How to Divide a Fraction By a Fraction

A lot of people hate working with fractions. Are you one of them? Usually you don't have to as an adult until your children come home with math homework and need help. Then you have to try to remember how they work. Perhaps the most complicated task is to divide a fraction by a fraction. Here's a review about how to do it.

Difficulty: Moderate

Instructions

Things You'll Need:

• pencil
• paper
• patience

1. 
   Two-thirds divided by four-fifths

   Copy the problem on a piece of paper. Even if your child resists this as an extra step or bother, it is a good discipline that will become more and more essential as the math gets more and more complex. Suppose the problem is two-thirds divided by four-fifths.

2. Invert the second fraction and restate the problem as a multiplication problem. This works because the inverse of four-fifths is its opposite, five-fourths (if you multiply four-fifths by five-fourths you get the number, 1) and the operation of multiplication is the opposite of division. So this new problem has the same value as the original

3. 
   Two-thirds times five-fourths equals ten-twelfths

   Multiply the numerators of the two fractions (2 x 5 = 10) to arrive at a new numerator. Multiply the denominator of the two fractions (3 x 4 = 12) to arrive at a new denominator. Your answer to this point is ten-twelfths but this is not in its lowest terms.

4. 
   Ten-twelfths equals five-sixths

   Reduce the fraction to its lowest terms by dividing both the numerator, 10, and the denominator, 12, by the common factor, 2. The final answer is five-sixths.

5. 

   Place the final answer in the original equation.