Question

Which statement correctly compares 11/20 an 5/9

A:11/20<5/9
B:11/20>5/9
C:11/20=5/9

Answer 1

`(11)/(20) =(11 * 9)/(20 * 9)=(99)/(180) \\ \\ (5)/(9)=(5 * 20)/(9 * 20)=(100)/(180) \\ \\ 99<100 \Rightarrow (99)/(180)<(100)/(180) \Rightarrow \boxed{(11)/(20) < (5)/(9)} \Leftarrow \hbox{answer A}`

Answer 2

`(11)/(20)<(5)/(9)`

A is correct.

Explanation:

Given:
`(11)/(20)\text{ and }(5)/(9)`

We need to compare the two fraction.

We can compare either greater , less or equal.

If we compare two fraction. First we make their denominator same.

Denominators are 20 and 9

We will find the LCD of 20 and 9

20 = 2 x 2 x 5

9 = 3 x 3

LCD = 2 x 2 x 3 x 3 x 5 = 180

`\text{First Fraction}\rightarrow (11* 9)/(20* 9)\Rightarrow (99)/(180)`

`\text{Second Fraction}\rightarrow (5* 20)/(9* 20)\Rightarrow (100)/(180)`

Now, we can see their denominator are same.

We will compare the numerator.

99<100

Thus,

`(99)/(180)<(100)/(180)`

`(11)/(20)<(5)/(9)`

Hence,
`(11)/(20)<(5)/(9)` correct.