Lesson Adding Fractions

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This Lesson (Adding Fractions) was created by by mathick(4) About Me : View Source, Show
About mathick:
To add fractions that have the same denominator (number on bottom), just add the numerators and keep the denominator the same:

3%2F7+%2B+2%2F7+=+5%2F7.

The general rule for adding fractions with identical denominators is:


a%2Fc++%2B++b%2Fc++=++%28a%2Bb%29%2Fc .

So, for example, 3%2F8++%2B++6%2F8++=++9%2F8, and 12%2F87++%2B++5%2F87++=++17%2F87. Try one like this.

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%2F5+%2B+1%2F4

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%2F5 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%2F5 and has a denominator of 20,
we multiply both the numerator and denominator of 3%2F5 by 4:

3%2F5++=++%283%2A4%29%2F%285%2A4%29++=++12%2F20.

Now we need to find a fraction that is equivalent to 1%2F4 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%2F4 and has a denominator of 20, we multiply both the numerator and denominator of 1%2F4 by 5:

1%2F4++=++%281%2A5%29%2F%284%2A5%29++=++5%2F20+.

Now we’re ready to answer the original problem:

3%2F5+%2B+1%2F4++=++12%2F20+%2B+5%2F20++=++17%2F20.

Try one out!

Here's another example:

2%2F3+%2B+5%2F8.

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

Find a fraction equivalent to 2%2F3 having a denominator of 24:

2%2F3+=+%282%2A8%29%2F%283%2A8%29+=+16%2F24.

Find a fraction equivalent to 5%2F8 having a denominator of 24:


5%2F8+=+%285%2A3%29%2F%288%2A3%29+=+15%2F24.

Add: 2%2F3+%2B+5%2F8++=+16%2F24+%2B+15%2F24+=+31%2F24.


Try one!


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