Math Problem Statement

What is the sum of the mixed numbers 6 1/3 and 2 2/3?

Solution

The image shows the addition of two mixed numbers:

613+2236 \frac{1}{3} + 2 \frac{2}{3}

Step-by-Step Solution:

  1. Convert the mixed numbers to improper fractions:

    • For 6136 \frac{1}{3}: 613=6×3+13=18+13=1936 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}
    • For 2232 \frac{2}{3}: 223=2×3+23=6+23=832 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}
  2. Add the improper fractions: Since both fractions have the same denominator, you can directly add the numerators: 193+83=19+83=273\frac{19}{3} + \frac{8}{3} = \frac{19 + 8}{3} = \frac{27}{3}

  3. Simplify the result: 273=9\frac{27}{3} = 9

Final Answer:

613+223=96 \frac{1}{3} + 2 \frac{2}{3} = 9

Would you like more details or have any questions?


Here are 5 related questions:

  1. How do you convert other mixed numbers into improper fractions?
  2. What is the process of adding fractions with different denominators?
  3. How can you subtract mixed numbers?
  4. What are mixed numbers and how do you simplify them?
  5. Can you convert improper fractions back into mixed numbers?

Tip: When adding mixed numbers, converting them into improper fractions first makes calculations easier.

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Math Problem Analysis

Mathematical Concepts

Addition of Mixed Numbers
Improper Fractions
Simplification

Formulas

Mixed number to improper fraction: a b/c = (a * c + b) / c
Addition of fractions with like denominators: a/c + b/c = (a + b)/c

Theorems

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Suitable Grade Level

Grades 5-6