Lesson 12
Fractional Lengths
Let’s solve problems about fractional lengths.
Problem 1
One inch is around \(2\frac{11}{20}\) centimeters.
![Ruler. Top of ruler, inches. Bottom of ruler, centimeters.](https://cms-im.s3.amazonaws.com/xEw1VDwDZyLFET2bBPDbtGAk?response-content-disposition=inline%3B%20filename%3D%226-6.4.PP.Image.New.33.png%22%3B%20filename%2A%3DUTF-8%27%276-6.4.PP.Image.New.33.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T020402Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3312578cc4acbb94213be7f354e8680af9ebe6522fe35ac9f80e39f850f3f212)
- How many centimeters long is 3 inches? Show your reasoning.
- What fraction of an inch is 1 centimeter? Show your reasoning.
- What question can be answered by finding \(10 \div 2\frac{11}{20}\) in this situation?
Problem 2
A zookeeper is \(6\frac14\) feet tall. A young giraffe in his care is \(9\frac38\) feet tall.
- How many times as tall as the zookeeper is the giraffe?
- What fraction of the giraffe’s height is the zookeeper’s height?
Problem 3
A rectangular bathroom floor is covered with square tiles that are \(1\frac12\) feet by \(1\frac12\) feet. The length of the bathroom floor is \(10\frac12\) feet and the width is \(6\frac12\) feet.
- How many tiles does it take to cover the length of the floor?
- How many tiles does it take to cover the width of the floor?
Problem 4
The Food and Drug Administration (FDA) recommends a certain amount of nutrient intake per day called the “daily value.” Food labels usually show percentages of the daily values for several different nutrients—calcium, iron, vitamins, etc.
Consider the problem: In \(\frac34\) cup of oatmeal, there is \(\frac{1}{10}\) of the recommended daily value of iron. What fraction of the daily recommended value of iron is in 1 cup of oatmeal?
Write a multiplication equation and a division equation to represent the question. Then find the answer and show your reasoning.
Problem 5
What fraction of \(\frac12\) is \(\frac13\)? Draw a tape diagram to represent and answer the question. Use graph paper if needed.
Problem 6
Noah says, “There are \(2\frac12\) groups of \(\frac45\) in 2.” Do you agree with him? Draw a tape diagram to show your reasoning. Use graph paper, if needed.