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FIFTH GRADE / ADDITION of FRACTIONS / TEST 1.2

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
   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. Which number amounts to 225 3/4 in case the number , quarter of it and its 1/16 ths are added ?

a) 172
b) 153
c) 236
d) 122
Try the choices, the number can not be an odd number because it has 3/4 added to a whole number .
Pay attention to 1/16 ths of the numbers given in the choices, they all are between 8 and 15 .
2. 1/7 + 2/9 + 2 1/7 ?

a) 141/63
b) 61/29
c) 443/157
d) 158/63
It is equal to 2 + 2/7 + 2/9 .
3. (1/5 + 1/15) + ( 1 1/25 + 1 1/35) = ?

a) 1226/525
b) 234/55
c) 489/107
d) 611/525
First separate the whole number and write in the form 2 + ... . Multiples of 35 are 35 , 70 , . , 140 and 175 means the common denominator of the second paranthesis is 175 .
4. (1/3 + 3/4) + (1 + 1/3)/3 = ?

a) 45/27
b) 55/36
c) 41/29
d) 61/39
(4/3) / 3 = 4/9 .
5. (3 1/2 + 2/3) + (2 3/4 + 8/5) = ?

a) 411/49
b) 387/37
c) 511/60
d) 447/45
Separate first the whole numbers. In case of addition a number may get out of the paranthesis with its (same) sign .
y
6. 7/48 + 11/60 + 3 20/24 = ?

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



a) 479/240
b) 3 + 479/240
c) 999/240
d) 99/24


First we are supposed to reduce the fractions if possible.
The fraction part of 3 + 20/24 is reducible, all others irreducible. Reduce them by 4 .
ry2 shows how to find LCM (Least Common Multiple) of 48 and 60 which will also be true for 24.
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. Which result is obtained if the operation defined below in the figure is performed with the numbers given in the figure ?

!


a) 277/60
b) 331/60
c) 325/60
d) 283/60
Just place the numbers into their correct places .
We want you to get acquainted with the matrices via this simple operation .
8. An auto driver traveling from Ankara to Istanbul takes a breather after traveling 1/3 rds of the way and a second breather after 2/5 ths. What is the total fractional part he has left behind ?

a) 7/11
b) 2/3
c) 1/3
d) 11/15
This is the first step of question 19 of "http://www.test-dr.com/education/5th-Grade-Mathematics/addition-of-fractions-5.1.1.html" .
9. The heights of the green and light yellow regions of IV are equal. What will then be the total fractional part of green regions in the rectangle formed by II, III and IV ?

!


a) 19/32
b) 19/96
c) 21/106
d) 17/35


Neglect the upper half and divide the result you obtained by 2 .
10. 3 different masons build a 100 m2 wall in 10, 9 and 9 1/2 hours respectively. How many m2 will they build in an hour if all work together ?

!


a) 457/329
b) 327/564
c) 551/3787
d) 541/1710
1/10 + 1/9 + 2/19 = ?
11. 1 3/4 + 2 7/9 is equivalent to ...

!
a) 54/32 .
b) 2 3/4 + 4 7/9 .
c) 326/72 .
d) 1 6/8 + 2 14/18 .
Equivalent fractions are reduced/expanded forms of each other .
y
12. 2/945 + 7/1680 + 11/840 = ?

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

RY1 RY2



a) 27/1381
b) 293/15120
c) 7/1527
d) 347/4317
1680 = 2x840.
Is 1680 = 700 + 700 + 280 divisible by 7 ?
How to find GCD of 7 and 1680 is shown in ry1.
LCM is in ry2 .
13. A seat multiplex is divided into 3 theatres. The 27/80 of the seats are in Theatre 1, and there are as many as 15/80 of the total number of seats more seats in Theatre 2 than in Theatre 3. Which fraction of the seats are then either in Theatre 1 or Theatre 2 ?

!


a) 31/40
b) 61/80
c) 76/142
d) 17/32
Take the simplest case of 80 seats. In Theatre 2 and 3 there should be 53 seats. 53/2 = 26 1/2 .
There should be 15 more in T-2 which means 26 1/2 - 7 1/2 = 19 seats in T-3. And of course 34 in T-2 .
14. Terry goes to shopping mall with $500. He buys PSP for his son and then he buys a toy for his daughter for half the price of PSP. Then he spends 1/10 ths of money's rest on food, leaving him with $270. How much ($) should the price of PSP be ?

!


a) 500/3
b) 100/3
c) 200/3
d) 400/3
Before food he must have $300. Let the price of PSP be P, (1+1/2)xP should be $200
15. The sum of 1 + 36/A is desired to be an integer. How many A (natural number) values are possible ?

a) 9
b) 6
c) 4
d) 3
A+36 should be divisible by A. 1 is an integer which means 36/A should be an integer. 36 is divisible by A if A=1, ...
16. The question is below in the figure .

!


a) 3
b) 4
c) 2
d) 5/3
Each element of the numerator is twice the corresponding element in the denominator .
17. 1/2 + 3/(4x5) + 6/(7x8) + 9/(10x11) = ? ?

a) 323/385
b) 144/175
c) 71/98
d) 221/259
1/2 + 3/20 + 3/28 + 9/110 = (110+33+18)/220 + 3/28 = ...
y
18. In a class 7/48 of students got an A from math. and 1/12 of class got an A from both math. and physics. Which of the followings is true ?

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


a) Max. number of students who got other grades than A from math. and an A from physics is 41 .
b) Max. number of students who got an A from physics is 40 .
c) Max. number of students who got an A from only physics is 7 .
d) Max. number of students who got other grades than A is 42 .
Have a look at ry1 . Just to get acquainted with set theory .
19. A group of boys and girls has an average age of 11. It is known that the number of boys is twice the number of girls. Which choice is most likely to be the average number that may the sum of the ages of 1/4 of the girls and 1/2 of the boys ?

a) 45
b) 54
c) 53
d) 47
The simplest group consists of 4 girls each having an age of 13 and 8 boys each being 10 years old. 1/4 of the girls is a girl with most probable age of 13
20. Natural numbers from 1 to 54 are written from left to right consecutively just one after another and a new 99 digit number is obtained. What will be the sum of inverses of the 50 th and 70th digits from the left ?

a) 29/33
b) 13/21
c) 5/9
d) 7/12
The inverse of a digit D is 1/D . The question is very simple indeed and you have to see the structure and pinpoint the digits very quickly. This means gaining precious time.
The first 9 elements are the 9 digits. So for the other 45 numbers there are 90 digits . 10th digit is tens' of 10, i.e. 1. 30th digit is 2 and 50th digit 3. 90th digit is 5.
21. From a mixture whose half is water 20 l. of water has evaporated. 3/10 ths of the resulting mixture is water. How many liters was the original mixture ?

a) 70
b) 85
c) 57
d) 68
These type of problems are more easily solved by trial and error. Just try the answers .
Let he amount of mixture be B at the beginning and E at the end. We have to find 2 equations:
1. E = B - 20 .
2. (3/10)xE + 20 = B/2.
Putting 1 in 2 we have (3/10)x(B-20) + 20 = B/2 which means B/2 - 3xB/10 = 14
y
22. 1/h + 1/|CD| + 1/|AB| = ?

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

RY1 RY2



a) 3/17
b) 4/21
c) 2/13
d) 1/6


Learn 3-4-5 triangle, it is important. Have please a look at ry1 for the rest.
The question reduces to 1/12 + 1/20 + 1/30 = ?
23. Which addition below has the smallest result ?

a) 5/11 + 1/10
b) 2/15 + 3/11
c) 3/19 + 11/15
d) 10/9 + 1/10
The last two are around 1 whereas the first two are around a half .
24. 21/3 + 32/4 + 43/5 = ?

a) 21 2/7
b) 23 3/5
c) 17 3/4
d) 15 7/8
The first two are 7 and 8 .
25. How many many natural numbers, 0 excluded, A make 5/(A+5) + 1/2 an improper fraction ?

a) 4
b) 8
c) 5
d) 6
5/(A+5) ≥ 1/2 .
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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