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SIXTH GRADE / NATURAL NUMBERS and BASIC OPERATIONS on THEM / TEST 1.3

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.

  THE NATURAL NUMBERS ARE
 ♦ 
JUST THE NUMBERS WE USE AS WE COUNT  SOMETIMES ZERO IS ADDED TO THEM FOR CONVENIENCE.
 ♦ THEY ARE A TINY PART OF REAL NUMBERS WITH A MEASURE OF ZERO.


TWO FACTS ARE OF IMPORTANCE:
1. THE 4 OPERATIONS DEFINED ON THEM ARE BASIC.
2. BASES ARE ESSENTIAL FOR EFFICIENT USE OF THEM.
1. Why summands should commute by summation ?

!


a) This is a property of summation.
b) By definition.
c) So should be the numbers.
d) Otherwise the lengths of the street measured different ways do not overlap.
The order of measurement and placement should not change the total length .
2. Why should summation of 3 or more numbers be associative ?

!


a) This is a property of summation.
b) Otherwise the lengths of the street measured different ways do not overlap.
c) By definition.
d) So should be the numbers.
Hangi iki kısmı önce ölçersek ölçelim sokağın toplam uzunluğu değişmemelidir, "bir/aynı" olmalıdır .
3. Why should multiplication be commutative ?

!


a) This is a property of multiplication.
b) By definition.
c) Otherwise the area of the rectangle would change depending on the order of measuement/replacement.
d) So should be the numbers.
Imdependent of the order of measurement and replacement, the area of the rectangle is to be the same .
4. Why should multiplication of 3 or more numbers be associative ?

!


a) So should be the numbers.
b) Otherwise the volume of the rectangular prism could change depending upon the base chosen .
c) By definition.
d) This is a property of multiplication.
The volume of a rectangular prism must be the same independent of the face taken as base .
5. Why should the multiplication be distributive (over summation) ?

!


a) Otherwise the sum of the areas of rectangles might not be the area of the total .
b) So should be the numbers.
c) This is a property of multiplication.
d) By definition.
The total area of the big rectangle should not be different from the total of the areas of the parts.
y
6. Jimmy has 3 tiles with the digits 0, A and B upon them. A and B are unknown but their sum is 10. He formed all possible 3-digit numbere formable with these tiles. What should be the sum of these 3-digit numbers ?

!


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



a) 2010
b) 1900
c) 2120
d) 2110


Have a look at ry1 but the prctical way of solving is to try to find the sum of all 3-digit numbers formable with , e.g. , 0, 2 and 8 .
Having had a look at ry1, you must have seen the number is the sum is the sum of 10x1 , 10x10 and 20x100 .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which of the followings is equal to 83 x ( 17 - 14 + 23) ?

1- 83 x 26
2- 83x17 + 83x9
3- 83x17 - 83x14 + 83x23
4- 83x3 + 83x23

a) only 1
b) 1 and 4
c) 3 and 4
d) all
Each one is 2158 .
8. What should be if 21 x ( + 17) = 21 x 17 + 21 x 5 ?

a) 21
b) 17
c) 5
d) 15
Remind you of the distributivity .
9. Aaaron and Nathalie play together a computer game. At the first level Aaron got 1785 and Nathalie got 1994 points. At the 2nd level NAthalie got 1785 points and their points equaled. How many points should Aaron have got at the second level ?

!


a) 2010
b) 1994
c) 2012
d) 1998
Remember the commutativity .
10. If 21 + ( + 17) = + , = ?

a) 38
b) 75
c) 57
d) 46
First add the given numbers .
11. For which operation may the following partly given table be ?

!


a) -
b) :
c) +
d) x
The existence of an absorbing element is observed .
y
12. The hudreds of a 3-digit number is increased and the tens decreased by 6 and the number obtained 2 less than thrice the original number. What should be the product of the digits of the original number ?

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

RY1 RY2



a) 17
b) 14
c) 21
d) 12
Here is 1 unknown, the number, and to consider this fact is right. Let the number be S. It is increased by 600 and decreased by 60 which means a net increase of 540. The relation is S + 540 = 3xS - 2 i.e. 2xS = 542 . Have also a look at ry1 .
13. Which of the followings may A be if A and B are digits and (A-2)x(B-3) = 5 ?

a) 3 and 5
b) 3 and 7
c) 2 and 3
d) 2 and 7
5 is prime and its factors may only be 1 and 5 which means A-2 should be either 1 or 5 .
14. Reilly the junior's piggy bank had 8 cents at 31st of July and he decided to spare every day thrice the money his bank has in, beginning with August the 1st. How much should he spare on 5th of August ?

a) 4466 cents
b) 3124 cents
c) 6144 cents
d) 1712 cents


The amounts he should have spent every day : 1st of August 24 cents; 2nd of August 96 cents; 3rd of August 384 cents and 4th of August 1536 cents ...
15. Ali took 5 math exams in a year and from the first one she got 70. From even numbered exams he got 15 more relative to the previous and from odd numbereds she got 10 less than the previous. Which total did she get from these 5 exams of the year ?

a) 375
b) 380
c) 400
d) 350
Grades: 70, 85, 75, 90 and ...
16. Which of the followings is/are supposed to be an even number if A, B and C are ?

1- (A+B+C)/2
2- A.B.C/2
3- (A+B+C)/3
4- A·B·C/4

a) all
b) 1 and 3
c) 2, 3 and 4
d) 2 and 4
2+6+8 = 16 and 16/3 = ... 2+2+2=6 and 6/3 = ... .
17. Which of the following operations is/are correct ?

1. 404 · (5 + 8) = 5252
2. (307 – 207) : 5 + 4 = 30
3. 161 : 23 + 420 : 60 = 12
4. 161 - 488 : 8 = 110

a) only 1
b) 1 and 2
c) 2 and 3
d) 1, 2 and 3
4x101x13 = 13x404 = 4040 + 1212.
y
18. A and B are two natural numbers. If tens' of each is increased by 1 and ones' of each by 2, the product of these increases by 528. A+B = ?

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


a) 44
b) 27
c) 35
d) 32
Have please a look at ry1 .
19. A and B are nonzero natural numbers and A/8 + B = 16 is valid. What may be the max. value for A ?

a) 16
b) 120
c) 64
d) 128
A happens to be max. when B is min. .
20. Which is the biggest attainable number by using exactly 3 number from the ones seen in the figure below ?

!


a) (29+15)x29
b) 29x(19+15)
c) 29x19x15
d) 29x(19-15)
3 different numbers are to be used .
21. In which of the following equations may the ♦ not be replaced by 17 ?

1- (8:2)·(20-♦) = 52
2- 8·(30-♦) = 240 - 8x♦
3- 8·(40:10-♦:17) = 8x4 - 8
4- 8·(30-♦) = 104

a) 1
b) 2
c) 2 ve 3
d) 1 ve 4
4x3 = 12 .
y
22. ABCD and ACBD are 4-digit numbers. What will be the difference of the digits B and C if the difference of these numbers is 630 ?

!


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

RY1 RY2



a) 5
b) 7
c) 8
d) 4


asume ABCD is the bigger. Expand the numbers in the form 1000xA + 100xB + ... ... If nec. have a look at ry1.
23. Which choice of signs make (545 � 5) � 11 � 9 = 41 a valid equation ?

a) + , : ve -
b) - , - ve x
c) : , - ve x
d) x , - ve x
Signs of 4 basic operations are meant .
24. How is the number 930 to be attained using the prime numbers in the green region ?

!


a) (17+31)· 13
b) (17+13)· 31
c) (43+31)· 7
d) (43+7)· 31
Exact 930 ... .
25. What is the total of the numbers in the green region of the previous question ?

a) 255
b) 128
c) 156
d) 342
3+5+7+13+17+31+37+43 = ?
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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