A park ranger hiked 1/4 mi to a lookout, another 1/3 mi to a bird's nest, and finally 1/6 mi to a campsite. How far did the park ranger hike?
Understand the Problem
The question is asking to determine the total distance hiked by a park ranger by adding up several fractions of a mile.
Answer
The park ranger hiked $\frac{3}{4}$ mi.
Answer for screen readers
The park ranger hiked $\frac{3}{4}$ mi.
Steps to Solve
- Identify the fractions to add The park ranger hiked the following distances:
- $d_1 = \frac{1}{4}$ mi (to the lookout)
- $d_2 = \frac{1}{3}$ mi (to the bird's nest)
- $d_3 = \frac{1}{6}$ mi (to the campsite)
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Find a common denominator To add the fractions, we need a common denominator. The denominators are 4, 3, and 6. The least common multiple (LCM) of these numbers is 12.
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Convert each fraction to have the common denominator Now we convert each fraction:
- $d_1 = \frac{1}{4} = \frac{3}{12}$
- $d_2 = \frac{1}{3} = \frac{4}{12}$
- $d_3 = \frac{1}{6} = \frac{2}{12}$
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Add the fractions Now that the fractions have a common denominator, we can add them together: $$ \text{Total distance} = \frac{3}{12} + \frac{4}{12} + \frac{2}{12} $$
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Simplify the result Combine the numerators: $$ \text{Total distance} = \frac{3 + 4 + 2}{12} = \frac{9}{12} $$ Now simplify: $$ \frac{9}{12} = \frac{3}{4} $$
The park ranger hiked $\frac{3}{4}$ mi.
More Information
The total distance of $\frac{3}{4}$ mi means the park ranger covered a significant distance, which is quite common for outdoor activities. Adding fractions is a vital skill in both everyday calculations and more complex mathematics.
Tips
- Not finding a common denominator before adding fractions, which can lead to incorrect results.
- Forgetting to simplify the final answer can result in an unnecessarily complex fraction.
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