# The numerator and the denominator of a fraction are consecutive numbers. if the fraction is equivalent to a fraction whose denominator is 24,how many fractions canbe named as such

1
by aj121202

2014-11-04T09:35:04+08:00
Hmmm... this one is tricky I suppose...

but I'll try...

consecutive numbers means numbers which follows each other in order without gaps...

so it can be 1, 2, 3 or 10, 11, 12... etc

so if the fraction is equivalent to a fraction whose denominator is 24...

we must find numbers that can be divide exactly to 24... those are 2, 3, 4, 6, 8 and 12 except for 1(because it can give  us not a fraction but a whole number)

the fraction can be:

1/2 which is equal to 12/24

and

2/3 which is equal to 16/24

and

3/4 which is equal to 18/24

and

5/6 which is equal to 20/24

and

7/8 which is equal to 21/24

and

11/12 which is equal to  22/24

now you may now already notice that the numerator is lesser than it's denominator, we may now do the opposite

we may have:

3/2 which is equal to 36/24

and

4/3 which is equal to 32/24

and

5/4 which is equal to 30/24

and

7/6 which is equal to  28/ 24

and

9/8 which is equal to 27/24

and lastly

13/12 which is equal to  26/24

and now for the real question you have. How many fraction can be named such?

let us list all of those...

1. 1/2
2. 2/3
3. 3/4
4. 5/6
5. 7/8
6. 11/12
7. 3/2
8. 4/3
9. 5/4
10. 7/6
11. 9/8
12. 13/12

So we have 12 fraction to be named.

I hope this helps.