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FIFTH GRADE / MULTIPLICATION of FRACTIONS / 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
  AS WE HAVE NOTED EARLIER
 ♦ 
MULTIPLICATION IS REPEATED SUMMATION  MODELED COMPACTLY IN TWO DIMENSIONS
 ♦ SO IT IS (PSEUDO) TWO DIMENSIONAL.

THERE ARE TWO GOLDEN RULES:
1. NUMERATORS ARE MULTIPLIED, USED AS THE RESULT'S.
2. DENOMINATORS ARE MULTIPLIED, USED AS THE RESULT'S.
1. What is the following figure trying to conduct ?

!


a) Change of units may make natural numbers fractions.
b) Our definition of operations are to be units independent.
c) Our abstarctions are to be consistent to describe natural phenomena.
d) All of the above.
This is a very simple question whose main aim is to warn you about abstractions.
2. (432/123)x(132/243) = ?

a) 1 354/376
b) 1 335/369
c) 2 127/649
d) 2 047/397
First are the fractions to be reduced to simplest forms. First may be reduced by 3 and gives 144/41. The second may also be and 44/81.
Now we have 144x44/41x81. 144 in numerator and 81 in denominator may be reduced by 9 to obtain 16x44/41x9 = 704/369 = ... .
3. Both figures are squares, the second having 7/10 ths of the side of the first. What will be the product of the fractions of blue parts ?

!


a) 35/157
b) 38/149
c) 45/128
d) 54/177
The fraction of blue areas in the first square, considering symmetry or reduction by 2, is 9/16 . The second has double symmetry or reduction by 4 which gives 5/8 .
The ratio of the sides is immaterial, the multiplication is 9/16 x 5/8 = ?
4. What will be the product of the smallest and biggest fractions shown in the figure below ?

!


a) 17/4800
b) 15/3600
c) 13/2900
d) 11/2400
3/40 x 17/360 = 1/40 x 17/120 = ?
5. 189/2520 x 285/1521 = ?

a) 17/1257
b) 19/1352
c) 21/1457
d) 13/1566
The GCD of the first is 63 and the second 3. So 3/40 x 95/507 = 3x95/40x507 = 19/8x169 = ?
y
6. 3 x 1/5 = ?

!


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



a) 2/7
b) 4/9
c) 3/7
d) 3/5


Just to give a reson for multiplication of numerators . Please have a look at ry1 .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. What will be the product of two fractions whose numerators are both 25 and denominators are the greatest 2-digit even number and the least 3-digit odd number ?

a) 1050/9800
b) 9/4900
c) 625/9898
d) 925/9080
25/98 x 25/101 = ? where 98 x 101 = 9800 + 98 .
8. 1/2 x 1/3 x 1/4 x 1/5 x 1/6 x 1/7= ?

a) 1/5040
b) 1/4080
c) 1/2400
d) 1/720
6!=1x2x3x4x5x6=720 .
9. 1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7 = ?

a) 480/953
b) 480
c) 720/5603
d) 1/7
Take care of common terms in numerators and denominators and reduce .
10. 1 x 3/4 x 8/9 x 15/16 = ?

a) 5/8
b) 7/9
c) 551/840
d) 771/956
First reduce .
11. (1/3 + 1/4) x 5/3 = ?

a) 45/46
b) 35/36
c) 29/37
d) 47/51
Paranthesis first .
y
12. 1/4 x 1/5 = ?

!


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

RY1 RY2



a) 1/25
b) 1/15
c) 1/30
d) 1/20
Just like question 6, but this time denominators .
13. What is the total relative decrease in temperature if it happens to decrease by 1/10 in each of the three consecutive days ?

!
a) (27 1/10) / 100
b) 27/100
c) 30/100
d) (25 1/5)/100
Take the initial value of the temperature as 100 °F . The first day it drops to 90 °F; the second day to 81 °F and the third day to 81 - 81/10 °F. From here you can deduce.
The total drop is 10+9+8 1/10 = 27 1/10. Relative means the result of the total drop is to be divided by the original value (100 °F).
14. In which figure the green covered area is 1/2 of 3/8 ?

!
a) III
b) I
c) II
d) IV


1/2 of 3/8 is 3/16 (of the whole rectangle) .
15. 12 1/5 x 17 3/4 = ?

a) 109
b) 20933/20
c) 17 3/20
d) 4331/20
12 1/5 = 12 + 1/5 and either the rule of multiplication of summation is to be applied or the mixed numbers are to be converted to improper fractions.
The first method : (12 + 1/5)x(17 + 3/4) = 12x17 + 12 x 3/4 + 1/5 x 17 + 1/5 x 3/4 = ?
The second : 61/5 x 71/4 = ?
16. A cyclist took 2 000 km. , driving each day the same amount of distance, in 30 days. Which fraction is driven in a week and what is the amount (km.) driven in a week ?

!
a) 7/30 ; 1400/3
b) 7/30 ; 2000/3
c) 7/30 ; 2000/7
d) 7/30 ; 200/7
A week is 7 days, the trip duration was 30 days .
17. Binary operations do normally have two elements both of which changes after the operation. The identity element is an exception. It leaves other elements unchanged when combined with them.
Which choice may be the identity element in multiplication and division ?

a) 2
b) 1
c) 3
d) 5
Example: 17 x 1 = 17 .
y
18. What will be the result of multiplication 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) 4/9
b) 3/5
c) 4/7
d) 2/9
The numerator of the fraction left : 3/2 - 10/12 .
The numerator of the fraction right: 1 - 1/3
19. Which point corresponds to AxB on the scaled number line below in the figure ?

!


a) III
b) I
c) II
d) IV
The number line is scaled .
20. A clearance sale offers an additional 1/2 off items that are already reduced by 2/10. This of course is not the same as 7/10 off the original price. What will be the product of fractional prices of both cases ?

a) 3/17
b) 3/25
c) 2/15
d) 1/9
1 - 2/10 = 4/5 and 1/2 x 4/5 = 2/5 . 1 - 7/10 = 3/10 .
21. A triangular number is a number obtained as the sum of consecutive integers. That means nth triangular number is the sum of all integers from 1 to n . Let Tn indicate the nth triangular number. T3/T5 x T4/T6 = ?

a) 4/21
b) 3/17
c) 7/63
d) 6/49
The sum of all integers from 1 to n is nx(n+1)/2 .
y
22. Janet picked a bad of oranges to give to her friends. To the first of her friends, she gave 1/4 ths of the oranges she had and another two beside. To her second friend she gave 1/4 ths of the remaining oranges and another five beside. To her third friend she gave half of the remaining oranges and another one beside. By this time, she had seven oranges left.
2nd friend met Mrs. Petersen on the way home. She gave 1/4 ths of the oranges to her. Mrs. Petersen gave then 1/3 rds of the oranges she got to her son. How many ?


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

RY1 RY2



a) 2
b) 4
c) 1
d) 3


First solve for the original number of oranges as in Q.-22 of "http://www.test-dr.com/education/5th-Grade-Mathematics/subtraction-of-fractions-5.1.3.html" .
2nd friend got 12 oranges. 1/4 x 1/3 = 1/12 .
23. Which multiplication below has the smallest result ?

a) 5/22 x 3/2
b) 1/157 x 13/5
c) 23/159 x 11/145
d) 27/39 x 1/100
Certainly not a and b , seek among the others . c seems to be around 1% .
24. (2 1/3 - 1/3) x (2 - 1/5) = ?

a) 3 - 1/5
b) 4 - 2/5
c) 5 - 3/7
d) 2 - 3/7
First paranthesis gives 2 .
25. Which property should the integer A have in order to make 1/(A+1) x 3 a mixed number ?

a) 1/(A+1)≥1/3
b) A ≠ 1
c) A < 0
d) A > 0
1/(A+1)≥1/3.
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
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