A whole number represents one complete object. One apple is one whole. Cut it in two and you have fractionated it. Now it is in two parts. One part can be represented as the fraction 1/2. The denominator tells how many parts the whole has been divided into, and the numerator tells you the number of those parts being considered. For example, 3/5 indicates that the whole has been divided into five parts, of which three are being used. Remember that zero can never be a denominator because you cannot divide by zero.
A fraction does not always have to be written as a number with a numerator and a denominator. You can write a fraction as a decimal. For example, 0.5 is the decimal way of writing 1/2. In a decimal fraction, the numerator is the number to the right of the decimal point, and the denominator is 10, or a power of 10. The number of digits to the right of the decimal point determine the power of 10. For example, 0.50 would be the second power of 10 (50/100) because there are two digits after the decimal point. Now consider that 0.375, with three digits after the decimal, would be 375/1,000. A fraction can also be written as a percentage. One-half, or 0.5, can be multiplied by 100 to become 50 percent. You can obtain any percentage by multiplying a decimal number by 100.
In a proper fraction, the numerator is smaller than the denominator. One-half, 2/3 and 3/4 are all examples of proper fractions. Note that a proper fraction is always less than a whole number. When the numerator is larger than or equal to the denominator, it is an improper fraction. For instance, 4/3, 6/5 and 4/4 are examples of improper fractions. In a fraction, you can consider the denominator to be the whole, since it tells us how many parts the whole has been divided into. For example, 2/3 tells that the whole has been divided into three parts. Put those three parts together to get the whole.
A mixed number is the sum of two parts -- a whole number and a fraction -- written together. For example, if you want to say that you have two and a half pizzas, you would write it as 2 1/2 pizzas. This tells that you have a whole, and a part, of something. A mixed number can be converted into an improper fraction in two easy steps. Multiply the whole number by the denominator, then add the numerator to the product. The denominator does not change. Put the result as the numerator on the same denominator. So 2 1/2 converted would be (2 * 2 + 1)/2 = 5/2. Scientists prefer improper fractions rather than mixed numbers, to avoid confusion between a mixed fraction and the algebraic concept of multiplication. In algebra, the number 2 1/2 would imply two times one-half, which equals one.