Question
Evaluate. \[ \frac{2}{3}+\frac{5}{6} \cdot \frac{1}{2} \] Write your answer in simplest form.
Ask by Ball Floyd. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{13}{12} \).
Solution
To evaluate the expression (2/3) + (5/6) · (1/2), follow these steps:
1. First, perform the multiplication: (5/6) · (1/2) = 5/12.
2. Then, add the result to 2/3. To add 2/3 and 5/12, convert 2/3 to a fraction with denominator 12: 2/3 = 8/12.
3. Now add: 8/12 + 5/12 = 13/12.
Thus, the answer in simplest form is 13/12.
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Simplify this solution Beyond the Answer
To evaluate the expression \(\frac{2}{3}+\frac{5}{6} \cdot \frac{1}{2}\), we first need to perform the multiplication. \[ \frac{5}{6} \cdot \frac{1}{2} = \frac{5 \cdot 1}{6 \cdot 2} = \frac{5}{12} \] Now, we can add \(\frac{2}{3}\) to \(\frac{5}{12}\). To do this, we need a common denominator. The least common denominator (LCD) of 3 and 12 is 12. Next, we convert \(\frac{2}{3}\) to have a denominator of 12: \[ \frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12} \] Now, we can add the two fractions: \[ \frac{8}{12} + \frac{5}{12} = \frac{8 + 5}{12} = \frac{13}{12} \] Thus, the final answer in simplest form is: \[ \frac{13}{12} \]
