Math Problem Statement

Work out 2 1/3 + 1 1/3. Give your answer as a mixed number.

Solution

To solve 213+1132 \frac{1}{3} + 1 \frac{1}{3} and express the answer as a mixed number, follow these steps:


Step 1: Convert each mixed number into improper fractions

  • 213=63+13=732 \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
  • 113=33+13=431 \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}

So the problem becomes: 73+43\frac{7}{3} + \frac{4}{3}


Step 2: Add the improper fractions

Since the denominators are the same, you can add the numerators directly: 73+43=113\frac{7}{3} + \frac{4}{3} = \frac{11}{3}


Step 3: Convert the improper fraction back to a mixed number

Divide the numerator (11) by the denominator (3):

  • 11÷3=311 \div 3 = 3 remainder 22.

So: 113=323\frac{11}{3} = 3 \frac{2}{3}


Final Answer:

323\boxed{3 \frac{2}{3}}

Let me know if you'd like a detailed explanation of any step or have further questions!


Related Questions:

  1. How do you subtract mixed numbers with different denominators?
  2. What are the steps to multiply mixed numbers?
  3. How can you simplify an improper fraction to a mixed number?
  4. What is the difference between a proper fraction and an improper fraction?
  5. How can you convert a mixed number into a decimal?

Tip:

Always simplify your fractions after performing operations to ensure the final result is in its simplest form!

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Improper Fractions
Addition of Fractions

Formulas

Converting mixed numbers to improper fractions
Addition of fractions: a/b + c/b = (a+c)/b
Converting improper fractions to mixed numbers

Theorems

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Suitable Grade Level

Grades 5-7