Explaining fractions in a consistent way I'm trying to explain fractions to a keen 8 year old. I could think of two approaches:
(1) Total Parts divided among Some People (Numerator = no. of pizza)
$\frac{1}{2}$ is the slice if 1 pizza is divided among 2 people
$\frac{12}{4}$ is 12 pizza divided among 4 people (each gets 3)
But explaining $\frac{3}{4}$ gets messy. Take 3 pizza, but divide it among 4 people and notice that each gets the shape that looks like 3 quarters.
(2) Some Parts out of Total Parts (Consider only 1 pizza overall)
$\frac{3}{4}$ Take 1 pizza. Divide by 4. Pick 3 parts out of 4 total parts 
But explaining $\frac{12}{4}$ is messy. Take 1 pizza. Divide by 4. You need 3 such pizza.
Any suggestions on how to use a consistent explanation ? I want to avoid saying: imagine "Approach 1" for some fractions, and imagine "Approach 2" for some other fractions.
I understand Mathematics Stack Exchange usually has difficult questions, but it also states that it is "Q&A for people studying math at any level".  Hence I'm hoping this genuine question is not out of place.
 A: Approach two's 12/4 looks inconsistent for a 8-year-old indeed;
the 3/4 scenario for approach one may be explained using easily-divisible objects like sticks or cups of water (sticking 3 sticks together to get '3' and divide between '4' people equally).
Hope it helps, wish the kid will be a great mathematician.
A: You can explain 3/4 as being three 1/4 pizzas. The denominator of a feaction generally represents howany parts we will break 1 into, the numerator counts howany of these parts we have. With this in mind it is not too much of a leap for a kid to conceptualize 5/4 as "five pieces of pizza each of which is one quarter of a whole pie". 
I would reccomend first practicing examplesthe where the numerator is less than. The denominator. You can draw pictures of arrangements of quarter circles and ask the kid to tell you in each case how many quarters there are. Finally draw a whole pizza and an extra quarter pizza slice next to it. If the kid is used to counting quarters they should be able to extrapolate that there are 5/4 of a pizza presented to them because that is how many quarter slices they see in front of them. 
