Question

lf p/q is a fraction whose value is greater than 1, which of the following is a fraction whose value is always less than 1 ? (a)p/q×p/q (b)q/3p (c)q/p (d)p+q/q​

Answer 1

Given: p/q is a fraction whose value is greater than 1

To find: Which of the following is a fraction whose value is always less than 1 ?

Solution:

• Now we have given that p/q is a fraction whose value is greater than 1.

• That means p > q.

• The options given are: (a)p/q×p/q (b)q/3p (c)q/p (d)p+q/q​

• Considering one by one:

                 a. p/q x p/q = (p/q)^2

                 Since p/q is greater than one then the square will be always greater than one.

                 eg: 7/3 > 1, (7/3)^2 = 49 / 9 > 1

                 (b) q/3p

                 Since q < p so this will always be less than 1.

                 eg: 7/3 > 1, 3/3(7) < 1

                 (c)q/p

                 Since q < p so this will always be less than 1.

                 eg: 7/3 > 1, 3/7 < 1

                 (d)p+q/q​

                 eg: 7/3 > 1, 3 + 7/7 = 10/7 > 1

                 So this will be always greater than 1.

Answer:

             So the second and third option are correct.

Answer 2

Given: p/q is a fraction whose value is greater than 1

To find: Which of the following is a fraction whose value is always less than 1 ?

Step-by-step explanation:

• Now we have given that p/q is a fraction whose value is greater than 1.

That means p > q.

The options given are: (a)p/qxp/q (b)q/ 3p (c)q/p (d)p+q/q

Considering one by one:

a. p/q x p/q = (p/q)^2

Since p/q is greater than one then the square will be always greater than one.

eg: 7/3 > 1, (7/3)^2 = 49/9 > 1

(b) q/3p

Since q<p so this will always be

eg: 7/3 > 1, 3/3(7) < 1

less than 1.

(c)q/p

Since qp so this will always be

eg: 7/3 > 1, 3/7 <1

less than 1.

(d)p+q/q

eg: 7/3 > 1, 3+ 7/7 = 10/7 > 1

So this will be always greater

than 1.

Answer:

So the second and third option are correct.