1. An artist is using tiles and boards for a project. A tile has length 2 thirds , ft and width 2 thirds , ft . A board has length 1 half yd and width 1 half yd.
a. What is the ratio of the length of the tile to the length of the board?
b. What is the ratio of the area of the tile to the area of the board?
2. Diana is going camping with her family. Their campsite is 3 fourths mile away. They walk at a steady speed of 1 , and 1 eighth mi/h. How many minutes will it take them to get to the campsite?
3. A recipe calls for 1 half cup of ingredient A for every 1 , and 2 thirds cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
4. Reasoning A carpenter uses 9 , and 1 half ft of cedar for every 5 , and 2 thirds ft of redwood for a construction project.
a. If the carpenter uses 4 , and 3 fourths ft of cedar, how much redwood does he need?
b. Is there more than one way to find the amount of redwood? Explain.
5. Al made a tree house last summer. He started by making a model. The model included a window with height 1 third in. and width 1 sixth in. The actual tree house window had height 1 half yd and width 1 fourth yd. Al incorrectly said that the ratio of the height of the window in the model to the height of the window in the tree house was 2 thirds .
a. What was the correct ratio?
b. What was Al's likely error?
A. He found the ratio of the widths instead of the ratio of the heights.
B. He found the ratio of height to width for one window instead of the ratio of the heights.
C. He reversed the order of the terms of the ratio.
D. He did not convert one of the units before finding the ratio.
6. An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1 third in. and width 1 sixth in. The actual tiles have length 1 fourth ft and width 1 eighth ft.
a. What is the ratio of the length of a tile in the model to the length of an actual tile?
b. What is the ratio of the area of a tile in the model to the area of an actual tile?
c. Describe two ways to find each ratio.
7. Timothy gets a phone call from some of his friends. They say they will be at the library in 40 min and ask him to meet them there. He decides to walk to the library which is 5 eighths mi away. He walks at a steady speed of 1 , and 1 fourth mi/h.
a. Will he get there before his friends?
b. Describe three ways you could solve this problem.
8. An object is traveling at a steady speed of 10 , and 1 tenth km/h.
a. How long will it take the object to travel 4 , and 9 tenths km? Round to the nearest integer to find the estimated answer.
b. Find the exact answer.