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FIFTH GRADE /SUBTRACTION / 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.

 (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 .
1. How many of the following subtractions are incorrect ?

390944-728=390284   321-236=85      555-260=295      770-111=659


a) 1
b) 2
c) 3
d) 4
First is certainly incorrect ... .
2. What should A be, if [(1+9)-(1+9) + (Ax6-25)] = 120 - (1+10) + 10 ?

a) 14
b) 24
c) 32
d) 332
The equation means 6xA - 25 = 119 .
3. What is the difference of the 20th and 15th triangular numbers ?

!


a) 50
b) 80
c) 90
d) 110
nth triangular number is the sum of numbers from 1 to n. 20th is 20x21/2 = 210 olur. 15th is 15x16/2 = 120 .
Since nth triangular number is the sum of numbers from 1 to n, the difference is 20+19+18+17+16 = ...
4. How many couples of 2-digit numbers exist whose difference is 49 ?

a) 42
b) 41
c) 51
d) 52
99-50 is an example. So is 59-10 . 58-9 is not because 9 is not a 2-digit number.
5. Which of the following statements is false ?

a) The 3 elements of subtraction are minuend, subtrahend and difference.
b) The sum of the 3 elements of subtraction equals twice the minuend.
c) The subtrahend can not be a negative number.
d) Check of correctness of subtraction is done via addition.
Subtraction is defined also for negative integers and numbers .
y
6. What can be said about the difference if a 3-digit number and its digits reversed form are subtracted, the smaller from the bigger ?

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



a) It is an indefinite multiple of 9
b) It is 9 times the difference of the digits
c) It is 9 times the sum of the place values
d) It is 99 times the difference of the digits at hundreds' and ones' places


Please have a look at ry1.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Holy is 17 years old and Moly is 7 years younger. What will be the difference of their ages in 2022 if they both live then ?

a) 22
b) 17
c) 19
d) 7
The difference of ages does not change .
8. 6400 - 3200 - 1600 - 800 - 400 - 200 - 100 - 50 - 25 = ?

a) 50
b) 25
c) 100
d) 200


Suppose we subtract another 25 from it, we get 0 because 25+25 = 50, 50+50=100, 100+100 =200 etc.
9. A, B and C are digits and 4BC - BCA = 108 is valid. What should A, B and C respectively be ?

a) 4 , 2 and 2
b) 4 , 3 and 2
c) 3 , 5 and 4
d) 8 , 6 and 3


Write them under each other, you will soon see that B = 3 or 2 .
10. A, B, C and are digits and A38B - 6BC4 = 2D48 is valid. What should A, B, C and D respectively be ?

a) 4 , 8 , 2 and 3
b) 6 , 2 , 4 and 1
c) 4 , 7 , 2 and 6
d) 8 , 2 , 3 and 1
This is easier than the previous one. B should be 2 and ...
11. (2500 - 5 x 28) - ( 88 - 44 x 2) = ?

a) 2360
b) 4360
c) 3460
d) 1480
The 2nd paranthesis is equal to 0 .
y
12. When a 3-digit number and its digits reversed form are subtracted, the smaller from the bigger, the difference is desired to be 792. How many numbers permit this desired result ?


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

RY1 RY2



a) 117
b) 100
c) 10
d) 1
ry1 gives the solution .
13. A and B of the following figure are natural numbers. Which choice gives them ?

!


a) 12 and 14
b) 14 and 15
c) 16 and 15
d) 16 and 13
208 is nearly 225 which is the square of the 15 . So try numbers in the neighborhood of 15.
14. The perimeter of the figure below is 38 cm. What should the length of the part with a question mark be ?

!


a) 5 cm.
b) 2 cm.
c) 4 cm.
d) 3 cm.
Think as if the figure is a rectangle; the perimeters are the same .
15. What is the following figure trying to convey ?

!


a) -4 = -4
b) -(-4) = +4
c) 3 = 3
d) 4 = 4
If a negative number in a negative paranthesis is not treated as a positive number, we lose consistency .
16. If the larger of two digits is multiplied by 2 it happens to be equal to the smaller multiplied by 5. In addition, if twice the smaller is subtracted from twice the larger, the difference is 12.
In which choice may these two digits be given ?

a) 12 and 6
b) 8 and 4
c) 10 and 4
d) 8 and 6
Let the smaller be 1, the second can not be integer. Try the smaller equals 2, the bigger should be 5, the couple does not satisfy the second condition .
Let the larger be A and smaller B. 2xA = 5xB and 2x(A-B)=12 i.e. A=B+6 . Putting B+6 in the first gives 2xB + 12 = 5xB i.e. B=4
17. The Computer Store has reduced the price of a computer by $225. What is the original price of the computer if the sale price is $1275 ?

!


a) $1500
b) $1550
c) $1600
d) $1400
1275 + 225 = ?.
y
18. What is the difference of the 100. and 99. square numbers ?

!


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


a) 199
b) 1999
c) 101
d) 1001
1002 - 992 = ?. You can certainly calculate the result.
For a good possible way, have a look at ry1.
19. What will be the difference of the sum of the squares of the numbers from 1 to 10 and the sum of the numbers from 1 to 10 ?

a) 360
b) 330
c) 324
d) 320
1st method to calculate may be the direct method: The sum of the numbers from 1 to 10 is , from nx(n+1)/2 = 5x11 = 55. The first term is 1+4+9+16+25+36+49+64+81+100 = ?
2nd method : For each number 1≤A≤10 A2 - A = Ax(A-1) and it is enough to sum these last terms. For A=1 this term vanishes. The sum of te other terms 2x1+3x2+4x3+5x4+6x5+7x6+8x7+9x8+10x9 = 2x(1+3)+4x(3+5)+6x(5+7)+8x(7+9)+90 = 2x4+4x8+6x12+8x16+90=385 .
20. Which of the following sums is likely to be the outcome of the difference of the sum of the squares and the sum of the first 20 natural numbers, 0 excluded ?

a) 2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+80=2360
b) 2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+80=2660
c) 2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+380=2640
d) 2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+380=2660
Just as in the previous question .
21. What is the difference of the explicitly calculated difference of the sum of the squares and the sum of the first 20 natural numbers and the right choice of the previous question ?

a) 0
b) 1
c) 10
d) 100
Just make the explicit calculation with the help of a calculator .
y
22. We seem to be entering into an epoch forcing us to be extremely economical that you may happen to feel within the bones. That means we have to find ways to make even our calculations economically, with the least possible number of operations.
How many more operations do we need if we calculate the difference of the sum of the squares and the sum of the first 20 natural numbers explicitly without making use of any formula with respect to the right choice of question 20 ?

Note: The notation in the figure below is something you will learn soon, do not force yourself to understand it, just get used to it.


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

!
RY1 RY2



a) 30
b) 50
c) 40
d) 20


Have please a look at ry1 .
23. Which of the choices is equivalent to 2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+380=2660 and reduces the required number of operations ?

a) 4x(115+6x3+8x4+10x5+12x6+14x7+16x8+18x9)=2660
b) 4x(105+6x3+8x4+10x5+12x6+14x7+16x8+18x9)=2660
c) 4x(105+6x4+8x4+10x5+12x6+14x7+16x8+18x9)=2660
d) 4x(105+6x3+8x4+10x50+12x6+14x7+16x8+18x9)=2660
2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+380 has all terms as multiples of 4. After we write it in 4x(.+.+....) form, some of the terms are easily added .
24. (101 000 - 1000)-(100 100 - 100) = ?

a) 0
b) 10
c) 100
d) 1
Both of the parenthesis are 100 000 .
25. 485692137 - 346834376 ?

a) 138857763
b) 138857769
c) 138857761
d) 138857751
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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