Chapter 6: Rationals: Multiplication,
Division, and Applications

by
Millard Lewis and John Moore

## Day One: Multiplying Fractions

__ Objectives: __ 1. The students will reflect on what fractions
represent.

2. The students will be able to visualize the fraction multiplication
process.

3. The students will reinforce what they have learned through practicing
multiplication of fractions.

__ Recall: __ A fraction is merely a defined part of a whole.
For example, if you had an apple and you cut into 5 equal parts, each piece
would represent 1/5. (Notice that if you put the five pieces back together,
or 1/5 + 1/5 + 1/5 + 1/5 + 1/5, then you would get 5/5 of an apple, which
is 1 apple.)

If you had a circle and you wanted to show 3/5 of that circle, into how
many equal sections would you have to divide your circle? How many of these
sections would you need to shade?

To explore the concept of 3/5 interactively, **press
here.**

Now that you've refreshed your memory on what exactly a fraction is,
let's discuss how to multiply fractions. Recall the apple example above.
If we add 1/5 + 1/5 + 1/5 + 1/5 + 1/5, isn't that the same as saying 5 *
(1/5)? So, to multiply 5 and 1/5, you need to multiply the numerators (you
may need to rewrite 5 as 5/1!) to find the new numerator and then multiply
the denominators to find the new denominator, which turns out to be 5/5.
(Just like our example above!)

Let's look at a new way to represent multiplication of fractions. **Press here!**

Now try some grids on your own. **Click here!**
Examples:

1) 4/7 * 2/3 = (4*2)/(7*3) = 8/21 [Beware of answers that are not in
lowest terms! This one is, however...]

2) -(5/8) * 2/9 = (-5*2)/(8*9) = -(10/72) [Not in lowest terms! Divide
numerator and denominator by their greatest common divisor.] = -(5/36) [Remember
when you keep and lose negatives!]

3) -(2 3/4) * -(1 3/8) = [Make improper fractions...] -(11/4) * -(11/8)
= 121/32 = 3 25/32 [Note: What happened to the negatives?!?]

Now, practice some on your own! Good luck!!!

Worksheet
on Multiplying Fractions