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A fraction is the ratio of two whole numbers, or to put it simply, one whole number divided by another whole number. We write a fraction like this:


















The top part of the fraction is called the numerator and is also referred to as the dividend of the fraction. The bottom part is called the denominator and is also referred to as the divisor of the fraction.
Normally the numerator (top of fraction) is smaller than the denominator (bottom of fraction) in which case the fraction is called a 'Proper Fraction'. If the numerator (top) is equal to or larger than the denominator (bottom) then the fraction is called an 'Improper Fraction'.


















A proper fraction is always less than the whole number 1 and we can relate proper fractions to a part of a whole object. We use the denominator (bottom) to divide the object into that number of parts and then we take the numerator (top) number of parts and we can say we have that fractions part of the whole object.






















The interesting thing is that we know we have the exact same amount of orange as before when we had divided the orange into 4 parts and took 3 parts. This tells us that the


















We say these fractions are 'Equivalent'. In our example having taken 3 of the 4 parts of the orange and then divided all the parts into 2, we could have instead divided these parts into 3 or 4 or 5 or more equal parts, which means the following are all equivalent:


















Now try this, divided the numerator (top) of all these equivalent fractions by 3 and divide the denominator (bottom) by 4, and you should get:


















This gives us a clue to the rule that tells us when two fractions are equivalent. Two fractions are equivalent if you can find a whole number which when divided into both the numerator (top) and denominator (bottom) of one fraction gives the other fraction OR if there is a third fraction that can be found that is equivalent to both.






















Mixed Fractions
If we have one whole orange and a half an orange then we say we have one and a half oranges, this is a mixed fraction and we write it as:


















A mixed fraction really means a mix of a whole number and a fraction. We can also cut the whole orange in half and then we have 3 halves of orange:


















As you can see it is possible to convert a mixed fraction to an improper fraction and you will soon see, convert an improper fraction to a mixed fraction.
To convert a mixed fraction to an improper fraction multiply the whole number by the denominator (bottom) of the fraction and add the result to the numerator (top).
To convert an improper fraction to a mixed fraction divide the denominator (bottom) into the numerator (top). The number of whole times the denominator (bottom) goes into the numerator (top) is the whole number part of mixed fraction. The remainder (multiply the whole number by the denominator (bottom) and subtract from the numerator (top)) becomes the numerator (top) of fraction, if the numerator (top) becomes zero then there is no fraction part at all, just a whole number. For the addition and subtraction of fractions it can be slightly better to use mixed fractions, for multiplication and division it is much better to use improper fractions. The 'Fraction calculator' can deal with either although it may internally convert between them to do the calculation.
One final note, a whole number can also be written as an improper fraction, the whole number becomes the numerator (top) and the denominator is 1.


















It is sometimes useful to do this.











