# Lesson 12

Fractional Lengths

### Problem 1

One inch is around \(2\frac{11}{20}\) centimeters.

- 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?

### Solution

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### 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?

### Solution

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### 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?

### Solution

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### 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.

### Solution

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(From Unit 4, Lesson 11.)### Problem 5

What fraction of \(\frac12\) is \(\frac13\)? Draw a tape diagram to represent and answer the question. Use graph paper if needed.

### Solution

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(From Unit 4, Lesson 7.)### 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.

### Solution

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(From Unit 4, Lesson 6.)