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
To add on to the explanation, fractions are a way to represent numbers that are not whole numbers or integers. A fraction consists of two parts: a numerator and a denominator. The numerator represents the number of parts you have, and the denominator represents the total number of equal parts that make up a whole.
For example, in the fraction 2/3, the numerator is 2 and the denominator is 3. This means that you have 2 out of 3 equal parts.
Fractions can also be used to represent division. When you divide one number by another, you can express the result as a fraction. For example, 1 divided by 4 can be written as 1/4.
To determine the value of a fraction, you can divide the numerator by the denominator. In the case of 2/3, if you divide 2 by 3, you get approximately 0.66666666666, which can be rounded to 0.67. So, the value of the fraction 2/3 is approximately 0.67.
It's important to note that fractions can also be simplified. If the numerator and denominator have a common factor, you can divide both by that factor to simplify the fraction. For example, the fraction 4/8 can be simplified to 1/2 by dividing both the numerator and denominator by 4.
In summary, fractions are a way to represent numbers that are not whole numbers or integers. They consist of a numerator and a denominator, and can represent parts of a whole or the result of division.