model 5 smallest and largest fraction/numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Let the three fractions be p, q and r,

where p < q < r.

According to the question,

$r/p$ = $7/6$ ⇒ r = $7/6$ p

Again, middle fraction

= q = $7/6$ - $1/3$ = ${7-2}/6$ = $5/6$

∴ p+q+r = 2$11/24$

⇒ p + $5/6$ + $7/6$p = $59/24$

⇒ p+${7p}/6$ = $59/24$ - $5/6$

⇒ ${6p+7p}/6$ = ${59-20}/24$ = $93/24$

⇒ 13p = $39/24$×6 = $39/4$

⇒ p = $39/{4×13}$ = $3/4$

Answer: (b)

$8/15, 14/33, 7/13, 11/13$

$8/15$ = 0.53$\ov{3}$

$14/33$ = 0.$\ov{42}$

$7/13$ = 0.538

$11/13$ = 0.846

∴$11/13>7/13>8/15>14/33$

Answer: (c)

Decimal equivalents :

$4/9$ = 0. 4: $√{9/49}$ = $3/7$ = 0.43

0.45 : $(0.8)^2$ = 0.64

∴ Least number = 0.43 = $√{9/49}$

Answer: (b)

$7/6$ = 1.166 ; $7/9$ = 0.777; $4/5$ = 0.8 and $5/7$ = 0.714

Therefore, the smallest number is $5/7$

Answer: (b)

LCM of 3, 2 and 6 = 6

∴ $(3)^{1/3}$ = $(3^2)^{1/6}$ = $(9)^{1/6}$

$(2)^{1/2}$ = $(2^3)^{1/6}$ = $(8)^{1/6}$

$(1)^{1/6}$ = 1; $(6)^{1/6}$ = $(6)^{1/6}$

Answer: (b)

If the number be x, then

x – 31 = 75 – x

⇒ 2x = 75 + 31 = 106

⇒ x = 53