Question
5. Evaluate. \( \frac{1}{3} \times\left(\frac{3}{4}+\frac{1}{2}\right) \)
Ask by Salinas Parsons. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The evaluated expression is \(\frac{5}{12}\).
Solution
**Step 1:** Evaluate the expression inside the parentheses:
\[
\frac{3}{4} + \frac{1}{2}
\]
**Step 2:** Find a common denominator. The least common denominator for 4 and 2 is 4. Rewrite \(\frac{1}{2}\) as:
\[
\frac{1}{2} = \frac{2}{4}
\]
**Step 3:** Add the fractions:
\[
\frac{3}{4} + \frac{2}{4} = \frac{3+2}{4} = \frac{5}{4}
\]
**Step 4:** Multiply by \(\frac{1}{3}\):
\[
\frac{1}{3} \times \frac{5}{4} = \frac{5}{12}
\]
Thus, the evaluated expression is:
\[
\frac{5}{12}
\]
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Simplify this solution Bonus Knowledge
To evaluate the expression, we start by adding the fractions inside the parentheses: First, we need a common denominator for \( \frac{3}{4} \) and \( \frac{1}{2} \). The least common denominator is 4. We can rewrite \( \frac{1}{2} \) as \( \frac{2}{4} \): \[ \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \] Now we substitute this back into the original expression: \[ \frac{1}{3} \times \frac{5}{4} \] To multiply the fractions, we multiply the numerators and the denominators: \[ \frac{1 \times 5}{3 \times 4} = \frac{5}{12} \] Thus, the evaluated result of the expression is: \[ \frac{5}{12} \]
