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Answer :
Let's solve the problem step by step.
First, we need to simplify the expression [tex]\(\left(\frac{3}{6}+\frac{1}{4}\right)+\frac{6}{9} \cdot \frac{2}{3}\)[/tex].
1. Simplify [tex]\(\frac{3}{6}\)[/tex]:
[tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
2. Add [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
To add these fractions, find a common denominator. The common denominator of 2 and 4 is 4.
[tex]\(\frac{1}{2} = \frac{2}{4}\)[/tex]
Now, add [tex]\(\frac{2}{4}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Calculate [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex]:
First, simplify [tex]\(\frac{6}{9}\)[/tex]. It simplifies to [tex]\(\frac{2}{3}\)[/tex].
Now multiply [tex]\(\frac{2}{3} \times \frac{2}{3}\)[/tex]:
[tex]\(\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]:
Find a common denominator for [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]. The least common multiple of 4 and 9 is 36.
Convert each fraction:
[tex]\(\frac{3}{4} = \frac{27}{36}\)[/tex]
[tex]\(\frac{4}{9} = \frac{16}{36}\)[/tex]
Now, add them together:
[tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Simplified Result:
[tex]\(\frac{43}{36}\)[/tex] can also be written as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
So, the final simplified result is [tex]\(\frac{43}{36}\)[/tex] or [tex]\(1 \frac{7}{36}\)[/tex], which matches the choice [tex]\(1 \frac{7}{36}\)[/tex] from the options given.
First, we need to simplify the expression [tex]\(\left(\frac{3}{6}+\frac{1}{4}\right)+\frac{6}{9} \cdot \frac{2}{3}\)[/tex].
1. Simplify [tex]\(\frac{3}{6}\)[/tex]:
[tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
2. Add [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
To add these fractions, find a common denominator. The common denominator of 2 and 4 is 4.
[tex]\(\frac{1}{2} = \frac{2}{4}\)[/tex]
Now, add [tex]\(\frac{2}{4}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Calculate [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex]:
First, simplify [tex]\(\frac{6}{9}\)[/tex]. It simplifies to [tex]\(\frac{2}{3}\)[/tex].
Now multiply [tex]\(\frac{2}{3} \times \frac{2}{3}\)[/tex]:
[tex]\(\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]:
Find a common denominator for [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]. The least common multiple of 4 and 9 is 36.
Convert each fraction:
[tex]\(\frac{3}{4} = \frac{27}{36}\)[/tex]
[tex]\(\frac{4}{9} = \frac{16}{36}\)[/tex]
Now, add them together:
[tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Simplified Result:
[tex]\(\frac{43}{36}\)[/tex] can also be written as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
So, the final simplified result is [tex]\(\frac{43}{36}\)[/tex] or [tex]\(1 \frac{7}{36}\)[/tex], which matches the choice [tex]\(1 \frac{7}{36}\)[/tex] from the options given.
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