Question

6. Which of the following fraction is the smallest fraction?
(a)61/256
(b)31/128
(c)121/512
(d)42/150​

Answer 1

Given,

Fraction=61/256, 31/128, 121/512, 42/150

Solution:-

• To calculate the smallest fraction , we have to find lcm of all denominator of fraction, than comparing the all fraction to eachother]

Lcm of 256, 128, 512, 150=38400

2|256, 128, 512, 150

2|128, 64, 256, 75

2|64, 32, 128, 75

2|32, 16, 64, 75

2|16, 8, 32, 75

2|8, 4, 16, 75

2|4, 2, 8, 75

2|2, 1, 4, 75

1, 1, 2, 75

• Now we have to divide all fraction of denominator by obtaining lcm separately]

For the 1st fraction:(a)

=>61/256 (38400÷256=150)

• Now, multiple in both numerator and denominator by 150 here]

$\tt{\implies \dfrac{61\times\:150}{256\times\:150}}$

$\tt{\implies \dfrac{9150}{38400}}$

For the 2nd fraction:(b)

=>31/128 (38400÷128=300)

$\tt{\implies \dfrac{31\times\:300}{128\times\:300}}$

$\tt{\implies \dfrac{9300}{38400}}$

For the 3rd fraction:(c)

=>121/512 (38400÷512=75)

$\tt{\implies \dfrac{121\times\:75}{512\times\:75}}$

$\tt{\implies \dfrac{9075}{38400}}$

For the 4th fraction:(d)

=>42/150 (38400÷150=256)

$\tt{\implies \dfrac{42\times\:256}{150\times\:256}}$

$\tt{\implies \dfrac{10752}{38400}}$

If we comparing the given above fraction we get that Option-C is the smallest fraction amount all the fraction

$\rm{\underbrace{Answer-option-(c)}}$

Answer 2

Given:

Fraction=> 61/256, 31/128, 121/512, 42/150

Option-(c)