Thursday, February 24, 2011

Operations with Fractions

Addition

For any fractions a/b and c/d
a/b +c/d =ad/bd + bc/bd = (ad+bc)/bd

Addition for fractions is the same as with whole numbers.  The challenge comes when the denominators are not the same, for example 1/2 + 1/4.  When this occurs the smallest common denominator must be determined before solving the problem.  Multiplying the denominators together will always get a common denominator, but not necessary the smallest one.  Click here for how to find the smallest common denominator.  After converting to a common denominator, simply add the numerators together.

Subtraction

For any fractions a/b and c/d
a/b - c/d  =  ad/bd - bc/bd = (ad - bc)/bd

Subtraction for fractions is the same as with whole numbers.  A common denominator must be obtained before the solution is found.  When finding the difference between two mixed numbers, work the whole number part and fraction parts separately remembering to regroup as needed. 


Multiplication

Whole number times a fraction: For any whole number k and fraction a/b
k = a/b = ka/b
 
Multiplication of a whole number and a fraction really is repeated addition, which is the same as with whole numbers. 3 x 1/2 which means 3 of 1/2 = 3/1 x 1/2 = 3/2.  Written in lowest terms, this is  1-1/2.


 For any fractions a/b and c/d
a/b x c/d = ac/bd

Multiplication of a fraction times a fraction can be illustrated by the rectangular model.

Division

For any fractions a/b and c/d, with c/d not equal to 0 
a/b divided c/d = a/b x d/c = ad/bc

Division of fractions is done much the same as dividing whole numbers.  Yet, one method that is currently taught is to invert the divisor and multiply.   3/4 divided 7/8 = 3/4 x 8/7 = 24/28 = 6/7
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3 comments:

  1. Amber13February 26, 2011 at 1:38 PM

    I think you did a very good job of laying out all of the operations and explaining them so they can be understood. The video is also nice because it works threw the problem with a visual and is auditory. Keep up the good work!

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  2. mathmonkey9February 27, 2011 at 7:53 PM

    The second video i thought was helpful when talking about multiplication as "groups". Unfortunately some of the word were small but i liked the use of the problem and the number line and how I could relate the two together.

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  3. Adam F.March 10, 2011 at 9:49 PM

    Jodi, I think you could take ANY topic and explain in a way that is not only easy to understand, but also fun to listen to. Any questions I had about operations with fractions were answered in your post. I get confused on when to use common denominators and when to just multiply across, but, after reading your post, not anymore! I like your videos as well. You remind me a lot of past teachers I have had and that is definitely a grat thing!

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