Dividing+fractions

Dividing Fractions
An instructional sequence for learning how to divide with fractions is similar to the one for multiplying. ** 1. Dividing a fraction by a whole number – “Partitioning” into equal groups ** 1/4 ÷ 2 means to start with 1/4 of something and divide that quantity equally into 2 groups – in this case, with 1/8 in each group. 6 ÷ 1/2 means “How many 1/2’s are in 6?” Since there are 2 halfs in each whole, times six wholes, there are 12 halfs in 6 wholes. (This is a simple origin of “invert and multiply.”)
 * 2. Dividing a whole number by a fraction – “Measurement division”**

3/4 ÷ 1/4 means “How many 1/4’s are in 3/4?” A simple drawing can show that there are 3 fourths in 3/4. This is a little trickier when there aren’t an integer number of the divisor in the dividend. 3/4 ÷ 1/2 means “How many 1/2’s are in 3/4?” You can see from the drawing above that there is one full 1/2 in the shaded 3/4, plus another half of a 1/2. The answer is 1 1/2. This means there are 1 1/2 halves in 3/4.
 * 3. Dividing a fraction by a fraction – Also a case of measurement division**

If you use the traditional procedure for calculating the answer (invert and multiply) you will get the same answer.

**Assignment:** Have your students work through the section of the Student Packet on Dividing Fractions. As you plan the lessons, decide which tasks should be done in groups of 2, which should be done individually, and where you should have whole class discussions. Allow students to work at the tasks without giving them answers. Let them use fraction manipulatives, or encourage them to make drawings. Don't just tell them the procedure (algorithm) - let them get to the point where it is obvious, by the work they've done with drawings. Then record your observations, suggestions for improvements, interesting comments or solutions by students, etc. in the discussion tab for this page.