Applying Basic Math Operations To Fractions


Learning about fractions can be complicated if one does not have the necessary knowledge which involves utilising the core operations. In some problems, one may be required to perform only one basic operation while in others one is needed to combine the operations. The four basic operations in mathematics are the addition, subtraction division and multiplication. Anyone who might not have proficiency in applying the four basic operations using whole numbers may as well struggle to use the operations to solve fractions since fractions are more complicated than whole numbers.

A fraction may have two meanings where in one a fraction implies a part of the whole figure while the second involves the division of two numbers. It is made of two parts the numerator which is the top number of the fraction and the denominator which is the lower number. There are special fraction calculator which are designed to solve fractions, but one should also possess the knowledge on how to solve the fractions manually.

The first two operations that can be carried out is the addition of fractions. The operations are the simplest especially if we have a common denominator. If the denominator is remained constant in the two fractions to be added, then we only need to add the numerators using the usual method.



The denominator remains as nine while we add up five and three and the result is eight-ninths. In the second example since nine is common, we subtract three from five remaining with two-ninths. There are cases where the denominators differ, and hence we cannot apply the operations as in the example above. In such cases, we find a common denominator by use of the least common multiple.


In the example above we have two different denominators in six and three. We find their least common multiple which in the above case is six. We then convert the two fractions into new fractions with the new common denominator. Since in the first fraction the denominator is six there is no change, but in the second we multiply both numbers by two so that the denominator changes to six without modifying the value of the fraction. Subtraction is done in the same manner.

One may wonder how to do multiplying fractions or divide the fractions. In multiplication, we multiply the denominator and the numerator to find the result while simplifying if need be.


In the division of fractions, one needs to flip the second fraction by writing the numerator as the denominator and the denominator as the numerator. One then multiplies the two fractions to obtain the result.

5/6  ?  5/9      =    5/6  x9/5      = 45/30

We simplify the above result by dividing the numerator and the denominator by a common divider. We first divide both by three and obtain fifteen-tenths. We divide further by five, and the final result is three halves. That is how easy it is to multiply and divide fractions. Learn more about calculators at


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