Morgan walks 1 5/8 meters. Henry walks 1 1/8 meters more than Morgan. Zoe walks 2 3/8 meters more than Henry. How far does Zoe walk?
Understand the Problem
The question involves calculating the distances walked by Morgan, Henry, and Zoe based on the given values and relationships. It requires understanding how to add fractions and apply the information step by step to find Zoe's total distance.
Answer
Zoe walks \( 4 \frac{5}{8} \) meters, or \( \frac{37}{8} \) meters.
Answer for screen readers
Zoe walks ( 4 \frac{5}{8} ) meters, or ( \frac{37}{8} ) meters.
Steps to Solve
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Identify Morgan's Distance Morgan walks ( 1 \frac{5}{8} ) meters. First, convert this mixed number to an improper fraction: [ 1 \frac{5}{8} = \frac{8 \times 1 + 5}{8} = \frac{13}{8} ]
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Calculate Henry's Distance Henry walks ( \frac{5}{8} ) meters more than Morgan. Therefore, calculate Henry's distance: [ \text{Henry's distance} = \frac{13}{8} + \frac{5}{8} = \frac{13 + 5}{8} = \frac{18}{8} = \frac{9}{4} ]
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Determine Zoe's Distance Zoe walks ( 2 \frac{3}{8} ) meters more than Henry. First, convert this mixed number to an improper fraction: [ 2 \frac{3}{8} = \frac{8 \times 2 + 3}{8} = \frac{19}{8} ] Now, calculate Zoe's distance: [ \text{Zoe's distance} = \frac{9}{4} + \frac{19}{8} ] Convert ( \frac{9}{4} ) to eighths: [ \frac{9}{4} = \frac{18}{8} ] So, now add: [ \text{Zoe's distance} = \frac{18}{8} + \frac{19}{8} = \frac{18 + 19}{8} = \frac{37}{8} ]
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Final Conversion Convert ( \frac{37}{8} ) back to a mixed number: [ \frac{37}{8} = 4 \frac{5}{8} ]
Zoe walks ( 4 \frac{5}{8} ) meters, or ( \frac{37}{8} ) meters.
More Information
Zoe's total walking distance combines her additional distance over Henry and highlights how to work with improper fractions and mixed numbers. This problem illustrates basic fraction addition and is useful for understanding relative distances.
Tips
- Not converting mixed numbers properly: Always convert them into improper fractions for easier calculations.
- Adding fractions with different denominators: Remember to find a common denominator before adding.
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