# Lesson 13

Rectangles with Fractional Side Lengths

### Problem 1

1. Find the unknown side length of the rectangle if its area is 11 m2. Show your reasoning.
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.

A:

$$w \boldcdot 462 = 16\frac12$$

B:

$$16\frac12 \boldcdot w = 462$$

C:

$$462 \div 16\frac12 = w$$

D:

$$462 \div w= 16\frac12$$

E:

$$16\frac12 \boldcdot 462 = w$$

### 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.

### Solution

(From Unit 4, Lesson 12.)

### Problem 6

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

### Solution

(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. $$\frac56$$

### Solution

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.