Math Problem Statement

Sally walked ¾ of the lengths of the Tremont Trail before stopping for a rest. The Tremont Trail is 3 ½ miles. How far had Sally walked on the trail?

Solution

To find out how far Sally walked on the Tremont Trail, we need to calculate 34\frac{3}{4} of the total trail length, which is 3123 \frac{1}{2} miles.

Step 1: Convert the mixed number to an improper fraction

First, convert 3123 \frac{1}{2} miles to an improper fraction:

312=723 \frac{1}{2} = \frac{7}{2}

Step 2: Multiply by 34\frac{3}{4}

Now, multiply 72\frac{7}{2} by 34\frac{3}{4}:

72×34=7×32×4=218\frac{7}{2} \times \frac{3}{4} = \frac{7 \times 3}{2 \times 4} = \frac{21}{8}

Step 3: Convert the result to a mixed number

Convert 218\frac{21}{8} back to a mixed number:

218=258\frac{21}{8} = 2 \frac{5}{8}

So, Sally walked 2582 \frac{5}{8} miles on the Tremont Trail.

Final Answer:

Sally walked 2582 \frac{5}{8} miles before stopping.

Would you like further details on the steps or any clarifications?

Here are 5 related questions to explore:

  1. How much farther does Sally need to walk to complete the trail?
  2. What fraction of the trail has Sally yet to walk?
  3. If the total trail length were doubled, how far would Sally have walked?
  4. How would the result change if Sally walked 56\frac{5}{6} of the trail instead of 34\frac{3}{4}?
  5. If Sally walked the trail at a pace of 2 miles per hour, how long did she walk before stopping?

Tip: Converting mixed numbers to improper fractions makes multiplication easier when dealing with fractions!

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Multiplication of Fractions

Formulas

Fraction Multiplication: a/b * c/d = (a*c) / (b*d)

Theorems

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Suitable Grade Level

Grades 5-6