\frac{\frac{2}{3}}{\frac{1}{3}+\frac{2}{3}}+1
Answer (2)
The value of the expression 3 1 + 3 2 3 2 + 1 simplifies to 3 5 . This involves simplifying the denominator, performing the division, and then adding 1 to the result. The final answer is 3 5 .
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Simplify the denominator: 3 1 + 3 2 = 1 .
Divide 3 2 by the result from the previous step: 1 3 2 = 3 2 .
Add 1 to the result from the previous step: 3 2 + 1 = 3 5 .
The final answer is 3 5 .
Explanation
Understanding the Expression We are given the expression 3 1 + 3 2 3 2 + 1 and we want to evaluate it. To do this, we will first simplify the denominator, then perform the division, and finally add 1.
Simplifying the Denominator First, let's simplify the denominator: 3 1 + 3 2 = 3 1 + 2 = 3 3 = 1 .
Substituting Back Now, we can substitute this back into the original expression: 1 3 2 + 1 .
Performing the Division Next, we perform the division: 1 3 2 = 3 2 .
Adding 1 Finally, we add 1 to the result: 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 cooking, measuring ingredients, or splitting a bill with friends. Understanding how to simplify and evaluate expressions with fractions is a fundamental skill in mathematics and has practical applications in various real-life scenarios. For example, if you are following a recipe that calls for 3 2 cup of flour and you only have measuring spoons, you need to understand fractions to measure the correct amount. Similarly, if you are splitting a $15 bill three ways, you need to divide $15 by 3, which can be represented as the fraction 3 15 .
