Math Problem Statement

what is the midway point between 3 2/3 and 5 1/6

Solution

To find the midway point between 3233 \frac{2}{3} and 5165 \frac{1}{6}, we can follow these steps:

  1. Convert the mixed numbers to improper fractions:

    • 323=1133 \frac{2}{3} = \frac{11}{3}
    • 516=3165 \frac{1}{6} = \frac{31}{6}
  2. Find a common denominator:

    • The least common denominator (LCD) of 3 and 6 is 6.
    • Convert 113\frac{11}{3} to a fraction with denominator 6:
      113=226\frac{11}{3} = \frac{22}{6}.
  3. Add the two fractions:

    • 226+316=536\frac{22}{6} + \frac{31}{6} = \frac{53}{6}.
  4. Divide by 2 to find the midpoint:

    • 536÷2=536×12=5312\frac{53}{6} \div 2 = \frac{53}{6} \times \frac{1}{2} = \frac{53}{12}.
  5. Convert 5312\frac{53}{12} back to a mixed number:

    • 5312=4512\frac{53}{12} = 4 \frac{5}{12}.

Thus, the midway point between 3233 \frac{2}{3} and 5165 \frac{1}{6} is 45124 \frac{5}{12}.

Would you like further details or clarification?


Here are 5 related questions for you to explore:

  1. How do you convert mixed numbers to improper fractions?
  2. What are other methods for finding the midpoint of two numbers?
  3. How do you find the least common denominator (LCD) of fractions?
  4. How do you multiply and divide fractions?
  5. Can you calculate the average of three mixed numbers?

Tip: When dividing fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Averages

Formulas

Midpoint = (a + b) / 2
Conversion of mixed numbers to improper fractions

Theorems

Arithmetic Mean Theorem

Suitable Grade Level

Grades 6-8