A zookeeper is 5 3/4 tall. An adult giraffe in his care is 14 3/8 feet tall a. How many times as tall as the zookeeper is the giraffe? b. what fraction of the giraffes height is the zookeepers height? (need help with b)
A zookeeper is 5 3/4 tall. An adult giraffe in his care is 14 3/8 feet tall a. How many times as tall as the zookeeper is the giraffe? b. what fraction of the giraffes height is the zookeepers height? (need help with b)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A zookeeper is 5 3/4 tall. An adult giraffe in his care is 14 3/8 feet tall
a. How many times as tall as the zookeeper is the giraffe?
b. what fraction of the giraffes height is the zookeepers height?
(need help with b)
![The problem involves comparing the height of a zookeeper to that of an adult giraffe in fractional terms.
**Problem Statement:**
The zookeeper is \(5\frac{3}{4}\) feet tall. An adult giraffe in his care is \(14\frac{3}{8}\) feet tall.
**Questions:**
a. How many times as tall as the zookeeper is the giraffe?
**Working:**
To calculate this, we convert the mixed numbers to improper fractions:
- Zookeeper: \(5\frac{3}{4} = \frac{23}{4}\)
- Giraffe: \(14\frac{3}{8} = \frac{115}{8}\)
Then divide the giraffe's height by the zookeeper's height:
\[
\frac{115}{8} \div \frac{23}{4} = \frac{115}{8} \times \frac{4}{23} = \frac{460}{184} = 2.5
\]
Thus, the giraffe is 2.5 times as tall as the zookeeper.
b. What fraction of the giraffe's height is the zookeeper’s height?
The answer is \(\frac{2}{5}\), based on the inverse of the previous calculation.
**Notes:**
These solutions are derived from basic operations involving fractions and provide a practical application of proportional reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43552b06-4ca0-4626-9ba7-0ceb014960ee%2F664d6e96-c99c-40c2-b8f5-2718766b139e%2Fb9cjzpdt.jpeg&w=3840&q=75)
Transcribed Image Text:The problem involves comparing the height of a zookeeper to that of an adult giraffe in fractional terms.
**Problem Statement:**
The zookeeper is \(5\frac{3}{4}\) feet tall. An adult giraffe in his care is \(14\frac{3}{8}\) feet tall.
**Questions:**
a. How many times as tall as the zookeeper is the giraffe?
**Working:**
To calculate this, we convert the mixed numbers to improper fractions:
- Zookeeper: \(5\frac{3}{4} = \frac{23}{4}\)
- Giraffe: \(14\frac{3}{8} = \frac{115}{8}\)
Then divide the giraffe's height by the zookeeper's height:
\[
\frac{115}{8} \div \frac{23}{4} = \frac{115}{8} \times \frac{4}{23} = \frac{460}{184} = 2.5
\]
Thus, the giraffe is 2.5 times as tall as the zookeeper.
b. What fraction of the giraffe's height is the zookeeper’s height?
The answer is \(\frac{2}{5}\), based on the inverse of the previous calculation.
**Notes:**
These solutions are derived from basic operations involving fractions and provide a practical application of proportional reasoning.
![**This Just In. Giraffes are Tall.**
A zookeeper is \(5 \frac{3}{4}\) feet tall. An adult giraffe in his care is \(14 \frac{3}{8}\) feet tall.
a. **How many times as tall as the zookeeper is the giraffe?**
To solve this, convert the mixed numbers to improper fractions:
- Zookeeper's height: \(5 \frac{3}{4} = \frac{23}{4}\)
- Giraffe's height: \(14 \frac{3}{8} = \frac{115}{8}\)
Now, divide the giraffe's height by the zookeeper's height:
\[
\frac{115}{8} \div \frac{23}{4} = \frac{115}{8} \times \frac{4}{23} = \frac{460}{184} = 2 \frac{1}{2}
\]
The giraffe is \(2 \frac{1}{2}\) times as tall as the zookeeper.
b. **What fraction of the giraffe’s height is the zookeeper’s height?**
Use the reciprocal from part a, \(\frac{1}{2 \frac{1}{2}} = \frac{2}{5}\).
This means the zookeeper's height is \(\frac{2}{5}\) of the giraffe's height.
***Note***: Mathematical calculations and working steps are visible on the paper, with annotations to clarify each step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43552b06-4ca0-4626-9ba7-0ceb014960ee%2F664d6e96-c99c-40c2-b8f5-2718766b139e%2Fvuo4ea.jpeg&w=3840&q=75)
Transcribed Image Text:**This Just In. Giraffes are Tall.**
A zookeeper is \(5 \frac{3}{4}\) feet tall. An adult giraffe in his care is \(14 \frac{3}{8}\) feet tall.
a. **How many times as tall as the zookeeper is the giraffe?**
To solve this, convert the mixed numbers to improper fractions:
- Zookeeper's height: \(5 \frac{3}{4} = \frac{23}{4}\)
- Giraffe's height: \(14 \frac{3}{8} = \frac{115}{8}\)
Now, divide the giraffe's height by the zookeeper's height:
\[
\frac{115}{8} \div \frac{23}{4} = \frac{115}{8} \times \frac{4}{23} = \frac{460}{184} = 2 \frac{1}{2}
\]
The giraffe is \(2 \frac{1}{2}\) times as tall as the zookeeper.
b. **What fraction of the giraffe’s height is the zookeeper’s height?**
Use the reciprocal from part a, \(\frac{1}{2 \frac{1}{2}} = \frac{2}{5}\).
This means the zookeeper's height is \(\frac{2}{5}\) of the giraffe's height.
***Note***: Mathematical calculations and working steps are visible on the paper, with annotations to clarify each step.
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