Lesson 6 Multiply Fractions

    • Let’s multiply two non-unit fractions using diagrams and expressions.

Warm-up Which One Doesn’t Belong: More Pieces

Which one doesn’t belong?

  1. Diagram. Square, length and width, 1. Partitioned into 4 rows of 3 of the same sized rectangles. 6 rectangles shaded.
  2. Diagram. Square, length and width, 1. Partitioned into 4 rows of 3 of the same sized rectangles. 3 rectangles shaded.
  3. Diagram. Square, length and width, 1. Partitioned into 7 rows of 4 of the same sized rectangles. 6 rectangles shaded.
  4. Diagram. Two squares. Each square, length and width, 1. Each square partitioned into 4 rows of 3 of the same sized rectangles. 3 rectangles shaded in each square.

Activity 1 Many Expressions

Explain or show how each expression can represent the area of the shaded region in square units. Be prepared to share your thinking.

Square, length and width, 1. Partitioned into 6 rows of 5 of the same size rectangles. 8 rectangles shaded. 

Activity 2 More Patterns

  1. Complete the table.

    diagram

    multiplication expression

    shaded area (square units)

    A
    Square, length and width, 1. Partitioned into 4 rows of 5 of the same size rectangles. 6 rectangles shaded.
    B
    Square, length and width, 1. Partitioned into 4 rows of 5 of the same size rectangles. 12 rectangles shaded. 

    diagram

    multiplication expression

    shaded area (square units)

    C
    Diagram. Square, length and width, 1. Partitioned into 4 rows of 5 of the same size rectangles. 20 rectangles shaded.
    D
    Diagram. Rectangle. Length, 2. Width, 1. Partitioned into 4 rows of 10 of the same size rectangles. 24 rectangles shaded.

  2. What patterns do you notice in the table?

  3. Explain or show how the expression represents the last diagram in the table.

Practice Problem

Problem 1

  1. Write a multiplication expression for the area of the shaded region. Explain your reasoning.

  2. What is the area of the shaded region in square units?