Question

Which number has the lowest value ? a) 1/4 – 1/6 b) 1/3 – 1/9 c) 1/3 – 1/6 d) 1/6

Answer 1

1/6 has the lowest value..
Hope it helped you....

Answer 2

Answer:

Option (a)  $\frac{1}{4}$ -  $\frac{1}{6}$  has the least value.

Step-by-step explanation:

We need to find the lowest value out of the following:

(a)  $\frac{1}{4}$ -  $\frac{1}{6}$

(b)  $\frac{1}{3}$ -  $\frac{1}{9}$

(c)  $\frac{1}{3}$ -  $\frac{1}{6}$

(d)  $\frac{1}{6}$

We need to solve the given numbers

=> (a)  $\frac{1}{4}$ -  $\frac{1}{6}$ = $\frac{1*3 - 1*2}{12}$ = $\frac{3 - 2}{12}$ = $\frac{1}{12}$

    (b)  $\frac{1}{3}$ -  $\frac{1}{9}$ = $\frac{1*3 - 1*1}{9}$ =  $\frac{3 - 1}{9}$ = $\frac{2}{9}$

    (c)  $\frac{1}{3}$ -  $\frac{1}{6}$ = $\frac{1*2 - 1*1}{6}$ =  $\frac{2 - 1}{6}$ =  $\frac{1}{6}$

    (d)  $\frac{1}{6}$

Now, as all of them have different denominators,

we take LCM of 12, 9, 6 so that they have same denominator.

=> (a)  $\frac{1}{12}$ =  $\frac{1}{12}$ * $\frac{3}{3}$ = $\frac{3}{36}$

    (b)  $\frac{2}{9}$ =  $\frac{2}{9}$ * $\frac{4}{4}$ = $\frac{8}{36}$

    (c)  $\frac{1}{6}$ =  $\frac{1}{6}$ * $\frac{6}{6}$ = $\frac{6}{36}$

    (d)  $\frac{1}{6}$ =  $\frac{1}{6}$ *  $\frac{6}{6}$ = $\frac{6}{36}$

Now we can easily compare the numerators.

As we know that 3 < 6 < 8

=>  $\frac{3}{36}$ <  $\frac{6}{36}$ <  $\frac{8}{36}$

=> $\frac{1}{12}$ <  $\frac{1}{6}$ <  $\frac{2}{9}$

=>  $\frac{1}{4}$ -  $\frac{1}{6}$ <  $\frac{1}{3}$ -  $\frac{1}{6}$ =  $\frac{1}{6}$ <  $\frac{1}{3}$ -  $\frac{1}{9}$

Therefore,  $\frac{1}{4}$ -  $\frac{1}{6}$  has the least value.

Option (a) is correct.