Multiplying and Dividing Fractions

• While you may think multiplication and division are more difficult than addition and subtraction, the opposite is true when it comes to fractions. To multiply two fractions, first multiply the top parts (the numerators) of the first fraction and second fraction. Write down the product of the numerator and draw a line underneath it. Then multiply the bottoms (the denominators) of the first and second fraction. Write that product underneath the numerator product. For instance 2/3 multiplied by 4/5 equals 8/15 because 2 times 4 equals 8 and 5 times 3 equals 15.
  
  To divide two fractions, all you have to do is flip the denominator and numerator for the second fraction and multiply that by the first fraction. For instance, 2/3 divided by 6/7 is the same thing as 2/3 multiplied by 7/6. Multiply the 7 and 2 to get 14. Draw the fraction line under the 14. Then multiply the 6 and 3 to get 18 and write it underneath the 14. You are left with 14/18. As you will see in the next section, 14/18 is an unsimplified fraction.
  
  

Simplifying Fractions

• While 14/18 is a fraction, it is not a simplified fraction because there's a way to express this fraction using numbers smaller than 14 or 18. To simplify the fraction, see if there are any numbers that divide evenly into both 14 and 18. As you scan through your times tables, you will realize that 2 divides evenly into 14 and 18. Divide 14 by 2 and 18 by 2 to simplify your fraction to 7/9.
  
  In some cases, you can simplify your fractions before you multiply them. If you have a fraction in which the numerator of the first fraction and the denominator of the second fraction (or vise versa) are both divisible by the same number, you can divide each by that number. For instance, take the problem 3/4 times 12/5. The denominator of the first fraction (4) and the numerator of the second fraction (12) are both divisible by 4. Divide each by 4 and you are left with 1 as the first fraction's denominator and 3 as the second fraction's numerator. To keep track of your work, cross out the original numerator and denominator in pencil and write the simplified numbers beside the cross-out marks. You are left with 3/1 times 3/5, which equals 12/5. Had you not simplified your fractions before you multiplied, you would come up with the answer of 36/20, which is a much more difficult fraction to simplify.
  
  

Adding and Subtracting Fractions

• Adding Fractions Examples
  
  Adding and subtracting fractions is easy if the denominator of both fractions is the same. To return to our pizza example, if you eat three of the eight pieces and your friend eats two of the eight pieces, the two of you ate a total of five pieces or 5/8 of the entire pizza. However if you eat three of the pieces and your friend eats two pieces of a pizza with larger slices, you can't simply add 3 and 2 to find your new fraction. Likewise, to find what 3/8 plus 2/5 equals, you can't simply add 3 and 2. To get around this problem, you need find a common denominator.
  
  There are many ways to find a common denominator, but the most straightforward is to multiply the first fraction's denominator (8) by the second fraction's denominator (5) to equal a common denominator (40 in this case). Now that you have the common denominator, you need to convert your original fractions into fractions with the new denominator. To do this for the first fraction, multiply its numerator (3) by the original denominator of the second fraction (5) to equal 15. Put 15 over 40 and you have 15/40, which is the same thing as 3/8. Do the opposite with your second fraction. Multiply the second fraction's numerator (2) by the first fraction's denominator (8) to equal 16. Put the 16 over the 40 to get 16/40. Now add 15/40 to 16/40 to equal 31/40.
  
  An easier way to rewrite fractions in terms of common denominators is to draw a line from your first denominator to your second denominator. Mark this line with an A. Then draw a line from your first numerator to your second denominator and mark this line with a B. Finally draw a line from your second numerator to your first denominator and mark this line with a C. The lines will tell you what you need to multiply. First multiply line A to get your common denominator. Then multiply line B to get your first expanded fraction's numerator. Finally multiply line C to get your second fraction's numerator. (See image for an illustration.)
  
  Subtraction works the same way as addition. Once you're able to find a common denominator, you will leave that denominator alone as you subtract the second numerator from the first. Your final answer will then be the difference of numerators over the common denominator.