What are Fractions?
Numbers equal to one integer divided by another integer. Integers are whole numbers, like 1, 2, 3 etc.
Fractions are numbers like 2/3. These numbers are solutions of equations that don't always have a solution in terms of integers.
The equation 2x=4 has the solution
x = 2, because 2*2 = 4. But the equation
3x = 2 doesn't have a solution in the form of an integer. If you could divide both sides by 3 you would get: x = 2/3. However this is just a formal operation, because at this stage we don't know how to divide 2 by 3.
We now *define* the number denoted by 2/3 to be the solution of the equation 2x=3. This number is called a fraction.
You can approximate fractions by attempting to divide 2 by 3 using e.g. long division. You then get the decimal expansion: 0.66666666666....
In general, the fraction a/b is the solution of the equation:
bx = a