gb
     Test     
-Dr.
com
hz

FOURTH GRADE / MATHEMATICS /ADDITION of FRACTIONS 1.1

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

   WITH INCLUSION of FRACTIONS
 ♦ 
COUNTING FORWARD TENDS TO BE  ADDING END-TO-END, SUMMING.
 ♦ HOWEVER BIG/SMALL THEY ARE, WE SHOULD BE ABLE TO SUM.

THERE ARE TWO GOLDEN RULES:
1. DENOMINATORS SHOULD BE EQUAL, OR EXPANDED/REDUCED AND MADE EQUAL.
2. THE MOST EFFICIENT WAY GOES THROUGH THE LEAST COMMON DENOMINATOR (LCD).
y
1. How many ,with a single number, apples are there in the figure below ?

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

RY1 RY2



a) an half and a quarter
b) nearly one
c) three-quarters
d) more than a half


When we see a group of objects we usely group them and count the ones of the same group. In groups there should be same objects or assumedly same objects.
Have also a look at ry1.
2. In the figure below plastic water pipes are seen. The one seen at left has an inner diameter of half an inch and is called half inch pipe. What is the one at the right supposed to be called ?



Note: The measures are given for outer diameters because of convenience.

a) medium size
b) three-quarter
c) pretty thick
d) full measure
The question is just to remind of the importance of unit fraction ... .
3. As it is seen in the first two questions we need to make the denominators of "1/2" and "1/4" a "4" , which is the smallest common multiplier of 2 and 4. To this end the greater fraction is ..... by multiplication of its numerator and denominator by 2.

Which of the followings fills in the blank spaces in the previous question ?

a) expanded
b) increased
c) decreased
d) left unchanged
This operation is called fraction expansion .
4. There are infinetely many ways of fraction expansion, there are infinetely many natural numbers that can be used for multiplication.
Which of the followings is not an expanded version of 3/7 ?

a) 6/14
b) 66/140
c) 120/280
d) 3663/8547
6/14 and 66/140 both can not be !
5. Which of the following numbers can be common denominators of the fractions 3/8 and 5/26 ?

I = 52
II = 104
III = 208
IV = 416

a) all
b) I , II ve IV
c) III and IV
d) II , III and IV
52/8 is not a natural number .
6. Which of the followings is/are true ?

I: If a number is a multiple of the number B, it should be divisible by B without remainder.
II: The least common multiple should be the multiple of each denominator included in the sum.
III: The least of the common multiples is called least multiple.
IV: As we expand fractions we make use of greatest common divisor.


a) Only I
b) Only II
c) I and II
d) I , II and III
With choice III the word "commmon" fails .
7. Which of the following statements are true ?

I: Prime factors are factors that are evenly dvivisible by only one and itself.
II: 1 is, by definition, not a prime factor.
III: The result of multiplication of all prime factors is less then the number.
IV: During the calculation of the least common multiple, in case of repeating prime factors, the maximal number of them, only for one of the numbers is considered.


a) Only I
b) I and IV
c) All
d) I , II and IV
Considering 1 as prime and prime factor is not convenient, may result in never ending loops in case of machine calculations.
In case you have difficulties with statement IV, go to the next question before answering .
8. Which multiplication gives the least common multiple of 132 and 12 ?



a) 2 x 2 x 3
b) 2 x 2 x 3 x 11
c) 2 x 2 x 3 x 3 x 11
d) 2 x 3 x 11
As factors we must have :
I- All factors that are not common.
II- The maximal number of common factors from only one of the numbers .
The common factors are 2 and 3 .
The number of repetitions is 2 for 2 and 1 for 3. Maximum no. of repetition for 2 is 2.
We get only 2x2 from 12 or 132 and not from both of them. So we get 2x2 instead of (2x2) x (2x2)
9. Which of the following statements are correct ?

I: 1 is a number that can not evenly be divided by 1 and itself.
II: Primes numbers are numbers taht can not be evenly divided by 1 and themselves.
III: 1 is not defined/accepted as prime.
IV: Consideration of 1 as prime is inconveniient for machine calculations.


a) all
b) I and II
c) I and III
d) I , II and III


Considering 1 as prime may lead to inconveniencies.
10. Which number is obtained in case of calculating the LCM of the denominators of 1/264 and 1/24 via the rules we learned ?



a) 264
b) 255
c) 132
d) 66
Since the fractions are not in their simplest forms, not reduced, the least common multiple (LCM) and the least ccommon divisor (LCD) are not the same .
11. The previous question reminds of a fact: Do always reduce and get the simplest form of fractions before working with them.
Which of the following statements is the best definition of reduction of fractions ?

a) Reduction is division of both the numerator and the denominator of a fraction by a number.
b) Reduction is division of both the numerator and the denominator of a fraction by the same number.
c) Reduction is division of both the numerator and the denominator of a fraction by the same number and use of the results as new num. and denom.
d) Reduction is finding a number that can divide the numerator and the denominator of a fraction without remainder, division of them by this number and their replacement by the results.
Definitions are very important they must be as complete as possible. There are lots of numbers that can divide (not evenly) and does not reduce.
12. The simplest possible form (complete reduction) of a fraction is obtained by reducing it with the ... . ?

a) the greatest common divisor
b) the least common multiple
c) the greatest divisor
d) the most common divisor
Under divisor a number that divides without remainder is understood.
13. Which of the following statements are correct ?

I: In order to find the GCD (gereatest common divisor) we need prime factorization as in LCM .
II: 1 is not a prime factor.
III: Multiplication of prime factors gives a result less than the number itself.
IV: For GCD we use (the multiplication of) the minimum of repeating common prime factors.


a) I and II
b) all
c) I , II and IV
d) II and IV
In case of GCD the minimal repeating common prime factors are considered. If 2 is a common prime factor and repeats thrice in one of the numbers and twice in the other, 2x2 is used in multiplicaiton of prime factors.
14. 30/108 + 5/7 = ?

a) 5/23
b) 125/126
c) 115/116
d) 25/33
Reduce first 30/108 via GCD to get 5/18.
15. Jane studied mathematics on saturday, sunday and monday for 3/4 , 7/9 and 17/36 hours respectively.
How many hours did she study on these days totally ?

a) 29/36
b) one and a half
c) 3
d) 2
The LCM of 3/4 and 7/36 is 36 .
16. What would be the answer of question ten, if Jane had studied only 9/36 hours on monday ?

a) 19/36
b) 1/2
c) 16/9
d) 5/3
9/36 is 1/4 and 1/4+3/4 is 1 .
17. 1/2 + 1/4 + 1/8 = ?

a) 4/9
b) 8/7
c) 7/8
d) 6/7
8 is the LCD
18. 1/3 + 1/6 + 1/9 = ?

a) 5/9
b) 4/9
c) 11/18
d) 21/18
This time LCD is 18 .
19. 1/5 + 1/7 + 1/10 = ?

a) 31/70
b) 3/7
c) 33/70
d) 1/2
70 is common denom.
20. 7/8 + 11/18 + 31/70 = ?

a) 4951/2520
b) 5015/2520
c) 4793/2520
d) 4861/2520
common denom is 2x2x2x3x3x5x7 .
21. Reconsidering questions 17 to 20, the answer calculated in question 20 is the answer of the sum ... .

a) 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+
b) 1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10
c) 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10
d) 1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1
So a relatively hard question is divided into parts and solved.
y
22. 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + ... + 1/65536 = ?

In case you need help ger the cursor on "y" or click at "ry1/2" .

RY1 RY2



a) 65535/65536
b) 65536/64556
c) 64556/65557
d) 1


The numerator is constant and the denominator is decreased by division by 2.
ry1 shows that the whole area will ultimately be covered and the total area, unit area, 1 , will be obtained.
23. A region got on 3. and 4. days of April 5/7 and 4/9 grams of rain per square meter. On the fifth of April the rain was one thirds of the previous days' total.
What will be the total of these 3 days in g./m2 ?

a) 190/126
b) 178/126
c) 219/126
d) 188/128
Determine first the last day's rain.
24. A farmer used 1/3 , half of the rest and the final rest of his land for wheat, barley and oath cultivation respectively. What is the ratio of the oath cultivated area to the total ?

a) 1/3
b) 1/4
c) 1/5
d) 1/6
rest is 2/3 rds . Final rest is half of 2/3 rds .
25. Eve is 147 cm. tall. Christa is 1/50 ths of her own length taller. How tall is then Christa ?

a) 160
b) 155
c) 145
d) 150
Try the given answers. 145 cm is out of queestion.
This is the feedback!
Return to Begin

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

Share |


  
=> test-dr.com
  Logout
   Login


Test-Dr.com
GOOD SITE





Test-Dr.com
USEFUL SITE

VoltRank: Link Exchange