1. Warm Up
On Sunday Miguel wanted to make brownies for his mom. The recipe called for ¾ cups of sugar to make 12 brownies, but Miguel only wants to make 6 brownies (1/2 of the recipe). How could Miguel find out how much sugar he needs to make his mom 6 brownies?

2. Multiply a Fraction by a Fraction Unit 9, Lesson 4

3. Suppose you sawed a board into 4 equal pieces. Each piece would be ¼.
Now let’s say you took one of those fourths and sawed it in half. What fraction of the original board would you have?
You would be taking ½ of ¼ or ½ x ¼ .
Let’s try! Label each of the fourths on top with number line labels.

4. *Circle ¼ of the bar
*Then “saw” it in half.
*To identify the new smaller fraction, divide each of the remaining fourths into halves.
*When the entire board is divided into equal parts, it becomes clear that each of the small sections is 1/8 of the whole.

5. Using Your Math Boards…
When you 2-split the fourths, what fraction did you get?
What equation describes this?
½ x ¼ = 1/8
What if you 3-split the fourths?
1/3 x ¼ = 1/12

6. Using Your Math Boards…
When you 2-split the eighths, what fraction did you get?
What equation describes this?
½ x 1/8 = 1/16
What if you 4-split the halves?
¼ x ½ = 1/8
What pattern do you see?

7. Multiplying two unit fractions yields a new unit fraction whose denominator is the product of the two factors.
x = FORMULA!!
When you take a fraction of a fraction, you are dividing the whole into smaller parts.
Smaller parts means there are more parts in a whole.
When there are more parts, the denominator is larger.

8. A board is 4/5 yd long. Think about how long 2/3 of the board would be.
We will take a fifths bar and circle 4/5.
How can you show 2/3 of the circled 4/5?
If you 3-split each fifth, how many parts will you have?
What denominator will our answer have?

9. Let’s break each fifths into thirds (fifteen pieces in all)
The green rectangle represents 4/5.
Now circle 2/3 of each fifth.

10. How many fifteenths are circled?
8; there are 4 groups of 2 circled
What is the answer to ?

11. When you take a fraction of a fraction, you are dividing the whole into smaller parts. Why do you get a larger denominator?
A larger denominator means that the whole is divided into more parts.
When there are more parts, what do you know about the size of the individual parts?
The individual parts are smaller.

12. Using your Math Boards…
Try to find a pattern!!
Using the sixths bar:
Using the sevenths bar:
Using the ninths bar:

13. What patterns did you find?
Why do you multiply the denominators?
Why do you multiply the numerators?

14. Homework
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