Area of Rectangles with Mixed Numbers

Videos, examples, solutions, and lessons to help Grade 5 students learn how to multiply mixed number factors, and relate to the distributive property and the area model.

New York State Common Core Math Module 5, Grade 5, Lesson 13

Common Core Standards: 5.NF.4b, 5.NF.6

Lesson 13 Concept Development

Problem 1
Find the area of a rectangle 1 1/3 inches × 3 3/4 inches and discuss strategies for solving.
Problem 2
Determine when the distributive property or the multiplication of fractions is more efficient to solve for area.
Problem 3
An 8 inch by 10 inch picture is resting on a mat. Three-fourths inch of the mat shows around the entire edge of the picture. Find the area of the mat not covered by the picture.

Lesson 13 Problem Set

1. Find the area of the following rectangles. Draw an area model if it helps you.
   a. 5/4 km x 12/5 km
   b. 16 1/2 m x 4 1/5 m
   c. 4 1/3 yd x 5 2/3 yd
   
2. Julie is cutting rectangles out of fabric to make a quilt. If the rectangles are 2 3/5 inches wide and 3 2/3 inches long, what is the area of four such rectangles?
   (Homework) 2. Chris is making a table top from some leftover tiles. He has 9 tiles that measure 3 1/8 inches long and 2 3/4 inches wide. What is the area he can cover with these tiles?
   
3. Mr. Howard’s pool is connected to his pool house by a sidewalk as shown. He wants to buy sod for the lawn, shown in grey. How much sod does he need to buy?
   (Homework) 3. A hotel is re-carpeting a section of the lobby. Carpet covers the part of the floor as shown below in grey. How many square feet of carpeting will be needed?

Lesson 13 Homework

This lesson shows how to find the area of a rectangle with fractional dimensions using three different methods: area model, distributive property, and multiplying improper fractions.

1. Find the area of the following rectangles. Draw an area model if it helps you.
   
2. Chris is making a table top from some leftover tiles. He has 9 tiles that measure 3 1/8 inches long and 2 3/4 inches wide. What is the area he can cover with these tiles?
   
3. A hotel is re-carpeting a section of the lobby. Carpet covers the part of the floor as shown below in grey. How many square feet of carpeting will be needed?

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