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SIXTH GRADE / NATURAL NUMBERS and BASIC OPERATIONS on THEM / TEST 1.1

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. Sue has read a book having 121 pages. How many digits should have been used to number the odd-numbered pages of this book ?

!


a) 205
b) 106
c) 304
d) 178
121/2=60 but the number of odd-numbered pages is 61 : 1,3,5,...,11,...,101,...,117,119 and 121. 5 of the numbers are single digit, 45 of them have two digits and 11 of them have 3 digits.
2. The book read by Sue (Q.-1) has of course some odd-numbered pages. How many digits should have been used to number the odd-numbered pages containing 0 as a digit ?

a) 105
b) 35
c) 17
d) 15
"0" exists only in pages from 101 to 109 .
3. The book read by Sue (Q.-1) has also some even-numbered pages. How many "0" digits should have been used to number the even-numbered pages of this little book ?

a) 17
b) 11
c) 12
d) 15
The digit "0" exists in 10,20,..., 100 (twice), 102,...,110 and 120 .
4. What may be the maximum value of the natural number D if the inequality D < 1900 - 90 : 5 is to be satisfied ?

a) 1882
b) 362
c) 1881
d) 361
Division has an higher priority in the order of operations since no parenthesis .
5. What should be the value of * if the equality 327 - (147 - 77) = 237 + ( * - 20 ) is valid ?

a) 20
b) 30
c) 40
d) 50
Left side is 327 - 70 = 257 .
y
6. Which figure may be the identity element if the table given below is valid ?

!


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



a) rectangle
b) pentagon
c) triangle
d) hexagon


Identity element has no effect on the other element in a binary operation. The identity element of summation is 0. Just replace the figures by 1, 0, 2, 4 and 3 respectively to see the situation better.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which of the following statements are true ?

1- summation and multiplication are commutative operations.
2- inverse operations, subtraction and division are commutative.
3- all basic operations are commutative .
4- commutativity means the order of operands may be changed.

a) only 1
b) 1 and 4
c) 3 and 4
d) 1 and 3
3/5 and 5/3 do not have same results .
8. What should be the value of A if (27 + A) + 17 = (17 + 27) + 34 is valid ?

a) 17
b) 34
c) 27
d) 44
Commutativity and associativity of summation permits to write 27 + 17 + A = 27 + 17 + 34 .
9. 1x1x1x100x1x1x1x10000x1x1x1x0x1x1x1000000 = ?

a) 0
b) 1000000
c) 1000000000000
d) 1
The product is 0 if any of the operands is .
10. What will be the product of numbers corresponding to points A and B on the number line ?

!


a) 4860
b) 5110
c) 3760
d) 4810
65x74 = ?
11. Which equality will be valid with only one operation changed ?

a) 14 + 4 = (4 x 8)/2
b) 16 + 4 = (4 x 8)/2
c) 12 + 4 = (4 x 8)/2
d) 10 + 4 = (4 x 8)/2
Replace the "+" sign by ":" in the choice ...
y
12. How may the operation 36x18 be done with a calculator having a defect "6" key ?

1- (28+8)x10 + 8 = ?
2- (28+8)x18 = ?
3- (30x18) + 90 + 18 = ?
4- 2x18x18 = ?

!


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

RY1 RY2



a) 2 or 4
b) 1 or 3
c) 2 or 3
d) 1 or 4
Have please a look at ry1. Since you are not supposed to know these details, try to answer the question under the fact that 1 do not produce a correct result.
13. A = 3 and B = 5 is given. A3 + B5 = ?

a) 2155
b) 5125
c) 4445
d) 3152
A3 = AxAxA and B5 = BxBxBxBxB.
14. 7200/900 + (78 - 18/3)/4 - 8 = ?

a) 22
b) 19
c) 27
d) 18


72/9 = 8 and 18/3 = 6 .
15. What should be the value of A if the equality 3 x (14+20) = 42 + A is valid ?

a) 60
b) 40
c) 55
d) 45
Since multiplication is distributive over summation 3 x 14 + 3 x 20 = 42 + A . And of course 3 x 14 = 42 .
16. A cyclist traveled 45 km at the seaside and 70 km via a tree-lined road. 10 km of this trip was both at the seaside and via the tree-lined road. How many km.s should he have taken during this trip ?

!
a) 115
b) 125
c) 95
d) 105
70+45 equals 115 but 10 km. is common ...
17. Which of the following equalities is/are correct ?

1- 8x(30-5) = 240 - 5
2- 8x(30-5) = 8x30 - 40
3- 8x(30-5) = 8x30 - 8x5
4- 8x(30-5) = 8x30 + 8x5

a) only 1
b) 2 and 3
c) 1 and 3
d) 3 and 4
Multiplication is distributive over summation i.e. ...
y
18. The prime factors of the operands are given. What should the result be ?

!


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


a) 9560
b) 10060
c) 10560
d) 10600
Just multiply the prime factors to find the operands .
19. What will be the result of respectively applying commutativity of summation, assosiciativity of multiplication and distributivity of multiplication over summation on Ax(B+C)xD ?

1- Ax(B+C)xD = (AxB+AxC)xD ; Ax(B+C)xD = Ax(C+B)xD ; Ax(B+C)xD = AxDx(B+C)
2- Bx(B+C)xD = (AxB+AxC)xD ; Ax(B+C)xD = Ax(C+B)xD ; Ax(B+C)xD = AxDx(B+C)
3- Ax(B+C)xD = Ax(C+B)xD ; Ax(B+C)xD = AxDx(B+C) ; Ax(B+C)xD = (AxB+AxC)xD
4- Ax(B+C)xD = (AxB+AxC)xD ; Ax(B+C)xD = Ax(C+B)xD ; Ax(B+C)xD = AxDx(BxC)

a) 3
b) 2
c) 1
d) 4
Commutativity of summation is A+B = B+A, associativity of multiplication is (AxB)xC = Ax(BxC)and ...
20. The equation 41 x (29 + 55) = ♦ x (29) + (41) x ♣ is written due to distributivity of multiplication over summation. What value should then the product ♦ x ♣ have ?

a) 41x29
b) 29x55
c) 41x55
d) 29x41x55
41 x (29 + 55) = 41x29 + 41x55
21. In which of the following equations may the ♦ be replaced by 7 ?

1- 8x(20-♦) = 164
2- 8x(30-♦) = 164
3- 8x(40-♦) = 184
4- 8x(30-♦) = 184

a) 3
b) 4
c) 2
d) 1
(A-7) = 184/8 = 23 . 164/8 = 20 1/2 , not a natural number .
y
22. A, B, C, D, E and F are consecutive digits. The product of numbers constructed with these digits, ABC x DEF happens to be EF0GG (with 0 = zero and G = 2x(A+3)). What should then the value of D is supposed to be ?

!


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

RY1 RY2



a) 4
b) 2
c) 3
d) 1


There exist 4 choices for A : 1,2,3 and 4. The first may be tried. The others end up with 6-digit products.
For a formal solution have please a look at ry1.
23. 325-108:27 = ?

a) 123
b) 231
c) 321
d) 132
No paranthesis means be guided by operation priority. Division has an higher priority; do first 108:27 yapılır ...
24. A simitchi has bought 150 simits 60 cents per piece and sold all of them 100 cents per piece. What amount has this simitchi earned on this day ?

!


a) 60 $
b) 40 $
c) 100 $
d) 10 $
Be careful of units .
25. Which of the following choices is (50x1001)x(50x1002) ?

a) 50x(1000+1)x50x(1000+2)=(50000+50)x(50000+50)
b) 50x(1000+1)x50x(1000+1)=(50000+50)x(50000+100)
c) 50x(1000+2)x50x(1000+2)=(50000+50)x(50000+100)
d) 50x(1000+1)x50x(1000+2)=(50000+50)x(50000+100)
1001=1000+1 and distributivity of multiplication ...
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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