Go to DIVIDE AND CONQUER to see notes and resources on fractions, decimals, proportions, and primes.

      Click on a graphic to see just the graphic.

      Many people can tell you that to divide two fractions, "Copy the first fraction. Invert and multiply the second fraction."

      Fewer can tell you the reason this is done.

      "Invert and multiply" summarizes the arithmetic which follows. It's a short cut. Just remember the answer, "invert and multiply," rather than complete the work each time.

      Keep in mind the following.

• You chose the format in which to complete the problem.
   
  
   
• Any number multiplied by its reciprocal (its multiplicitive inverse) is 1.
   
          
   
• Any number multiplied by 1 is the number.
  One is the multiplicative identity .
   
            (a)(1) = a
   
• Any number divided by one, is that number.
   
            a/1 = a
   
  Another way of saying this is "If 1 is the denominator of a fraction, just use the numerator."

      The goal is to make the division expression look like just one number, perhaps a fraction or mixed number, but, still just one number. Multiplying by the reciprocal and multiplying by 1 result in "the product of the first fraction and the reciprocal of the second" -- "copy the first, then, invert and multiply."