Lesson Adding Fractions

Source code of 'Adding Fractions'

This Lesson (Adding Fractions) was created by by mathick(4)

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To add fractions that have the same denominator (number on bottom), just add the numerators and keep the denominator the same:

{{{3/7 + 2/7 = 5/7}}}.

The general rule for adding fractions with identical denominators is:

{{{a/c  +  b/c  =  (a+b)/c}}} .

So, for example, {{{3/8  +  6/8  =  9/8}}}, and {{{12/87  +  5/87  =  17/87}}}.  <a href = "http://www.mathick.com/mathick.php?topic=addingfractions1">Try one like this.</a>

Adding fractions with different denominators is a bit more involved.  There are two steps:

1)	Convert the fractions to equivalent fractions that have the same denominator, and

2)	Do the addition or subtraction as before.

Example.  {{{3/5 + 1/4}}}

How do we get them to have the same denominator?

First, multiply the two different denominators together to find the new denominator.

For the problem above, the first denominator is 5, and the second denominator is 4.

So, for our common denominator, we�ll multiply 5 * 4 to get 20.

Next we want to find a fraction that is equivalent to {{{3/5}}} and has a denominator of 20.

Q.  What do you have to multiply 5 by to get 20?

A.  4

So, to find a fraction that is equivalent to {{{3/5}}} and has a denominator of 20,

we multiply both the numerator and denominator of {{{3/5}}} by 4:

{{{3/5  =  (3*4)/(5*4)  =  12/20.}}}

Now we need to find a fraction that is equivalent to {{{1/4}}} and has a denominator of 20.

Q.  What do you have to multiply 4 by to get 20?

A.  5

So, to find a fraction that is equivalent to {{{1/4}}} and has a denominator of 20, we multiply both the numerator and denominator of {{{1/4}}} by 5:

{{{1/4  =  (1*5)/(4*5)  =  5/20 }}}.

Now we�re ready to answer the original problem:

{{{3/5 + 1/4  =  12/20 + 5/20  =  17/20.}}}

Here's another example:

{{{2/3 + 5/8}}}.

Solution.
Multiply 3 by 8 to get the common denominator, 24.

Find a fraction equivalent to {{{2/3}}} having a denominator of 24:

{{{2/3 = (2*8)/(3*8) = 16/24}}}.

Find a fraction equivalent to {{{5/8}}} having a denominator of 24:

{{{5/8 = (5*3)/(8*3) = 15/24}}}.

Add:  {{{2/3 + 5/8  = 16/24 + 15/24 = 31/24}}}.