Fraction of Fraction

Fraction of Fraction

Today we will learn how to visualize and calculate how to multiply fractions by other fractions and find a fraction “of” another fraction

Multiple Choice

I loved this muffin so much that I only ate half of it so I could eat more later

Today, I’ll eat two third of this half.

How much muffin will I eat today?

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{2}{6}$

• $\frac{3}{5}$

Multiple Choice

Which visual would best represent this situation:

I’ll eat two third of this half.

Multiple Choice

What does this slice represent?

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{6}$

We can find fractions of fractions by creating visual models

A fraction “of” something can be thought of as multiplication

Multiple Choice

My goal today was to run  $\frac{1}{2\ }$  of a mile but I only ran  $\frac{1}{4}$  of that distance.  What visual best represents  $\frac{1}{4}\ of\ \frac{1}{2}\ ?$   

Multiple Choice

My goal today was to run  $\frac{1}{2\ }$  of a mile but I only ran  $\frac{1}{4}$  of that distance.  What is  $\frac{1}{4}\ of\ \frac{1}{2}\ ?$   

•  $\frac{1}{2}$  

•  $\frac{1}{4}$  

•  $\frac{1}{8}$  

•  $\frac{2}{6}$  

Area Models

Let's try another method

Fill in the Blank

What is the area of the blue rectangle?

Poll

What method did you use to solve?

• Counting all the Squares

• See it as “3 rows of 4” or “3 groups of 4”
  

• A = length x width
  
  

  $3\times4=12\ cm^2$

• Another way

We can use these for fractions too!

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Multiple Choice

Which of these models could represent  $\frac{2}{3}$  ?

Multiple Choice

Layer  $\frac{1}{5}$  on top of  $\frac{2}{3}$  , how many total squares are there now?

• 3

• 5

• 10

• 15

Multiple Choice

What is the area of a rectangle that is  $\frac{2}{3}$   of an inch wide and  $\frac{1}{5}$   of an inch long?

•  $\frac{2}{5}$  

•  $\frac{2}{15}$  

•  $\frac{2}{3}$  

•  $\frac{3}{5}$  

We can use area models to show multiplication

Multiple Choice

Which area model best represents a rectangle with a width of  $\frac{3}{4}$  and a length of  $\frac{2}{3}$  ?

Multiple Choice

What is the area of a rectangle that is  $\frac{3}{4}$   of an inch wide and  $\frac{2}{3}$   of an inch long?

•  $\frac{5}{7}$  

•  $\frac{6}{12}$  

•  $\frac{7}{12}$  

•  $\frac{5}{12}$