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FOURTH GRADE / MATHEMATICS / DIVISION of NATURAL NUMBERS 1.1

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" RIGHT FOR YOU.
 Method(s) of DIVISION of INTEGERS   is  (are)
 ♦ 
METHOD(s) of DETERMINING the RESULT  (QUOTIENT) of
 ♦ HOW MANY TIMES A NATURAL NUMBER  CALLED a  DIVISOR

 ♦ CAN BE SUBTRACTED FROM / IS CONTAIN-  ED IN ANOTHER NATURAL NUMBER CALLED
 a DIVIDEND


 and WHICH NATURAL NUMBER (REMAINDER,  LESS THAN DIVISOR) STAYS BEHIND.
  Ref.-1
1. What is the name of the number in the red rectangle in the figure below ?



a) integer
b) natural number
c) 48675
d) dividend
The elements of division are nemed as dividend, divisor and quotient ... .
2. Referring to the figure in question 1 , how is the number that will be under 75 (bottom) to be determined ?

a) by multiplication of ones of the quotient and the divisor
b) 72
c) by multiplication of ones of the quotient and the dividend
d) by multiplication of the dividend and the divisor
how is the "number" to be determined ...
3. What is the maximum possible remainder value in cases the divisor is the same as in question 1 ?

a) 8
b) 9
c) 3
d) 1
Max poss. remainder will be 1 less than divisor (for natural numbers) .
4. What will be the result of (75x15) - (75/15) = ?

a) 1125
b) 1120
c) 1116
d) 1006
It should be divisible by 5 .
5. What will be the dividend if the divisor , the quotient and the remainder respectively are 24, 358 and 9 ?

a) 8261
b) 8361
c) 8601
d) 8761
24x358 = 35800/4 - 358 = 17900/2 - 358 = 8950 - 358 = 8600 - 8 = 8592 .
y
6. Division is a short cut for subtraction as multiplication is for summation.
Which one of the choices may belong to the right "long way" of the division 1398/6 ?


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

  RY1 RY2



a) 100+10+10+10+3 = 133
b) 100+100+10+10+10+3 = 233
c) 100+10+10+10 = 130
d) 100+100+10+10+10 = 230
6 may be subtracted 100 times and there remains 798.
Repeating the same there remains 198.
Subtracting 6 an additional 10 times leaves 138 behind ...
7. The first stage of our division algortihm, as 1398/6 is calculated, is shown in the figure below.
Which of the choices expresses the meaning behind ?



a) No idea .
b) So is the rule .
c) The number of 6 in 12 is calculated .
d) There are 200 times 6 in 1300, with a remainder of 100.
Remember always that somthing called place value exits .
8. What will be the sum of all different and unique possible values of the remainder if the divisor is 11 ?

a) 55
b) 10
c) 45
d) 36
The sum of natural numbers from 1 to 10 is ... .
9. Matt's advisor adviced him to solve 100 test questions each and every day. Matt has done this and determined that he has solved 15200 test queestions between January 1 and May 31.
Which of the cases may be the quotient and the remainder of division of this mentioned year's date by 4 ?

a) 502 ve 1
b) 502 ve 0
c) 502 ve 3
d) 502 ve 2
February must have 29 days .
10. The result of a multiplication is 66675. What should be the second multiplicand if the first is 127 ?

a) 555
b) 375
c) 525
d) 645
Division is the inverse operation of multiplication .
y
11. "In order that a number will be divisible by 3 without remainder, its digit-sum must be a multiple of 3." is a rule. Sean, a curious pupil, claims to have found an explanation restricting himself to 2-digit numbers.
What may be Sean's explanation ?


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

RY1 RY2



a) no idea
b) in case of base 10, the numerical value is a multiple of 3 + the "sum of all digits (digit sum)" .
c) For 2-digit numbers, the sum of the number and its digits exchanged form is 99, which is a multiple of 3.
d) rules are nut to be explained, they are just rules.
The question is directed to understanding one of the existing "so called" rules .
12. 10 chewing gums are sold for $ 1. How many cents should little Chuck pay, having bought 3 of them ?

a) 10
b) 3
c) 30
d) 20
Find first the price of a gum in cents .
13. How will the division be simplified if both dividend and the divisor have the same number of zeros at the end ?

a) all common zeros at he end will be cancelled.
b) the last zeros of the divisor are droped.
c) the last zeros of the dividend are droped.
d) the zeros at ones are cancelled.
If both sides of an equation is divided by the same number nothing changes . So is it with the numeator and the denominator. Division of both dividend and divisor by the same number, e.g. 10, 100 or 1000, etc. does not affect the result
14. Two close friends have a fabric of 6 m. and want costumes. One's share should be 40 cm. longer since he is taller than the other.
Which of the followings is true for the length of the longer share ?

a) 6/2 m + 20 cm
b) 6/2 m + 40 cm
c) 6/2 m.
d) 6/2 m + 10 cm
In case of equal shares the length is 6/2 m.
15. During calculation of mathematical terms, the paranthesis should first be evaluated. The correct order of operations is ... .

a) division, multiplication, addition and subtraction
b) addition, multiplication, division and subtraction
c) multiplication, division, addition and subtraction
d) the order of operations is free without any constraints.
Multiplications are first .
16. What will be the result of 3x20:4x4 ?

a) 60/8
b) 15/4
c) 60
d) 15/8
60/16 .
17. 10011001:1001 = ?

a) 10001
b) 100001
c) 1001
d) 101
10010000/1001 + 1001/1001 .
18. What will be the remainder of 99999/8888 ?

a) 1099
b) 3001
c) 2231
d) 2531
The quotient should be 11 and 88880+8888 = ... ?
19. The remainders of the divisions 10/3 , 100/33 , 1000/333 and 10000/3333 are all 1.
What will be the remainder of the division having a dividend as the dividend's sum and a divisor as the divisor's sum ?

a) 1
b) 4
c) 0
d) 5
the remainder of 11110/3702 is ?
20. The next element of the sequence 3807 ; 1269 ; 423 ; 141 ; is ... .

a) 47
b) 51
c) 15
d) 20
check if a division is the basic operation, e.g. 3807/1269 = ? .
21. Which number A has the property 5xA + 100 = 385 ?

a) 57
b) 77
c) 55
d) 45
Subtract 100 from both sides of the equation and find the numerical value of 5xA .
22. The perforated plate seen in the figure below has a thickness of 2 mm. and is made of a metal with a density of 8 g./cm3. It weighs 16 kg.
What should be the ratio of weights of unperforated and perforated forms ?



a) 3
b) 2
c) 1/2
d) 4
change first all units to cm. and g. .
23. What will be the result of 1111/11 ?

a) 11
b) 111
c) 22
d) 101
Since the divisor is a 2-digit number, write the dividend as 1100 + 11 .
24. 66:6+60:10-15 = ?

a) 0
b) 2
c) -6
d) 15
First are divisions due .
25. 20527/13 = ?

a) 1579
b) 1371
c) 1313
d) 1513
Trial and error is rational . Multiply the numbers given in the choices by 13 and check which one gives a 7 at ones ...
This is the feedback!
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