Olympiad Test: Rational Numbers - CAT MCQ

Expressing in standard form, we get 
Express each rational number with L.C.M as denominator. L.C.M of 9 and 5 is 9 × 5 = 45. 

∴   

Comparing the numerators, we have −40<−36 . 

∴ 
for -ve number the lesser number is actually bigger

To express the fraction -28/84 as a rational number with a numerator of -4, you need to find a common factor to simplify the fraction. Both -28 and 84 are divisible by 4:

-28 ÷ 4 = -7 84 ÷ 4 = 21

So, -28/84 simplifies to -7/21. To express it with a numerator of -4, you can further simplify:

-7/21 = (-7 ÷ 7) / (21 ÷ 7) = -1/3

Now, to have a numerator of -4:

-1/3 * 4/4 = -4/12

Therefore, -28/84 expressed as a rational number with a numerator of -4 is -4/12.

 So,  
Hence, both (b) and (c) are false.

LCM of 5,10,15 and 20 which is 60. Now making the denominator same, we have . So descending order is that is 

LCM of 5,3 and 15 is 15

Additive inverse of 2 is −2
Multiplicative inverse of 2 is 1/2
∴ The sum of multiplicative inverse and additive inverse = 

Answer : 

ANSWER :- b 

Solution :- 7/8 - 2/3

= {(21-16)/24}

= 5/24

Hence the correct answer is 5/3.

5/4 – 8/3

Making the denominator equal:

[(5/4) x (3/3)] – [(8/3) x (4/4)]

= (15/12) – (32/12)

= (15 – 32)/12

= -17/12

-⅙ = -0.16

4/9 = 0.44

-6/7 = -0.85

⅖ = 0.40

-¾ = -0.75

Descending Order : - 4/9, 2/5, -1/6, -3/4, -6/7

Middle term : - -1/6

Arranging the given rational numbers in ascending order, we  get 
The two middle rational numbers  
Their average is 

-3/7-(-5/9)
-3/7+5/9
(-3*9 + 5*7 )/63
(-27 + 35 )/63
8/63

The correct answer is b

Let the number be x 

Then, 

X+(-4/7)=5/9

X=5/9+4/7

X= 35+36/63

X=71/63

Let x be subtracted from -7/11
then -7/11 - x= -2
-x= -2 + (7/11)
-x= -2 + 7/11
-x= -15/11
x= 15/11

Let the rational no be x
-3/5 X x = 21
x = (21 X5 )/ -3 
x = -35

The correct answer is a.

Let the other number be x 

x+(-11/5)= -3

x= -3+11/5

x=-15+11/5

x= -4/5