Lesson 13

Rectangles with Fractional Side Lengths

Let’s explore rectangles that have fractional measurements.

Problem 1

  1. Find the unknown side length of the rectangle if its area is 11 m2. Show your reasoning.
    A rectangle. 
  2. Check your answer by multiplying it by the given side length (\(3\frac 23\)). Is the resulting product 11? If not, revise your previous work.

Problem 2

A worker is tiling the floor of a rectangular room that is 12 feet by 15 feet. The tiles are square with side lengths \(1\frac13\) feet. How many tiles are needed to cover the entire floor? Show your reasoning.


Problem 3

A television screen has length \(16\frac12\) inches, width \(w\) inches, and area 462 square inches. Select all the equations that represent the relationship of the side lengths and area of the television.


\(w \boldcdot 462 = 16\frac12\)


\(16\frac12 \boldcdot w = 462\)


\(462 \div 16\frac12 = w\)


\(462 \div w= 16\frac12\)


\(16\frac12 \boldcdot 462 = w\)

Problem 4

The area of a rectangle is \(17\frac12\) in2 and its shorter side is \(3\frac12\) in. Draw a diagram that shows this information. What is the length of the longer side?

Problem 5

A bookshelf is 42 inches long.

  1. How many books of length \(1\frac12\) inches will fit on the bookshelf? Explain your reasoning.
  2. A bookcase has 5 of these bookshelves. How many feet of shelf space is there? Explain your reasoning.
(From Unit 4, Lesson 12.)

Problem 6

Find the value of \(\frac{5}{32}\div \frac{25}{4}\). Show your reasoning.

(From Unit 4, Lesson 11.)

Problem 7

How many groups of \(1\frac23\) are in each of these quantities?

  1. \(1\frac56\)
  2. \(4\frac13\)
  3. \(\frac56\)
(From Unit 4, Lesson 6.)

Problem 8

It takes \(1\frac{1}{4}\) minutes to fill a 3-gallon bucket of water with a hose. At this rate, how long does it take to fill a 50-gallon tub? If you get stuck, consider using a table.

(From Unit 2, Lesson 14.)