Test: Fractions - JAMB MCQ

Concept Used:

a/b and c/d are two numbers,

then (a × d) and (b × c) are need to be compared.

Calculation:

We have, 9/16 and 13/24 

⇒ 9 × 24 = 216

⇒ 13 × 16 = 208

⇒ 216 > 208

⇒ 9/16 > 13/24.

⇒ 2x = 2 - x

⇒ 3x = 2

⇒ x = 2/3

∴ The value of x is 2/3

The correct option is 3 i.e. 2/3

Given:

{(2.5)3 + (1.5)3}/{(2.5)3 – (1.5)3}

Calculation:

⇒ ? = {(2.5)3 + (1.5)3}/{(2.5)3 – (1.5)3}

⇒ ? = (15.625 + 3.375)/(15.625 - 3.375)

⇒ ? = 19/12.25

⇒ ? = 1900/1225 = 76/49

⇒ 59/20

(7/13) = 0.538

(2/3) = 0.666

(4/11) = 0.3636

(5/9) = 0.5555

Out of 2/3, 7/13, 4/11, 5/9

2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.

∴ The ascending order will be 4/11, 7/13, 5/9, 2/3.

Given:

Calculations:

= 9 × 17
=153

Given:

Calculation:

On picking fractions one by one,

⇒ 1 - 1/2 = 1/2

⇒ 2 + 1 = 3

⇒ 1 + 1/3 = 4/3

⇒ 1 + 4/3 = 7/4

⇒ 1 + 4/7 = 11/7

⇒ (13/5) × (45/26) × (20/3) = ?

⇒ (9/2) × (20/3) = ?

⇒ 3 × 10 = ?

⇒ ? = 30

Let the total number of students in the group be 1

Number of students who are below age 8 = 1 × 1/5 = 1/5

Remaining students = 1 – 1/5 = 4/5

Number of students who are above age 8 = 4/5 × 2/5 = 8/25

Number of students who are exactly 8 years old = 1 – 1/5 – 8/25 = 12/25

Short trick:

Let the total number of students be 25

Number of student who are below age 8 = 25 × 1/5 = 5

Remaining students = 25 – 5 = 20

Number of students who are above age 8 = 20 × 2/5 = 8

Number of students who are exactly age 8 = 25 – 5 – 8 = 12

Required fraction = 12/25

Given expression is,

⇒ ? = 144/18

⇒ ? = 8

Given:

The fractions are 13/19, 25/ 31, 28/31, 70/79.

Calculation:

The values are-

13/19 = 0.68

25/31 = 0.80

28/31 = 0.90

70/79 = 0.88

∴ Option C is correct.

Let the number of people be x and number of the chair be y.

Number of available chair = y × (9/13) = 9y/13

Number of empty chair = y - (9y/13) = 4y/13

Given, Number of empty chairs = 28

According to the question

4y/13 = 28

y = 28 × (13/4) = 91

Total number of chairs = 91

Number of chairs in which people are sitting = 91 - 28 = 63

Number of people who sit = x × (7/9) = 7x/9

According to the question

7x/9 = 63

x = 63 × (9/7) = 81

Total number of people are = 81

Chairs would have been still empty if everyone in the hall was sitting = 91 - 81 = 10

= 25/2 + 37/3 + 73/6

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick:

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)

= 36 + 1 = 37

Formula used :

(1 + 2 + 3 + 4 +     ......... + 99) = [ n ( n + 1 ) ] ÷ 2

Solution :

We can write all proper fractions whose denominators are less than or equal to 100 in given form :

⇒ 1/2 + (1/3 + 2/3) + (1/4 + 2/4 + 3/4) + ...  (1/100 + 2/100 + .. ..  99/100)

⇒ 1/2 + 3/3 + 6/4 + ..... + 4950/100

⇒ 1/2 + 1 + 3/2 + 2 + ........ + 99/2

We can also write this equation in following way :

⇒ 1/2 + 2/2 + 3/2 + ...... + 99/2

⇒ 1/2 ( 1 + 2 + 3 + ..... + 99 )

⇒  /2 [ ( 99 × 100) ÷ 2 ]

⇒ 99 × 25

⇒ 2475

Hence the correct answer is "2475".