Lesson 5 Multiply a Unit Fraction by a Non-unit Fraction

    • Let’s multiply a unit fraction and a non-unit fraction.

Warm-up Estimation Exploration: Shaded Rectangle

What is the area of the shaded region?

Diagram. Square, length and width, 1. Rectangle with length of about 1 half and width of about 3 fifths shaded.
Diagram. Square, length and width, 1. Rectangle with length of about 1 half and width of about 3 fifths shaded.

Record an estimate that is:

too low

about right

too high

Activity 1 Write Equations

Problem 1

Write a multiplication expression that represents the shaded region in each diagram.

  1. Square, length and width, 1. Partitioned into 3 rows of 5 of the same size rectangles. 2 rectangles shaded. 
  2. Diagram. Square, length and width, 1. Partitioned into 3 rows of 5 of the same size rectangles. 3 rectangles shaded.
  3. Square, length and width, 1. Partitioned into 3 rows of 5 of the same size rectangles. 4 rectangles shaded. 

Problem 2

  1. What patterns do you notice in the multiplication expressions?

  2. Han wrote this equation to represent the area of the shaded region. Explain how the diagram represents the equation.

    2.5cm65×13=615

Activity 2 Estimate With Expressions

Write a multiplication expression that might represent the area of the shaded region. Be prepared to explain your reasoning.

  1. Square, length and width, 1. Rectangle portion shaded, about 3 fourths of the length and 1 half of the width. 

     

  2. Square. Length and width, 1. Rectangle with width of about 2 thirds and length of about 1 fourth shaded. 
  3. Square, length and width, 1. Rectangle portion shaded, about 3 fourths of the length and 1 third of the width. 

     

  4. Diagram. Rectangle. Length, 2. Width, 1. Rectangle of length about 3 halves and width about 1 fifth shaded. 

Practice Problem

Problem 1

  1. Write an expression for the area of the shaded region.

    Diagram, square. Length and width, 1. Partitioned into 5 rows of 4 of the same size rectangles. 4 rectangles shaded.

  2. Explain how the diagram shows your expression.