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FOURTH GRADE / MATHEMATICS /ADDITION of FRACTIONS 1.2

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. 1/5 + 1/3 = ?

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

RY1 RY2



a) eight fifteenths
b) fifteen divided by eight
c) fifteen eighth
d) almost a half


Just to remind you of the necessity of equal denominators.
2. What is the sum of all fractions having numerators all 1 and denominators that are odd multiples of 5 and less than 45 ?

a) 105/525
b) 176/525
c) 150/525
d) 165/525
1/5 + 1/15 + 1/25 + 1/35 = ? is asked, common denom. is 525.
3. Two fractions:
* Both have as numerator a 1.
* One's denominator is the greatest 2-digit even number and the other's the least 3-digit natural number.

What will the sum of these fractions be ?

a) 199/9800
b) 97/4900
c) 99/4950
d) 99/4900
1/98 + 1/100 = ? Common denom. is 4900 .
4. The sum of 3 consecutive numbers is 21 .
What will be the sum of 3 fractions, all having numerator 7 and one of these 3 consecutives as the denominator ?

a) 59/24
b) 17/8
c) 73/24
d) 21/12
The 3 consecutives are 6, 7 ve 8 , and the fractions are 7/6+7/7+7/8 .
5. What will be the sum of 6 different fractions, whose numerators are all 1 and denominators are with 3 evenly divisible numbers less than 20 ?

a) 147/180
b) 150/180
c) 145/180
d) 151/180
1/3 + 1/6 + 1/9 + 1/12 + 1/15 + 1/18 = ? , common d. 180 .
6. Mannfred, Justin and Selma share the personal computer at home. They respectively use 2/5, 1/3 and 1/7 of the hard disk.
How much of the disk do have written data in ?

a) 29/35
b) 87/105
c) 89/105
d) 92/105
Common d. is 105 .
7. 3/12 + 2/12 + 7/12 + 2/17 + 7/17 = ?

a) 25/12
b) 26/17
c) 19/12
d) 23/17
The first 3 fractions wit 12 as denominator sum up to 1. So 1 + 9/17 = ?
8. If 1/11 + 12/33 = A/33 , what is A ?

a) 7
b) 8
c) 15
d) 27
The first fr. is eq. to 3/33 ... .
9. (2/7 + 3/5) + (4/5 + 11/7) = ?

a) 114/35
b) 111/35
c) 101/35
d) 91/35


Filter first the groups having common denominators; operation reduces to 13/7 + 7/5 = ?
65/35 + 49/35 = ?
Just sum 65 and 50 and subtract 1.
10. Two brothers' ages have a sum of 27 whereas the greater has an age which is a quarter of it more than younger brother's age.
How old is the elder ?

a) 10
b) 11
c) 12
d) 15
Just try, it is pretty easy to see . There are not very many candidates though .
11. In the class 4-A there are 45 pupils (still quite normal for a developing country). What is the fraction of the girls if 30 of them are boys ?

a) 2/3
b) 1/3
c) 3/4
d) 3/5
There must be 15 girls.
12. The Atalanta Coed School has 600 pupils 1/5 ths being jr. h. school pupils.
Girls being half of the primary school and 2/5 ths of the jr. h. school pupils , how many of the pupils of this school are girls ?

a) 290
b) 270
c) 288
d) 250
Nu. of Jr. H. Schoolers is 120.
13. Which of the following statements are correct ?

I: 4 quarters make a unit fraction.
II: Sum of 2 unit fractions of 5/4 makes an half.
III: Sum of 4 quarters is a fraction that is equivalent to unity.
IV: 5 quarters can not be handled as fraction.


a) I , II ve III
b) tümü
c) II ve III
d) II ve IV
Unit fraction is not unity, it is unity divided by the denominator of the fraction.
5 quarters is 1 and 1/4 , and 1 1/4 .
14. Mr. Baumont the retiree spends 2/9 ths of his salary, the same day he gets it, for bills and 2/7 ths for the school his jr. attends.
What part of the salary is spent the first day for these expenses ?

a) 32/61
b) 29/63
c) 32/63
d) 21/41
Common denom. is 63 .
15. Megapolis Istanbul and the capital Ankara have an important weight in Turkey. For example 11/90 ths of international post comes to Istanbul and 4/70 to Ankara.
What is their total share of international post ?

a) 113/630
b) 41/371
c) 59/489
d) 27/275
For convenience calculate a factor of ten bigger and then ... .
16. Which summation gives the greatest result ?

I : 5/11 + 11/12=?     II : 18/45 + 16/46=?      III : 4/6 + 2/7=?       IV : 16/23 + 8/24=?

a) I
b) II
c) IV
d) III
a and c greater than 1, b and d less than 1, take care .
17. Cindy and Aaron want to buy a perfume to present their mother for the Mother's Day. Cindy has $ 11 1/4 and Aoron has $ 17 1/2 .
What can the max. price of their present be ?

!
a) 113/4
b) 28 1/3
c) 114/4
d) 28 3/4
Tese are mixed numbers, calculate first the integer part.
18. The regular shapes in the figure below have a total area of 1 (unit) . The area of the pentagon is half the area of hexagon and the same ratio holds between square and pentagon.
How big is the sky blue colored area ?

!
a) 107/420
b) 143/420
c) 135/420
d) 21/84
The sky blue part of the square is 1/(4x7) = 1/28 .
Common denom. for 1/28 + 4/35 + 4/21 is 420 .
19. 95/65 is an improper fraction. What will be the result of converting it to a mixed number ?

a) 1 35/65
b) 1 6/13
c) 1 5/13
d) 1 25/65
Any reduction easily seen and applicable comes first .
20. 2 27/108 is a mixed number. Which result is attained if it is converted to an improper fraction ?

a) 241/108
b) 236/108
c) 9/4
d) 11/5
2x108 = 216 + ...
21. Which choice gives A, if 10/150 = A/30 ?

a) 3
b) 2
c) 4
d) 5/2
10/150 is equivalent to 1/15 kesridir.
y
22. A farmer set aside 1/10 ths of his land for vegetables, one half for grain and 1/5 ths for cultivation of legumes leaving the rest fallow.
On 1/3 rds and 5/9 ths of the area set aside for vegetables he planted tomatoes and beans (again a legume for his own family needs) respectively.
What is the ratio of these last two to the total area ?


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

RY1 RY2



a) 6/80
b) 8/90
c) 8/9
d) 11/90


with respect to the total land ... .
23. Which of the sums is less than a quarter ?

a) 25/110 + 15/105
b) 22/157 + 13/110
c) 23/159 + 11/145
d) 10/39 + 1/100
The answer may be b or c .
24. Which is the number whose half and a quarter add up to 72 ?

a) 96
b) 99
c) 98
d) 94
1/2 + 1/4 = 3/4 . Three fourths of the number should be 72 .
25. What will be the mean of 1/4 , 1/8 and 1/16 ?

a) 7/48
b) 5/13
c) 7/16
d) 21/16
Find first sum and divide by 3 .
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