Understanding the Expression
To solve the expression \(5 + \frac{2}{9} - 14 + \frac{7}{3}\), we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Step 1: Simplifying Whole Numbers
- Begin with the whole numbers: \(5\) and \(-14\).
- Calculate \(5 - 14\):
- \(5 - 14 = -9\)
Step 2: Adding the Fractions
- Now combine the fractions \(\frac{2}{9}\) and \(\frac{7}{3}\).
- To add these fractions, we need a common denominator. The denominators are \(9\) and \(3\). The least common multiple is \(9\).
- Convert \(\frac{7}{3}\) to have a denominator of \(9\):
- \(\frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9}\)
Step 3: Combine the Fractions
- Now add \(\frac{2}{9}\) and \(\frac{21}{9}\):
- \(\frac{2}{9} + \frac{21}{9} = \frac{2 + 21}{9} = \frac{23}{9}\)
Step 4: Final Calculation
- Now combine the whole number result with the fraction:
- \(-9 + \frac{23}{9}\)
- Convert \(-9\) to a fraction:
- \(-9 = \frac{-81}{9}\)
Final Step: Adding the Fractions
- Now add:
- \(\frac{-81}{9} + \frac{23}{9} = \frac{-81 + 23}{9} = \frac{-58}{9}\)
Final Answer
The final result of the expression \(5 + \frac{2}{9} - 14 + \frac{7}{3}\) is \(\frac{-58}{9}\).

-6.444