Chapter 6: Rationals: Multiplication, Division, and Applications
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!!!