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FOURTH GRADE / MATHEMATICS / ADDITION of NATURAL NUMBERS 1.3

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

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

   ♦ 
METHOD(S) of DETERMINING the RESULT of
   ♦ COUNTING FORWARD from a given INTEGER  NAMED as ADDEND (SUMMAND)


 by an AMOUNT of  ANOTHER  GIVEN  INTEGER  NAMED AGAIN as ADDEND (SUMMAND).

    Ref.-1
 * There are diff. methods all doing the same .
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1.
!

All the kids are counting and adding, there may be sheep not shown at the image.
Which coding is certainly not decimal ?


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RY2



a) all
b) the one at the left
c) the middle one
d) the one at the right


The digits are the ones used in decimal coding ... .
2. In a test any addition to be performed should be quick and correct. The figure below indicates important issues.

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What may "mod" mean ?

a) abbreviation for mode.
b) made
c) eliminate any multiple of (3 and 9 in digit sums)
d) fashion
Eliminating multiples of 3 and 9 may help in checking .
Even-odd check is to be added. It works well for the last digit.
3. Working with decimal coding the basics of addition consists of;
a- knowing sum of the 9 digits with each other well.
b- if the addition of digits happens to be a two-digit number to carry the tens' place to the next column.
Where is it more likely to make an error ?

a) by carry
b) both
c) by addition of digits
d) nowhere
Orderly work prevents this error but we do not always work orderly.
4. How many sheep are there in the figure below ?

!



a) 22
b) 23
c) 24
d) 25
Dogs are no sheep and count also legs in case of decision difficulties.
5. What does the figure want to convey ?

!



a) 3+2 = 2+3
b) 3+2 = 5
c) 3 x 5 = 15
d) added are the same objects
Though bacgrounds differ the triangles are the same, but that is not what the fig. transmits.
6. A man wanted to buy 3 sheep, met the shepherd and agreed upon a price of $ 90 per sheep. They went together where the fold is and the man has chosen 3 sheep after a careful examination. Gave the shepherd $ 300 and waited for $ 30. None came.
-Will you not give me $ 30, we agreed upon price.
-No. What we agreed upon was the price for an average sheep; you have chosen the best!

What is the moral of this story ?

a) the shepherd is right.
b) be careful with abstractions.
c) the shepherd is unjust.
d) the man is a miser.
Number are abstraction, each is unidentifiable. Object are mostly identifiable.
7. Calculate the result of the following two operations mentally an check the appropriate answer.

I - 387 + 654 = ?       II - 938 + 644 = ?

a) 1021 and 1522
b) 991 and 1392
c) 1051 and 1782
d) 1041 and 1582
The first form of mental calculations is based upon digital expansion, use of any trick is not made, the number 387 is thought as 3x100 + 8x10 + 7
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8. What is the sum of all natural numbers from 1 to 1000 ?

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RY1 RY2


a) 500500
b) 510000
c) 490500
d) 496000
The second form consists of using a formula we have learned before. This sum is 500x1001 = 500x1000 + 500
9. 1001 + 9999 = ? .

a) 12 000
b) 11 000
c) 10 500
d) 11 500
Here we make use of the fact that 1 + 999 = 1 000
10. 1282 + 765 + 351 + 1453 + 535 + 147 + 1718 = ?

a) 6755
b) 5333
c) 6251
d) 5478
Here we have to reorder: 1282 + 1718 + 765 + 535 + 1453 + 147 + 351 = 3000 + 1300 + 1600 + 100 + 251 =
11. 1776 + 235 = ?

a) 2071
b) 2021
c) 3027
d) 2011
Here we can make use of something we already know. 1776 is the year of Decleration of Independence and we have heard of 235th anniversary of DoI in 2011.
12. 12700 + 4800 + 1.14 x 12750 + 6500 + 1500 = ?

a) 45635
b) 43050
c) 40035
d) 38750
Here we can reorder and make use of something we already know: ...= 12700 + 12800 + 1.14x12750 = 3.14 x 12750 is something around 40000 (we know the diameter and the perimeter of the Earth)
13. Check the following additions and find the right choice .

I: 243 + 447 = 691    II: 789 + 449 = 1238     III: 1453 + 1789 = 3242


a) only II and III are correct
b) only I is correct
c) only II is correct
d) all are correct
Addition of two odd numbers gives an even, I can not be correct .
1238 - 449 = 1249 - 11 - 449 = 800 - 11 = 789 and III similarly .
14. In case of 4+5 = 9 , 12 + 23 = 35 and 17 + 22 = 39 the digit sums of the summands and the sum are equal whereas in case of 5 + 6 = 11 and 17 + 24 = 41 they are not .

What is the reason behind ?

a) in case of a carry the equality of the digit sums does not hold .
b) if the digit sums exceed 9, they need not to be equal
c) it is just so
d) this is something random, no regular behavior
15. What is the amount of change of digit sums for a carry ?

a) 1 for each carry
b) 3 for each carry
c) 9 for each carry
d) 7 for each carry
... because a ten is transferred as a one .
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16. Which of the following additions can not be correct ?

I: 799 478 + 372 935 = 1 173 413     II: 543 685 + 219 458 = 763 143    
III: 471 935 + 257 309 = 729 244


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RY1 RY2



a) Only III
b) Only II
c) Only I
d) II and III
Checking the multiples of 9 eliminated digit sums we see I is incorrect and only one of the choices contains it .
17. Calculate the following additions and check your result. Which choice gives their results ?

I: 478 799 + 173 413 = ?    II: 219 458 + 763 143 = ?


a) 652 212 and 982 601
b) 652 232 and 982 611
c) 652 102 and 982 581
d) 602 212 and 972 601
18. Calculate the following additions and check your result. Which choice gives their results ?

I: 471 309 + 729 244 = ?    II: 763 458 + 219 143 = ?


a) 900 553 and 982 901
b) 1 100 553 and 972 601
c) 1 200 553 and 982 601
d) 1 140 553 and 882 601
19. A 2 digit number BA decreases by 9 if the digits of ones and tens are exchanged.
Which of the followings must be true ?

a) A = B - 1
b) A = B
c) B = A - 9
d) A = 9
Considering Bx10 + A = Ax10 + B - 9 we find 10x(B-A) = (B-A) - 9 i.e. B - A = 1.
20. What is the total amount of steel consumed in 2002 and 2008 ?



a) 600 metric tonnes
b) 600 million tonnes
c) 600 thousand tonnes
d) 400 metric tonnes
21. The sum of the three red lines corrersponds to a population of ... billions .



a) 28
b) 30
c) 18
d) 20
Red lines correspond respectively to 10 , 6 and 4 billions.
22. Referring to the figure, about how many billions should the overall world population have been ?



a) 51.2 billions
b) 70 billions
c) 71.2 billions
d) 110.5 billions
Accept that the average human life has been around 50 years and there lived an average population of :
Between 10000 - 5000 BC about 50 millions.
Between 5000 BC - 0 about 200 millions.
Between 0 and 1900 AC about 400 millions and
Between 1900 - 2000 AC about 3 billions.
Based on our assupmtions, between 10000-5000 BC there lived 5 000 million /50 x 50 = 5 billion human on Earth. And the others are resectively 20 billion, 15.200 and 6 billion .
23. How many additions in the following row are correct ?

845+456=1256    352+347=699    149+674=823    151+54=205


a) 2
b) 3
c) 4
d) 1
Use the followings :
Addition of an even and an odd numbers gives an odd number .
If the digit sum of the summands is a multiple of 3, the digit sum of the sum is also ...
24. Which one is incorrect ?

a) 845+345=1190
b) 769+677=1443
c) 551+554=1106
d) 355+732=1087
25. One of the rows is already an equality.
Which of the choices make the other two ?



a) 4+1+1 = 6 and [4-(4:4)]! = 6
b) (4-4:2)x3 = 6 and (3:3)x3! = 6
c) (3:3x3! = 6 and (4-4:2)x3
d) (3:3)x3! = 6 and [4-(4:4)]! = 6
Remember the def. of factorial and make use of it .
This is the feedback!
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© 2011 , Ä°smail GERMAN. ALL RIGHTS RESERVED
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