before adding or subtracting two fractions they are converted why?

Question

before adding or subtracting two fractions they are converted into like fractions. Why?

Answer 1

We do this because it's easier for us to understand the addition/subtraction process, it simplifies the final answer, and thus allows us to do more with it.

 

Think of fractions like units. If you add 1 g + 1 kg, your final answer must only be one unit, so you have to convert gram to kilogram, or vice versa, so that your final answer is 1001 g or 1.001 kg.

 

A fraction like 4/3 ("four thirds") is 4 of something (thirds). If you want to add 5/6 ("five sixths"), you could just quit and say "I have four thirds and five sixths", but then you haven't really done anything. Instead, you can simplify by condensing into just one unit (13/6).

 

Now you can do more with this total. You can confidently say it's larger than 2/3 + 7/6, for example.

Answer 2

When adding and subtracting fractions, the bottom number of the fraction or the denominator has to be the same in both fractions.

 

Ex:

 

5/8 + 1/2

 

So to add these two fractions you need to have the same denominator. To achieve this you look for the smallest number that both 8 and 2 will go into. In this case, it is 16. Many time the common denominator will be the two numbers multiplied together.

 

So the next step is to change the fractions by multiplying the numerator and denominator by the number that will make the denominator equal to 16 :

 

 

 2       5           8       1                               10         8

__  *  __   +   __  *  __      this equals:        __   +  __

 2       8           8       2                               16        16

 

 

Now that the denominator is the same, you can easily add the fractions:   18/16

 

You can reduce this fraction by dividing 2 into the numerator and denominator: 9/8

 

With this particular example, it ended up being an improper fraction so you can further simplify it by making it a proper fraction: 1 and 1/8 (one and one eighth)

 

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