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Add, Subtract, Multiply, Divide Fractions

Below is a calculator that lets you add, subtract, multiply and divide fractions displaying where appropriate, the lowest common multiple (LCM) and the highest factor common to all denominators (HCF). First, a bit of theory :-

A fraction consists of two numbers - a numerator (the number at top) and a denominator (the number at bottom).

The numerator tells you the quantity of a particular quality (the denominator) you are dealing with.

Example : 5/12 says you are dealing with a quantity of 5 out of a whole divided into 12 parts.

Kinds of fractions

An improper or vulgar or common fraction is a fraction where the numerator (number at top) is larger than the denominator (number at bottom). Example : 38/7 which when converted gives a mixed fraction of 5 3/7. (See below)

A proper fraction is one where the numerator is smaller than the denominator.

A mixed fraction is a combination of a whole number and a proper fraction. Example : 7 3/5 (seven and three fifths), which converts to an improper fraction of 38/5.

To convert a mixed fraction to a vulgar fraction, you multiply the whole number by the denominator and add the numerator. Take 7 3/5 for example : 7x5=35+3=38 and you place this over the denominator (5) to complete the fraction, as above.

To convert an improper fraction to a mixed fraction, you find the whole number when multiplied by the denominator that gives a positive remainder less than the denominator. The remainder is now the new numerator. So we have the resulting whole number and the remainder(numerator)/denominator.

Use the calculator below to easily add, subtract, divide or multiply your fractions. You can add, subtract, divide or multiply 2 to 4 fractions at a time.

The lowest common multiple (LCM) and highest common factor (HCF) are calculated in appropriate cases.