Lesson 4 Equal Groups of Non-Unit Fractions

- Let’s multiply any fraction by a whole number.

Warm-up Notice and Wonder: Thirds

What do you notice? What do you wonder?

Activity 1 Jars of Jam

Problem 1

Elena fills 5 small jars with homemade jams to share with her friends. Each jar can fit $\frac{3}{4}$ cup of jam. How many cups of jam are in the jars? Explain or show your reasoning.

Problem 2

If you have time… Elena still has some jam left. She takes 2 large jars and puts $\frac{5}{4}$ cups of jam in each jar. How many cups of jam are in the jars?

Activity 2 How Do We Multiply?

Problem 1

This diagram represents $\frac{2}{5}$ .

Show how you would use or adjust the diagram to represent $4 \times \frac{2}{5}$ .
What is the value of the shaded parts in your diagram?

Problem 2

This diagram represents $\frac{5}{8}$ .

Show how you would use or adjust the diagram to represent $3 \times \frac{5}{8}$ .
What is the value of the shaded parts in your diagram?

Problem 3

Find the value of each expression. Draw a diagram if you find it helpful. Be prepared to explain your reasoning.

$2 \times \frac{1}{6}$
$2 \times \frac{4}{6}$
$2 \times \frac{5}{6}$
$4 \times \frac{5}{6}$

Problem 4

Mai said that to multiply any fraction by a whole number, she would multiply the whole number and the numerator of the fraction and keep the same denominator. Do you agree with Mai? Explain your reasoning.

Practice Problem

Problem 1

Draw a diagram to show $3 \times \frac{7}{8}$ .
How does the diagram help you find the value of the expression $3 \times \frac{7}{8}$ ?