$\frac{\frac{2}{3}}{\frac{1}{3}+\frac{2}{3}}+1$
Answer (1)
Evaluate the denominator: 3 1 + 3 2 = 1 .
Divide 3 2 by the result: 1 3 2 = 3 2 .
Add 1 to the result: 3 2 + 1 = 3 5 .
The final answer is 3 5 .
Explanation
Understanding the Expression We are asked to evaluate the expression 3 1 + 3 2 3 2 + 1 . To do this, we will first evaluate the denominator of the main fraction, then perform the division, and finally add 1.
Simplifying the Denominator First, we evaluate the denominator of the main fraction: 3 1 + 3 2 = 3 1 + 2 = 3 3 = 1.
Substituting the Result Now we can substitute this result back into the original expression: 1 3 2 + 1 = 3 2 + 1.
Adding the Fractions Finally, we add the fractions: 3 2 + 1 = 3 2 + 3 3 = 3 2 + 3 = 3 5 .
Final Answer Therefore, the value of the expression is 3 5 .
Examples
Fractions are used in everyday life, such as when splitting a pizza among friends or measuring ingredients for a recipe. Understanding how to simplify and evaluate expressions with fractions is a fundamental skill in mathematics and has practical applications in various real-world scenarios, from cooking to construction.
