Question

Identify the smallest of the fractions 4/5 , 4/7 , 4/9 , 4/11

Answer 1

Answer:

(4/11) is the smallest fraction.

Step-by-step explanation:

We have,

(4/5), (4/7), (4/9), and (4/11)

We can solve it in two ways,

Method 1 (LCM)

We know that,

To know which fraction is the smallest we need to have the like fraction.

Then, they must have the same denominators.

So, we must take their LCM

LCM (5, 7, 9, 11) = 3465

Then,

(4/5) × (693/693)

= (4 × 693)/(5 × 693)

= 2772/3465

Also,

(4/7) × (495/495)

= (4 × 495)/(7 × 495)

= 1970/3465

Also,

(4/9) × (385/385)

= (4 × 385)/(9 × 385)

= 1540/3465

Also,

(4/11) × (315/315)

= (4 × 315)/(11 × 315)

= 1260/3465

Hence, we see that,

1260 < 1540 < 1970 < 2772

= (1260/3465) < (1540/3465) < (1970/3465) < (2772/3465)

= (4/11) < (4/9) < (4/7) < (4/5)

Hence,

(4/11) is the smallest of the fractions

Method 2 (General equation/Short trick)

Let's observe some fraction,

(1/1) = 1

(1/2) = 0.5

(1/3) = 0.33

(1/4) = 0.25

(1/5) = 0.2

Here, if we observe, we see that,

As the denominator increase the value of fraction decreases

So,

If a fraction (m/n) = k

As n increases, k decreases.

Here, we are lucky to get 4 as the numerator for all the fractions, because if the fraction has different Numerators then this trick will not work.

So,

The fraction with the highest denominator will be the smallest.

Here out of 5, 7, 9, and 11

11 is the largest

Hence,

(4/11) is the smallest fraction.

Note : It is important that the numerators of the given fraction is the same if not the second method trick will not work and we must use the first method.

Hope it helped you and believing you understood it...All the best