Math Problem Statement

Add 3 4/5 + 2 5/6.

Solution

The problem asks you to add two mixed numbers:

345+2563 \frac{4}{5} + 2 \frac{5}{6}

Step-by-step solution:

  1. Convert the mixed numbers to improper fractions:

    • 345=3×5+45=15+45=1953 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}
    • 256=2×6+56=12+56=1762 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
  2. Find the least common denominator (LCD) of 5 and 6:

    • The LCD of 5 and 6 is 30.
  3. Rewrite both fractions with the common denominator:

    • 195=19×65×6=11430\frac{19}{5} = \frac{19 \times 6}{5 \times 6} = \frac{114}{30}
    • 176=17×56×5=8530\frac{17}{6} = \frac{17 \times 5}{6 \times 5} = \frac{85}{30}
  4. Add the fractions: 11430+8530=114+8530=19930\frac{114}{30} + \frac{85}{30} = \frac{114 + 85}{30} = \frac{199}{30}

  5. Convert the improper fraction back to a mixed number:

    • 19930\frac{199}{30} can be written as: 199÷30=6 remainder 19199 \div 30 = 6 \text{ remainder } 19 So, 19930=61930\frac{199}{30} = 6 \frac{19}{30}.

Final Answer:

345+256=619303 \frac{4}{5} + 2 \frac{5}{6} = 6 \frac{19}{30}

Would you like more details or have any questions about this solution?

Here are 5 questions to expand on this:

  1. How do you find the least common denominator (LCD) of two fractions?
  2. What are the steps to convert an improper fraction back into a mixed number?
  3. Can you explain why we convert mixed numbers to improper fractions when adding?
  4. How do you simplify fractions after adding or subtracting?
  5. What are some tips for handling fractions with large denominators?

Tip: Always ensure both fractions have the same denominator before adding or subtracting them.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Addition

Formulas

Convert mixed numbers to improper fractions
Find least common denominator (LCD)
Add fractions
Convert improper fraction back to mixed number

Theorems

Least Common Denominator (LCD)

Suitable Grade Level

Grades 5-7