Question

Which of the following is in ascending order?
(a)1/9 1/16 1/13
(b)1/13 1/16 1/9
(c)1/9 1/13 1/16
(d)1/16 1/13 1/9​

Answer 1

Answer :

(d) 1/16, 1/13, 1/9​.

Given :

• 1/9, 1/16, 1/13.
• 1/13, 1/16, 1/9.
• 1/9, 1/13, 1/16.
• 1/16, 1/13, 1/9​.

To find :

• which is in ascending order.

Solution :

⇒ Let's find which of the following is in ascending order.

→ The fractions are 1/9, 1/16, and 1/13.

• First, let's find the LCM of the denominators.

$\begin{array}{c|c} \sf \underline3 & \sf \underline{9,13, 16} \\ \sf \underline4 & \sf \underline{3, 13, 16} \\ \sf \underline3 & \sf \underline{3,13,4} \\ \sf \underline 4 & \sf \underline{1,13,4} \\ \sf \underline{13} & \sf \underline{1,13,1} \\ \sf & \sf \underline{1,1,1} \\ \end{array}$

LCM of 9, 16, and 13 = 3 × 4 × 3 × 4 × 13

= 12 × 3 × 4 × 13

= 36 × 4 × 13

= 144 × 13

= 1872

• Now, making the denominator the LCM.

⇒ 1/9 = 1 × 208/9 × 208

= 208/1872

⇒ 1/16 = 1 × 117/16 × 117

= 117/1872

⇒ 1/13 = 1 × 144/13 × 144

= 144/1872

• Now, let's compare them.

= 117/1872 ≥ 144/1872 ≥ 208/1872

= 1/16 ≥ 1/13 ≥ 1/9

• Therefore, option (d) 1/16 1/13 1/9​ is the right answer.