1. 4 5 x = 4 15

3. What is of 1?
What does it mean to multiply a number by a fraction? It means to take that fractional part of that number
The question asks what is ¼ of 1. That means, we have 1 of something and we want to find out what ¼ of that would be. Or, we have something and we want to find out how much ¼ of that would be.
We show the 1 and then we divide it into the 4 parts – as indicated
Once we shade in the numerator 1, we can see that ¼ of one = 1
Using our rules for multiplication, we know that any number multiplies by one, is that number.

4. Model x 2 = 4 8
When modeling the multiplication of fractions and whole numbers, students will model the fractions, add the numerators and add the denominators. The product should be 4/4 or 1, not 4/8

5. Of the cookies at Tammy's Bakery, 4 5 have vanilla frosting
Of the cookies at Tammy's Bakery, have vanilla frosting. Of the cookies with vanilla frosting, have lemon filling. What fraction of the cookies at Tammy's Bakery have both vanilla frosting and lemon filling?
1 3 of or x = 4 15
Show an area model to model one whole. Do we know how many parts to divide the whole into?
Yes.
The denominator of the fractional amount indicates how many parts we divide the whole into.
Show the whole being divided into 5 equal parts
Shade in 4 of the parts
We need to do the same for the second fraction 1/3
Show the whole
Show the whole being divided into 3 parts due to the denominator
Shade in 1 of the 3
When we merge these two models together, we see that we now have 15 pieces as our denominator and 4 as our numerator, we can see the new numerator in green where the yellow portions and the blue portions overlap.
4/15 of the cookies at Tammy’s bakery have vanilla and lemon frosting

7. The dogs at Anthony’s kennel are fed of a bucket of dog food each day. The puppies are fed as much dog food as the dogs. How many buckets of food are the puppies fed each day?
1 3 of = 2 9
Show an area model to model one whole. How do we know how many parts to divide the whole into?
Yes.
The denominator of the fractional amount indicates how many parts we divide the whole into.
Show the whole being divided into 3 equal parts
Shade in 1 of the parts
We need to repeat the action for the other fraction
Shade in 2 of the parts
We can model the multiplication of these two fractions by placing one model over the other. Two of the shaded portions overlap each other, this represents the 2 out of the 9 spaces. The puppies are fed 2/9 of a bucket of food each day.

10. Judy went to the grocery store and bought 1 3 of a pound of coffee
Judy went to the grocery store and bought of a pound of coffee. If of Judy's coffee was flavored, how many pounds of flavored coffee did Judy buy?
At Georgia Tech, of the students are enrolled in a robotics class. Of the students enrolled in a robotics class, are enrolled in a computer programming class. What fraction of the students at Georgia Tech are enrolled in a computer programming class?