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Answer :
Let's solve the problem step-by-step:
1. Simplify the Fractions:
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
2. Calculate the Sum Inside the Parentheses:
- [tex]\(\left(\frac{1}{2} + \frac{1}{4}\right)\)[/tex].
- First, find a common denominator, which is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex].
- Now add: [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Calculate the Product:
- [tex]\(\frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add the Results:
- Add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex].
- Find a common denominator, which is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{27}{36}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex] to [tex]\(\frac{16}{36}\)[/tex].
- Now add: [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Identify the Equivalent Answer:
- The fraction [tex]\(\frac{43}{36}\)[/tex] is the result.
- Converting [tex]\(\frac{43}{36}\)[/tex] to a mixed number gives [tex]\(1 \frac{7}{36}\)[/tex].
The correct answer to the problem is [tex]\(1 \frac{7}{36}\)[/tex].
1. Simplify the Fractions:
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
2. Calculate the Sum Inside the Parentheses:
- [tex]\(\left(\frac{1}{2} + \frac{1}{4}\right)\)[/tex].
- First, find a common denominator, which is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex].
- Now add: [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Calculate the Product:
- [tex]\(\frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add the Results:
- Add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex].
- Find a common denominator, which is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{27}{36}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex] to [tex]\(\frac{16}{36}\)[/tex].
- Now add: [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Identify the Equivalent Answer:
- The fraction [tex]\(\frac{43}{36}\)[/tex] is the result.
- Converting [tex]\(\frac{43}{36}\)[/tex] to a mixed number gives [tex]\(1 \frac{7}{36}\)[/tex].
The correct answer to the problem is [tex]\(1 \frac{7}{36}\)[/tex].
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