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FIFTH GRADE / MULTIPLICATION of FRACTIONS / TEST 1.3

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.

FRACTIONS' UTILITIES

(FAST) DAS SELBE AUF DEUTSCH
   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).
1. Pam walked 7/3 rds of a mile yesterday and 3/4 ths more than yesterday's distance today. How many miles has Pam walked in two days ?

!


a) 7 1/2
b) 75/11
c) 77/12
d) 67/11
Yesterday she walked 7/3 miles and today 7/3 x(1 + 3/4) which should be added, i.e. 7/3x(2 + 3/4) ...
2. [(5555/10)/(5555/100)] x [(5555/1000)/(5555/100)] = ?

a) 1
b) 10
c) 1/10
d) 2
Left of x sign we have a fraction whose numerator is 10 times its denominator because the same number is divided by 10 in the numerator and by 100 in the denominator .
3. Ali Haktan German did 1/3 rds of his homework yesterday. Today he did 1/4 ths more than yesterday in 3 hours . If he finishes the work tomorrow, how much time will he normally has spent for the whole work ?

a) 5 h
b) 36/5 h
c) 7 h
d) 37/6 h
Today he did 1/3 + 1/3 x 1/4 = 1/3 x (5/4)i.e. 5/12 of the work in 3 hours. That means he does 1/12 of it in 3/5 hours.
4. Muhammet Daghan German did 1/3 of his homework yesterday. Today he did 1/3 more than he will do till end of the work, in 4 hours. If he finishes the work tomorrow, how much time will he normally has spent for the whole work ?

a) 9 1/3 h
b) 10 h
c) 9 h
d) 10 1/2 h
Yesterday he did 1/3 of the work and there remained 2/3 of it. Let the amount of work remainig from yesterday be A. If he does 4/7 of A today, he will have done 1/3 more than 3/7 which he will do tomorrow. So to complete A he needs normally 7 hours .
5. 1/3 rds of a wire is marked and then the wire is cut from mark. 1/3 rds of bigger part of the cut wire is again marked and another cut is made. What will be the longest length among the parts so produced ?

a) 3/7
b) 4/9
c) 5/8
d) 3 7/8
The parts will be 3/9, 2/9 and 4/9 .
y
6. As we multiply two mixed numbers, e.g. A B/C and D E/F, we may use the methods of converting them to improper fractions or writing them as sum of two terms (in our case A + B/C and ...) and then multiply them. What do we need to show the equivalency of both methods ?

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



a) AxCxDxF+AxCxE+BxDxF+3xBxE = FxCxAxD+CxAxE+FxBxD+3xBxE
b) AxCxE+BxDxF+BxE = CxAxE+FxBxD+BxE
c) AxCxDxF+AxCxE+BxDxF = FxCxAxD+CxAxE+FxBxD
d) AxCxDxF+AxCxE+BxDxF+BxE = FxCxAxD+CxAxE+FxBxD+BxE


Please have a look at ry1.
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7. Chuck leaves his home and drives with an average speed of 90 km/hour for 2 1/2 hours till he stops for lunch. If he had driven 1/5 more he would have traveled 3/5 of the way to his destination. How many km. more does he have ?

!


a) 225
b) 245
c) 185
d) 250
He drove 225 km. till he stopped. 225 + 45 makes 270 which is 3/5 of his destination .
8. 1/5 x 2/3 x 2 3/15 = ?

a) 11/35
b) 6/17
c) 22/75
d) 2/3
1/5 x 2/3 x 33/15 and 3 and 33 are to be ... ?
9. How many feet is the length L of the ladder if 2/3 x L = 9 1/3 feet ?

!


a) 10
b) 14
c) 17
d) 9


2/3 L = 28/3 feet .
10. (1 + 1/2 + 1/3)x(1 + 1/4 + 1/9) = ?

a) 539/216
b) 343/127
c) 456/195
d) 389/159
They are the first 3 elements of the series 1/n and 1/n2 and important.
In this case do the summations first. They are 11/6 and 49/36 .
11. Federal spending in 2011 was $3.6 trillion. The item "Everything Else" which is fractionally 117/1000 includes education, science, NASA, energy, natural resources, justice, and agriculture, among other things. Education's share in this item is 10/39 . How much dollars were spent for education ?

!


a) 128 billion
b) 108 billion
c) 98 billion
d) 100 billion
10/39 x 117/1000 = 3/100 . 36x3 = 108
y
12. To the gridded red region two spherical bodies/particles enter from left as seen in the figure. They are scattered at each and every node. After being scattered each has a probabilty of 2/5 of traveling in each perpendicular direction and of 1/5 continuing in the same direction. The bodies take the distances between nodes in equal amounts of time which is given as tN. What will be the probabilty of finding a particle in the near vicinity of point A as the elapsed time after entrance approaches 3xtN ?

!


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

RY1 RY2



a) 4/25
b) 1/22
c) 1/12
d) 2/19
The three possible ways and their probabilities for one of the particles are in ry1.
The total probability is for one particle case is 2/125 + 4/125 + 4/125 . Symmetry requires twice an amount .
13. D=0 and A,B,C are digits different from 0. Using these digits 4-digit numbers are constructed. What will be the result of ABAB/ABD x BABA/BAD ?

a) 102/101
b) 1021/1001
c) 10201/100
d) 102
Just set A=1 and B=2. You now have 1212/120 x 2121/210. Write it in the form (1200/120 + 12/120) x (2100/210 + 21/210) = 101/10 x ... .
14. A candy shop has a box of Smarties weighing 7 2/3 lb . The owner splits all into cellophane packs weighing 1/33 lb each. If he sells 8/11 of the cellophane packs with a price of 3/4 of a dollar each, how much money will the shop take in ?

!


a) $108
b) $138
c) $133
d) $145
From each lb. of smarties he obtains 33 packs. 2/3 x 33 = 22 . A total of 253 packs whose 8/11 is sold. 8x23 = 184 .
15. A manufacturer wants to make shoulder bags with patch pockets in a contrasting color. Each bag requires 5/9 of a meter of material costing $5 per meter, and 2/5 meter of the contrast material at $6 per meter. How much will each bag cost ?

!


a) $5 7/45
b) $4 8/45
c) $5 8/41
d) $5 8/45
$25/9 for bag material and $12/5 for pocket material.
16. Timothy has a cookie recipe that calls for 3/4 cups of margarine to make 36 ginger snaps, and another recipe that uses 1/4 cups of margarine for 48 sandies. How many cups of margarine will he need if he wants to obtain 50 of each ?

!


a) 1 187/288
b) 1 87/288
c) 1 87/188
d) 1 87/281
He will need 3/144 cup for each ginger snap and 1/192 cup for each piece of sandies .
17. A girl is 36 years younger than her mother. In 8 years her age will be 2/3 of half of her mother's age. What is her present age ?

a) 12
b) 8
c) 14
d) 10
M-36 = G means M+8-44 = G and with (M+8)/3 = G+8 it means G+44 = 3xG + 24. So 2xG = 20 .
y
18. A cycler took 4 hours to cover 100 km. Each hour his average speed decreased by 1/8 . How many km./h. should his speed be in the last hour of the journey ?

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


a) 20 1/4
b) 19 1/3
c) 21 2/5
d) 22 3/7
Take care that is average speed is known. Look for further help in ry1.
19. The amount of federal spending in 2011 was $3.6 trillion. We further know that 23% means 23/100 of it. How many dollars should have been spent for health care ?

!


a) 8 280 000 000 000
b) 828 000 000 000
c) 828 000 000 000 000
d) 82 800 000 000 000
23/100 x 3 600 000 000 000 = ?
20. Hospital care's share in health care is about 7/25 and average duration of stay in hospitals is about five days. What is then the share of a day's stay in hospitals in health care budget ?

a) 5/99
b) 6/111
c) 8/139
d) 7/125
7/25 x 1/5 = ?
21. Federal Tax Receipts are roughly $2.3 trillion and 9/25 of it is from Social Security and Insurance. What is the share of this in Federal spendings ?

!


a) 21/100
b) 23/100
c) 19/100
d) 27/100
Receipts share is 23/36 . This means, without making any detailed calculations , ...
y
22. Looking at the figure below we see defence spendings share has decreased by 21/50 in the first 25 years and then by 12/50 in the following 24 years. Considering that the second rate is to be calculated for 25 years and the product of the rates is a plausible candidate to determine the behavior in the following 25 years, what will be the share of defence spendings in 2037 (% value is to be found)?

!


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

RY1 RY2



a) 19 83/100
b) 17 83/100
c) 11 83/100
d) 21 83/100


For the interval 1987-2012 it may be plausible to say defence spendings have decreased by 1/4 . Look at ry1.
Reduced by 1/4 from 29.7 % it will be 22.275 % and reduced again by 21/200 it will be, as a mixed number, 19 83/100 %.
23. Which multiplication below has the smallest result ?

a) 5/11 x 1/10
b) 3/11 x 2/15
c) 11/15 x 3/9
d) 10/9 x 1/10
a is smaller than d and c . a is 5/110 b is 6/165.
24. 21/3 x 32/4 + 43/5 x 54/6 x 63/7 = ?

a) 699 5/7
b) 702 3/5
c) 385/2
d) 998/3
First reduce the fractions: 7x8 + 43/5 x 9x9. Then multiplications: 56 + 3483/5 = 56 + 3480/5 + 3/5 = 702 ...
25. 27 2/5 x (3 1/6 - 2 1/6) = ?

a) 25 2/7
b) 27 2/5
c) 23 6/7
d) 19 7/8
3 1/6 - 2 1/6 = 1
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
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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