Lesson 12

Fractional Lengths

Problem 1

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

1. How many centimeters long is 3 inches? Show your reasoning.
2. What fraction of an inch is 1 centimeter? Show your reasoning.
3. 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.

1. How many times as tall as the zookeeper is the giraffe?
2. 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.

1. How many tiles does it take to cover the length of the floor?
2. 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.)