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 that Morgan, Henry, and Zoe walk, based on the provided fractions. We need to find the total distance that Zoe walks, given the distances walked by Morgan and Henry. Specifically, we need to compute how far Zoe walks by determining Henry's distance in relation to Morgan's distance.
Answer
Zoe walks $5 \frac{1}{8}$ meters.
Answer for screen readers
Zoe walks $5 \frac{1}{8}$ meters.
Steps to Solve
- Calculate Henry's Distance To find how far Henry walks, we start with Morgan's distance and add the additional distance that Henry walks.
Morgan's distance is $1 \frac{5}{8}$ meters.
Henry walks $1 \frac{1}{8}$ meters more than Morgan.
We can express this as: $$ \text{Henry's distance} = 1 \frac{5}{8} + 1 \frac{1}{8} $$
- Convert Mixed Numbers to Improper Fractions Convert the mixed numbers into improper fractions for easier addition.
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For $1 \frac{5}{8}$: $$ 1 \frac{5}{8} = \frac{8}{8} + \frac{5}{8} = \frac{13}{8} $$
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For $1 \frac{1}{8}$: $$ 1 \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} $$
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Add Henry's Distance Now we can add the two improper fractions: $$ \text{Henry's distance} = \frac{13}{8} + \frac{9}{8} = \frac{22}{8} = \frac{11}{4} \text{ (simplified)} $$
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Calculate Zoe's Distance Next, we find Zoe's distance by adding the additional distance she walks to Henry's distance. Zoe walks $2 \frac{3}{8}$ meters more than Henry.
Convert $2 \frac{3}{8}$ to an improper fraction: $$ 2 \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8} $$
Now, we calculate Zoe's total distance: $$ \text{Zoe's distance} = \frac{11}{4} + \frac{19}{8} $$
- Convert to a Common Denominator The common denominator of $4$ and $8$ is $8$. Convert $\frac{11}{4}$: $$ \frac{11}{4} = \frac{22}{8} $$
So, adding the fractions: $$ \text{Zoe's distance} = \frac{22}{8} + \frac{19}{8} = \frac{41}{8} $$
- Convert Improper Fraction Back to Mixed Number Lastly, convert $\frac{41}{8}$ back to a mixed number: $$ \frac{41}{8} = 5 \frac{1}{8} $$
Zoe walks $5 \frac{1}{8}$ meters.
More Information
This problem involved using addition of mixed numbers and improper fractions to calculate the distance walked by each person. Working with fractions is a vital skill in basic math and everyday computations.
Tips
- Adding Mixed Numbers Directly: Many students try to add mixed numbers without converting to improper fractions first, which can lead to incorrect answers.
- Misplacing the Fraction Parts: Ensure to keep track of the whole and fractional parts separately during calculations.
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