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SIXTH GRADE / NATURAL NUMBERS and BASIC OPERATIONS on THEM / TEST 1.2

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. A and B are two natural numbers whose sum is eleven. What is the greatest possible product of these numbers ?

!


a) 27
b) 30
c) 40
d) 35
As the figure happens to be more square-like, the area gets bigger .
2. The areas of the rectangles given in question-1 are plotted in the figure below. If we consider the increments of the areas from left to right, which of these increments give a natural number after division by 4 ?

!


a) 1., 3., 8. and 10.
b) 8. and 10.
c) 1. and 3.
d) all
First increment is eight, from ten to eighteen. 8/4 =2 which is a natural number.
The increments after the maximum are negative and ...
3. What is the minimum possible product of two natural numbers whose sum is 101 ?

a) 1000
b) 100
c) 500
d) 50
One of the factors should be the smallest natural number (no 0) .
4. What is the maximal sum of two natural numbers whose product is 120 ?

a) 361
b) 43
c) 62
d) 121
120 = 1x120 = 2x60 = 3x40 = 4x30 = ...
5. A, B, C and D of the following figure are digits and products across the diagonals are (Ax4xC and ...) 36. Which prime factors are possible for AxC and BxD ?

!


a) 1, 3 ve 9
b) 1 ve 3
c) 3 ve 9
d) 3
Both AxC and BxD should be 9. Factors of 9 are 1, 3 and 9 ...
y
6. A, B, C and D are different digits and products across the diagonals (Ax?xC and ...) are both 60. Which digit that may replace ? produces the highest no of choices for A ?

!


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



a) 5
b) 4
c) 8
d) 6


If 5 is placed instead of ?, AxC and BxD must both be equal to 12 .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which of the following statements is/are true ?

1- For any two natural numbers 'A' and 'B', A*B = B*A and this is called commutativity property of multiplication of natural numbers.
2- For any natural numbers 'A' , 'B' and 'C', (A*B)*C = A*B*C and this is called distributivity property of multiplication of natural numbers.
3- An identity element, for some particular operation, returns the input unchanged. For example, for multiplication, the identity element is 0, because a * 0 = a .
4- The result of combining an absorbing element of multiplication with any element of the the natural numbers is the absorbing element itself, 0 * any natural number = 0 .
a) only 1
b) 1 and 4
c) 3 and 4
d) 1 and 3
The result of combining an absorbing element of multiplication with any element of the the natural numbers is the absorbing element itself .
8. Look for the terms unknown and indicate them in the following two operations .

1- 28 658 : ... - 623 : 623 = 622
2- 321 � ... + 6 400 = 28 900 + 9 600

a) 28 and 100
b) 58 and 38
c) 50 and 100
d) 46 and 100
28 658 : ... = 623 and 321 � ... = 32 1000 .
9. [(53)2]1 = ?

a) 125 x 125
b) 25 x 125
c) 10 000
d) 100 000
[...]1 is the first power which is self; then we have [(53)2]1 = (53)2 .
If (53)2 , then (53) x (53) i.e. (5x5x5) x (5x5x5) = ...
10. 3 · 9 + (6 + 5) x 3 – 12 : 4 = ?

a) 64
b) 75
c) 57
d) 46
Multiplications and divisions do have priority .
11. Which is the best method to calculate 3 · 9 + (6 + 5) x 3 – 12 : 4 = ?

a) all
b) to bring into form (9 + 11 - 1) x 3
c) to perform first the division
d) to bring into form (9 + 11 + 1) x 3
12 : 4 = 3 and 3 is common factor of all terms, then (9 + 11 -1) x ... is permitted .
y
12. How many natural numbers that are less than 1 000 can be formed using the digits 0, 1, 2, 3, 4 and 5 ?

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

RY1 RY2



a) 999
b) 677
c) 645 or 646
d) 215 or 216
Have please a look at ry1 .
13. A, B and C are consecutive even or odd digits. What will be the sum of the numbers ABC+CBA formed by these digits ?

a) 444xA + 444
b) 222xA + 222
c) 222xA + 444
d) 222xA + 111
Evry consecutive digit is 2 greater than the previous .
14. A, B and C are consecutive even or odd digits. What will be the maximal sum of the numbers ABC+CBA formed by these digits ?

a) 1554
b) 754
c) 1444
d) 794


If C = 9 then B = 7 and A = 5 , i.e. 579 + 975 = ? .
15. A, B and C are natural numbers and A * B = 6, A * C = 22 are valid. What will be the maximal value of the product A * B * C ?

a) 162
b) 146
c) 212
d) 132
According to the first equality A = 1,2,3 and 6 but the second forces A to be either 1 or 2 .
There are two possibilities: A=1, B=6 and C=22 or A =2, B=3 and C=11.
16. A, B, C and D are possibly equal digits and the multiplication below is given. (A+B)xC-D = ?

!
a) 51
b) 39
c) 47
d) 77
A=4 because B=6. C must also be equal to 5.
743 x 86 = 63 898 i.e. D = 3
17. Which of the following equalities is/are correct ?

1. 404 · (5 + 8) = 35
2. (307 – 27) : 5 + 4 = 60
3. 181 · 23 + 47 · 67 = 3312
4. 303 - 488 : 8 = 242
a) yalnız 1
b) 2 ve 4
c) 1 ve 3
d) 3 ve 4
The first equation has an odd number at the left and an even at the right .
y
18. The multiplication below in the figure is given. (A+B)2 - 2·A·B + C2 = ?

!


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


a) 67
b) 43
c) 65
d) 49
Have please a look at ry1. If we substitute the values we find from, the question reduces to "52 - 12 + 62 = ?" .
19. What will be the sum of the 4 expressions below for A=1 and B=2 ?

1- A2 - 2·A·B + B2
2-(A+B)2
3-(A-B)2
4- A2 + 2·A·B + B2

a) 40
b) 20
c) 33
d) 51
The 2 equations (A+B)2 = 2 + 2·A·B + B2 and (A-B)2 = 2 - 2·A·B + B2 are valid. So the sum of the 4 expressions will be 4·(A2 + B2) . Otherwise you have to work with negative integers.
20. What is the absorbing element of the operation according to the table given below ?

!


a) triangle
b) circle
c) star
d) square
Absorbing element converts every other to self .
21. In which of the following equations may the ♦ not be replaced by 7 ?

1- 8:2x(20-♦) = 52
2- 8x(30-♦) = 164
3- 8x(40:10-♦:7) = 24
4- >8x(30-♦) = 184

a) 1
b) 2
c) 2 ve 3
d) 1 ve 4
(A-7) = 184/8 = 23 .
y
22. What is the value of the biggest sum that can not be formed by 5, 6 and 7 cents ?

!


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

RY1 RY2



a) 9 cents
b) 77 cents
c) $ 1001
d) 7 cents


This can be searched in Wikipedia under "Coin Problem" or "Frobeius Coin Problem" . Her we wanted to introduce you this in the simplest form. Have please a look at ry1.
23. Which choice of signs make 545 � 5 � 9 � 11 = 10 a valid equation ?

a) - , : and x
b) - , - and x
c) : , - and x
d) x , - and x
Signs of 4 basic operations are meant .
24. How many prime numbers are there in the green region ?

!


a) 11
b) 7
c) 8
d) 5
1 is not a prime by definition .
25. What is the to the nearest integer rounded density of primes of the green region of the previous question ?

a) 1
b) 0
c) 0.5
d) 2
Density of primes = number of primes / number of all numbers
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
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