Question

In a certain theater, there are 16 empty seats out of 240 total seats. Write a ratio of empty seats to total seats as a fraction in simplest form. Then explain

Answer 1

16/240

8/120

4/60

2/30

1/15

hope this helps

Answer 2

`(1)/(15)`

Explanation:

Number of empty seats = 16

Total number of seats = 240

To find : ratio of empty seats to total number of seats as a fraction in simplest form.

A fraction
`(x)/(y)` is said to be in simplest form if
`HCF\,(a,b)=1`

Solution:

ratio of empty seats to total number of seats = Number of empty seats / Total number of seats =
`(16)/(240)`

Here,
`(16)/(240)` is not in simplest form , so we need to solve it further .

`16=2*2 * 2* 2=2^4`

`240=2* 2* 2* 2* 3* 5=2^4* 3* 5`

We know that HCF is greatest common factor , so
`HCF(16,240)=HCF(2^4\,,\,2^4* 3* 5)=2^4=16`

Therefore,

`(16)/(240)=(1)/(15)`