Fraction rules

Simplifying fractions

If possible, it is often useful to simplify a fraction first, before you start to add, subtract, multiply or divide the fraction. To simplify a fraction, first go in search of the greatest common divisor of the numerator and denominator.

For example: 2530

The numerator (25) and the denominator (30) are both divisible by five (greatest common divisor). If you now divide the numerator and denominator by five, you can also already write the fraction as

255 / 305  =  56

More about: Simplifying fractions

Calculation rules to add and subtract fractions

When adding and subtracting fractions, the first thing the fraction should have is the same denominator. You can do this using the product of the individual denominators, but in many cases you can find a smaller denominator that is a multiple of the two denominators. A number does not change when you multiply it by one. So you can multiply the numerator and denominator by the same number. After all, if the numerator and denominator are the same then the fraction is equal to 1. For example:

34  +  16 = 912  +  212  =  1112

The common denominator we took was 12, this is the lowest common denominator that is both divisible by four and by six. You can also use the product of 4 and 6 (= 24): 18/24 + 4/24 = 22/24. This can be simplified to 11/12 (to simplify the fraction go and find the greatest common divisor of the numerator and denominator. In this example, the greatest common divisor is 2, so both the numerator and the denominator divide by 2 ).

More about: adding fractions and subtracting fractions

Calculation rules to multiply fractions

When multiplying fractions you multiply the numerators with each other and the denominators with each other. For Example:

23  X  34  =  612  ie  12

To simplify the fraction find the greatest common divisor of the numerator and denominator. In this example, the greatest common divisor is 6, so both the numerator and the denominator can be divided by 6.

More about: multiplying fractions

Calculation rules to divide fractions

When doing division of fractions, interchange the numerator and denominator of the second fraction, so 34 becomes 43. Then multiply the first fraction by this reversed second fraction. For example:

18 / 34  =  18 X 43  =  424  =  16

To simplify the fraction find the greatest common divisor of the numerator and denominator. In this example, the largest common denominator is 4, so both the numerator and the denominator can be divided by 4.

More about: dividing fractions

This page gives you a quick summary of the calculation rules for fractions.