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FIFTH GRADE / DECIMAL FRACTIONS, PERCENT and RATIO / 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.

FRACTION'S UTILITIES

FAST DAS SELBE AUF DEUTSCH
  WE HAVE HAD SOME SAMPLE PROBLEMS REGARDING THESE TOPICS.
 ♦ 
NOW IT IS TIME TO A BETTER STUDY.
 ♦ TO SOLVE CHALLENGING PROBLEMS.

THERE ARE TWO GOLDEN RULES OF SCHOLARLY LIFE:
1. TRY YOUR BEST TO UNDERSTAND.
2. DO YOUR BEST TO INFORM OTHERS.
1. Which of the following patterns may be used to express Africa's remaining oil reserves if we use their terms, multiply them with a coefficient which is either 0 or 1 and then sum ?

!


a) 1/2, 1/4, 1/8, 1/16, 1/32, ... .
b) 1/2, 1/4, 1/6, 1/2, 1/4, 1/6, ... .
c) 1/2, 1/2, 1/2, 1/2, 1/2, ... .
d) 1/3, 1/2, 1/3, 1/2, 1/3, 1/2, ... .
A1x1/2 + A2x1/4 + A3x1/8 + A4x1/16 + A5x1/32, .... may approach any fraction approximate enough where Ai is either 0 or 1 .
2. Which of the fractions below may be considered as an expansion of the fraction 44/81 ?

a) 2/9 + 2/18 + 2/27 + 4/36
b) 2/9 + 2/18 + 2/27 + 4/36 + 2/81
c) 2/18 + 2/27 + 4/36 + 2/81
d) 2/9 + 2/18 + 2/27 + 4/36 + 3/45 + 2/81
2/9 + 2/18 + 2/27 + 4/36 + 2/81 = 44/81. 2,2,2,4,2 may be considered as coefficients but the problem with 1/9, 1/18, 1/27 and 1/81 is that they can not approximate all possible fractions.
3. 44/99 = ?

a) 0.44
b) 0.444444444444...
c) 0.444444444445...
d) 0.45
Even decimal fractions can not expand all possible fractions with finite number of summands .
4. Which of the following fractions is 0.7999

a) 7999/1000
b) 7999/100000
c) 7999/100
d) 7999/10000
Just count the number of digits after the point and then put a 1 and as many 0's as the number of digits. In this special case we have multiplied by 10000 and divided the number so obtained by 10000 .
5. 0.075 x 285/1515 = ?

a) 75/5050
b) 57/4040
c) 44/4545
d) 66/6060
0.075 x 19/101 = 1425/101000 = 57/...
y
6. Which is the decimal equivalent of the the greatest fraction in the figure below ?

!


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



a) 0.075
b) 0.75
c) 0.075
d) 0.0750


The greatest fraction is 3/40 = 0.075. Look at ry1 for a calculation without formal division .
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7. Which decimal fraction corresponds to white parts in the 10x10 square ?

!


a) .59
b) .63
c) .61
d) .60
Count the colored region, take care of symmetry of "A".
8. What is "T" to "A" ratio in the figure of the previous question and how is it written as a decimal fraction ?

a) 1/6 and 1.66
b) 1/6 and 0.1666...
c) 1/6 and 16.66
d) 16/6 and 1.66
Count the no. of squares and ... .
9. Decimal representation of a number is called a repeating decimal (or recurring decimal) if at some point it becomes periodic, that is, if there is some finite sequence of digits that is repeated indefinitely. In case of previous question decimal representation of "1/6" has the repeating decimal 6. We used "..." to denote repetition but there is a better notation used internationally. Which of the followings may it be ?

a) 0.16
b) 0.1/6
c) 0.1¯6
d) 0.1‾6
0.16 is generally used almost all over the World .
10. What will be the sum of decimal fractions corresponding to points A and B ?

!


a) 0.133
b) 1.42
c) 0.142
d) 1.33
0.0645 + 0.0775 = ? Treat them as (645+775)/10000
11. Which of the corrsponding decimal fractions are wrong ?

a) 3 1/3 = 3.3
b) 6 1/6 = 6.16
c) 2 1/5 = 2.2
d) 3 1/4 = 3.025
.
y
12. 3.2 / 1.6 = ?

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

RY1 RY2



a) 2
b) 1.93
c) 1.95
d) 1.95
This is a tougher nut than it seems, have please a look at ry1 .
13. On January 5th of 2012 the air temperature in Istanbul was 1 °C . What should it have been 8th of this month if it happened to decrease by 1/10 in each of the three consecutive days ?

!
a) 0.725 °C
b) 0.729 °C
c) 0.8 °C
d) 0.81 °C
The initial value of the temperature is given as as 1 °C . The next day it drops to 0.9 °C; the second day to 0.81 °C and the third day to 0.81 - 0.81/10 °C.
The total drop is 0.1+0.09+0.081 = ? and ... .
14. What should be the result of the summation given in the figure below ?

!


a) 1.42
b) 1.47
c) 1.37
d) 1.4


0.5 + 0.46 + 0.46 = ?
15. 11.837 + ? = a natural number .

a) 1.223
b) 3.123
c) 0.132
d) 5.137
Forget about the whole number part. Just concentrate on the part after the point.
16. A cyclist took 2 000 km. , driving each day the same amount of distance, in 30 days. How many km. should he have driven a day ?

!
a) 66.7
b) 66.6
c) 66.7
d) 66.6
2000/30 = ?
17. Which of the choices are respectively the closest to 1.9 and 1.8 ?

a) 2 and 1.9
b) 2 and 1.99
c) 2 and 19/9
d) 2 and 17/9
9x1.9 = 10x1.9 - 10.9 - 1.9 = 1.9 = 18 .
y
18. What should be the ratio of perimeters of figure A to figure B ?

!


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


a) 25/27
b) 23/25
c) 24/25
d) 24/27
The ratio would be 1 if both figures were convex. Please look at ry1.
19. Point II corresponds to AxB on the scaled number line below in the figure. What is its decimal value ?

!


a) 0.075
b) 0.085
c) 0.85
d) 0.75
The number line is scaled . 1/2 x 3/2 = 3/4
20. Which of the followings is right ?

a) 3/17 = 0.17
b) 3/25 = 0.11
c) 2/15 = 0.13
d) 1/9 = 0.11
A repeating decimal is ... .
21. What is the place value of "2" in the decimal fraction 35.7523 ?

a) 2
b) 2/1000
c) 1/1000
d) 1.999
Place values (of 1) after the point are 1/10 , 1/100 , 1/1000 and 1/10000 .
y
22. What is the answer to the question seen in the figure below ?

!


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

RY1 RY2



a) 1000.01
b) 1001.1
c) 1000.1
d) 100.01


Have please a look at ry1 .
23. What is the decimal expansion of 325 27/108 ?

a) 3x100 + 2x10 + 5 + 2 x 1/100 + 5 x 1/100
b) 3x100 + 2x10 + 5 + 2 x 1/10 + 5 x 1/10
c) 3x100 + 2x10 + 5 + 2 x 1/10 + 5 x 1/100
d) 3x10 + 2x10 + 5 + 2 x 1/10 + 5 x 1/100
325 1/4 i.e. 325.25 .
24. (1.75 + 22.35) x (17.72 + 0.044) = ?

a) 428.1246
b) 428.2466
c) 428.1166
d) 428.1124
24.1 x 17.764 = (24 + 0.1)x(17 + 0.764) = 24x17 + 24x0.764 + 1.7 + 0.0764 = 408 + 24x0.750 + 24x0.01 + 24x0.004 + 1.7 + 0.0764 = 408 + 18 + .24 + 0.096 + ...
25. 54.07 - 45.007 = ?

a) 9.0063
b) 9.006
c) 9.063
d) 9.63
54-45 = 9 and .07 - .007 = ?
This is the feedback!

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FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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