to be extended.
d) Subtraction operation is hard to perform.
A similar situation arises when we want to subtarct seven matches from 5 matches.
We have to borrow two matches in order to realize the operation and what we borrowed is our liability, i.e. something negative from our point.
Negative numbers should be added to the (set of) natural numbers.
y
2. In case of subtracting many-digit numbers, how do we subtract greater numbers from the lessers having the same place values ?

a) From the place neighbor-left we borrow an amount of "1 x place value" .
b) Such a subtraction can not be done.
c) We exchange the numbers.
d) We subtract the lesser from the greater.
Here we borrow from inside, from the number's self . Handling the numbers like digits, we are always to remember their place values.
3.  One property of subtraction is that the sum of subtrahend and difference gives back the minuend.
The property given above implies that ... .

In case of need for tips or help, please get the mouse on "y" or click on "ry1/2 (ry2 exists)".

RY1 RY2


a) The sum of minuend, difference and the subtrahend is half of minuend.
b) The sum of minuend, difference and the subtrahend is twice the minuend.
c) The sum of minuend, difference and the subtrahend is thrice the minuend..
d) The sum of minuend, difference and the subtrahend is 4 times the minuend.
Please look at ry1 and ry2.
4.  The minuend of a subtraction operation is greater than the subtrahend by 2 .
What is to be said for the difference ?

a) can not be determined
b) is 4
c) is 2
d) may be any positive integer.
5. What is the difference between the least 6-digit and the greatest 4-digit numbers ?

a) 1
b) 11
c) 9991
d) 90001
They are 100000 and 9999 !
6. The number 101 is greater than the number 99; to find their difference is child play for us.
To realize the operation the regular way is little bit harder, we need to borrow twice.

Which figure below seems to correspond to the operation mentioned above ?



a) figure above.
b) figure below.
c) both of them.
d) both may correspond.
Depending on color being counted as an identfying property or not, both figures may or may not correspond to the abstraction.
In the abstract case evry and each "1" has the same properties and they are completely exchangeable.
7. Two operations below are incorrect.

I- 4753-3828=925    II- 14359-8685=5674   III- 3957-5345= 1388    IV- 7498-5639=1849

Which choice below indicates these two ?

a) I and II
b) II and III
c) III and IV
d) II and IV
Check first : Sign , even-odd , dismissing multiples of 3 in digit-sums.
y
8. The result of a subtraction is given as 128.
In case 30 is subtracted from minuend and 23 is added to the subtrahend the new difference will be ... .

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

RY1 RY2


a) 135
b) 121
c) 181
d) 75
please refer to ry1 .
9. Which number has the property that 60% of "thrice of it and 40" minus 50 is 100 ?

a) 35
b) 70
c) 105
d) 200/3
60% of thrice of it = 150 .
60% is 150 means whole is 250 (250*60/100 = 25*6 = 150) .
Thrice of the number = 210 .
10. What is the difference of the least 6-digit odd number having all digits different and greatest 4-digit even number ?

a) 92347
b) 92348
c) 113458
d) 113459
11. A similar relation to the relation between multiplication and summation exists between division and subtraction.

Which of the choices gives the corresponding divison operation to the subtraction 55 - 6 - 6 -6 - 6 - 6 - 6 - 6 - 6 - 6 = 1 ?

a) 55/6 = 9 and the remainder is 1
b) 55/9 = 6 and the remainder is 1
c) 55/9 = 6
d) 55/6 = 9
Division means finding how many times a number is to be found in another number, i.e, how many times it can be subtracted and what remains.
12. Which of the followings has the least difference ?

a) 349 - 223
b) 562 - 441
c) 883 - 761
d) 1751 - 1639
13. Answer this question and the consequent 2 by referring to the fig. below.

What will be the result of subtracting all of the blue numbers from the red number ?



a) 366
b) 281
c) 279
d) 359
14. What is the difference of the sums of brown-rimmed and orange-rimmed numbers ?

a) 2010
b) 1100
c) 1010
d) 1095
15. What is the difference of the sums of green-rimmed and yellow-rimmed numbers ?

a) 166
b) 176
c) 165
d) 185
y
16. In which of the 4 binary operations the change of the places of the operands does not effect the result ?

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

RY1 RY2



a) addition
b) addition and subtraction
c) addition and multiplication
d) addition, multiplication and division
please refer to ry1 .
17. 37943794379437943794379437940 - 7356735673567356735673567356 = ?

a) 30587058705870587058705870584
b) 75887588758875887588758875880
c) 30557055705570557055705570554
d) 77447744774477447744774477447
The ones should have a 4, i.e. two choices.
The question remaining is if tens has a 5 or 8.
18. The easiest way to answer the operation " 8056 - 497 = ? " is ... .



a) to add 3 to both of the operands and solve 8059 - 500 = ?
b) to borrow from the left-neighbor as in the figure's left.
c) to follow the way given in figure's right.
d) to use the formal method.
19. Which choice is the result of 8000008 - 2202020 = ?

a) 5777972
b) 5700008
c) 5700012
d) 5797988
Ones must be an 8 .
20. Which is the easiest way of calculating the result of 8000008 - 2002020 = ?

a) the formal way of subtraction.
b) to subtract 2 millions from 8 millions.
c) to subtract 2 millions from 8 millions, then subtract 2 thousands and then subtract 12, all mentally .
d) "a" or "c" depending on the self assessed mental capability.
The easiest way is of course c, if the subject has a memory good enough.
21. What will be the result of summing all consequent integers from 1 to 20 with interchanging signs ?
(i.e. 1-2+3-4+5-6+7-8+9-10+11-12+13-14+15-16+17-18+19-20 = ?)

a) 20
b) -10
c) -20
d) 0
Have to see that there exist 10 couples each giving a result of -1.
22. What will be the result of summing all consequent integers from 1 to 30 under the restriction that the numbers divisible by 5 (without remainder) will have a minus sign ?
(i.e. 1+2+3+4-5+6+7+8+9-10+11+12+13+14-15+16+17+18+19-20+21+22+23+24-25+26+27+28+29-30 = ?)

a) 255
b) 360
c) 465
d) 423
sum first from 1 to 30 via n(n+1)/2 and then subtract 10 times the sum of numbers from 1 to 6 .
23. 111 111 111 - 99 999 999 = ?

a) 11111112
b) 11111111
c) 11111110
d) 22222222
remember that 99 999 999 + 1 = 100 000 000 .
99 999 999 + 1 = 100 000 000 olduğu gerçeğini kullanınız.
24. 888888888888888 - 99999999999999 = ?

a) 777777777777779
b) 888888888888889
c) 788888888888889
d) 99999999999999
may seem complicated at first look, but similar to the previous question .
25. A cargo ship has 80 000 tons of load. In a port it discharges an amount of 29 400 tons and charges an additional load weighing the same as 1/2 of the after discharge staying load .
How many kg. of weight reduction must have occured ?

a) none, the load increases.
b) 3,100
c) 310,000
d) 3,100,000
It must have taken an additional load of 25 300 tons .
Take care of units ton-kg.
This is the feedback!
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