i need help answering the question below

Question

The manager at Fit Factory Health Club was going through is files for 2007 and discovered that only 5/6 of the members actually used the club. When he checked the numbers for 2006 he found that 8/9 of the members had used the club. What fractional part of the membership represented the decrease in the club usage?

Answer 1

Hello, Shay

Great to see that you are doing math.  This problem deals with subtraction of fractions.  the two fractions are 5/6 and 8/9.

 

The first thing that we have to do is the Least Common Denominator for the two fractions. In order to do that, we have to find the multiples of 9 and 6 and see which is the first number that they have in common/

 

multiples of 9: 9, 18, 27, 36 .....

multiples of 6: 6, 16, 18, 24 ......

 

So, the LCD will be 18.  Now I am going to set up proportions

 

8/9= x/18       x=16    Here 8/9= 16/18

5/6=y/18        x=15    And, 5/6=  15/18

 

Now that both fractions have the same denominator.  Just subtract the numerators and keep the same denominator:

 

16/18 -(15/18)= 1/ 18

 And that's you answer.. And keep doing your work. 

D.Y. T