Solution: To find the average, add the two lengths and divide by 2. First, convert the mixed numbers to improper fractions:

["The Ultimate Solution to Finding Averages: Master Averaging with Mixed Numbers Made Easy", "Understanding how to calculate an average is a fundamental math skill—essential not only in school but also in everyday life decisions, from measuring project timelines to analyzing data. One of the most widely used methods to find an average is simple: add the numbers together and divide by how many there are. But what happens when those numbers are mixed numbers—fractions with both whole numbers and fractions? Fear not! This guide reveals a clear, step-by-step solution to find the average of mixed numbers by converting them to improper fractions.", "---", "### Why Understanding Averages Matters", "Before diving into the solution, let’s clarify why averages matter. Whether you're tracking progress, comparing scores, or planning timelines, averages provide a single value that represents a group of data points. Accurately calculating them ensures better decision-making and clearer communication.", "---", "### The Basic Formula for Average", "At its core, the average (or mean) is found using this simple formula:", "[\n\ ext{Average} = \frac{\ ext{Sum of all values}}{\ ext{Number of values}}\n]", "For example, to average 3, 4.5, and 2.75, you first add them together and divide by 3. But when mixed numbers are involved, direct addition gets tricky—but with one simple technique, you can handle them with ease.", "---", "### When Faces Mixed Numbers: Add and Convert", "Mixed numbers combine a whole number and a fractional part, like ( 3 \frac{1}{2} ) or ( 5 \frac{3}{4} ). These are convenient in real life but pose challenges when adding because fractions must have the same denominator.", "The key solution: Convert each mixed number into an improper fraction before applying the average formula.", "How? Here’s how to convert a mixed number to an improper fraction in just three steps:", "---", "### Step-by-Step: Convert Mixed Numbers to Improper Fractions", "Step 1: Multiply the whole number by the denominator\nTake the whole number part and multiply it by the denominator of the fraction.", "Step 2: Add the numerator\nAdd the fractional numerator to the result from Step 1.", "Step 3: Keep the same denominator\nPlace the sum over the original denominator to form the improper fraction.", "Example: Convert ( 2 \frac{3}{5} )", "- Multiply: ( 2 \ imes 5 = 10 )\n- Add: ( 10 + 3 = 13 )\n- Result: ( \frac{13}{5} )", "Repeat this for each mixed number in your data set.", "---", "### Apply the Average Formula Using Improper Fractions", "Once all values are improper fractions, add them:", "- Find a common denominator if needed.\n- Add numerators across the shared denominator.\n- Divide by the total count of values.", "---", "### Real-Life Example: Finding the Average of Mixed Numbers", "Let’s find the average of ( 1 \frac{1}{3} ), ( 4 \frac{1}{2} ), and ( 2 \frac{2}{5} )", "Step 1: Convert each mixed number", "- ( 1 \frac{1}{3} = \frac{(1 \ imes 3) + 1}{3} = \frac{4}{3} )\n- ( 4 \frac{1}{2} = \frac{(4 \ imes 2) + 1}{2} = \frac{9}{2} )\n- ( 2 \frac{2}{5} = \frac{(2 \ imes 5) + 2}{5} = \frac{12}{5} )", "Step 2: Add the fractions", "Find a common denominator—15 works well:", "- ( \frac{4}{3} = \frac{4 \ imes 5}{3 \ imes 5} = \frac{20}{15} )\n- ( \frac{9}{2} = \frac{9 \ imes 7.5}{2 \ imes 7.5} ) → adjust properly:\n Use LCM 30:\n - ( \frac{4 \ imes 15}{15} = \frac{60}{30} ), but better use 30 as LCM of 3, 2, 5 is 30:\n - ( \frac{4}{3} = \frac{40}{30} ), ( \frac{9}{2} = \frac{135}{30} ), ( \frac{12}{5} = \frac{72}{30} )", "Now add:", "[\n\frac{40 + 135 + 72}{30} = \frac{247}{30}\n]", "Step 3: Divide by the number of values", "There are 3 numbers:", "[\n\ ext{Average} = \frac{247}{30} \div 3 = \frac{247}{30} \ imes \frac{1}{3} = \frac{247}{90}\n]", "You can leave the answer as an improper fraction, convert to a mixed number, or decimal ( \approx 2.74 ) for practical use.", "---", "### Why This Method Works", "Converting mixed numbers into improper fractions simplifies arithmetic operations by unifying both parts under a single denominator. This eliminates guesswork and prevents errors common in manual fraction addition—especially critical when working with averages that involve more than two numbers.", "---", "### Tools and Tips for Smooth Averaging", "- Use a fraction table: Print or visualize common denominators to assist LCM calculations.\n- Practice with real data: Track scores, project durations, or measurements regularly to build fluency.\n- Double-check: Always verify conversions and ensure all values use the same denominator before adding.", "---", "### Conclusion", "Finding the average of mixed numbers doesn’t have to be complicated. By converting each mixed number to an improper fraction first, you streamline the process and ensure accurate results every time. Master this simple solution, and you’ll confidently compute averages across math, science, business, and life’s daily challenges.", "Adopt this proven method—add, convert, average—and unlock clarity in every numerical comparison!", "---", "Keywords: average, average formula, mixed numbers, convert to improper fraction, average calculation, math tips, fraction addition, real-life math, how to find average, improper fraction average, math solution guide", "Meta Description: Simplify calculating averages with mixed numbers by converting fractions to improper fractions—step-by-step guide with example to master mathematical averaging techniques."]