Answer :
Let's solve this expression step-by-step:
1. Simplify the fractions and add them: We start with the expression [tex]\(\left(\frac{3}{6} + \frac{1}{4}\right)\)[/tex].
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- Now, let's find a common denominator to add [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]. The common denominator is 4.
- [tex]\(\frac{1}{2}\)[/tex] can be rewritten as [tex]\(\frac{2}{4}\)[/tex].
- Adding these fractions: [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
2. Multiply the fractions: Now let's solve [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex].
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
- Multiply [tex]\(\frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}\)[/tex].
3. Add both results together: Now, add the results from steps 1 and 2.
- You need a common denominator to add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]. The common denominator is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to a denominator of 36: [tex]\(\frac{3}{4} = \frac{27}{36}\)[/tex].
- Convert [tex]\(\frac{4}{9}\)[/tex] to a denominator of 36: [tex]\(\frac{4}{9} = \frac{16}{36}\)[/tex].
- Adding these fractions: [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
The result of the original expression [tex]\(\left(\frac{3}{6} + \frac{1}{4}\right) + \frac{6}{9} \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{43}{36}\)[/tex], which can also be expressed as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
1. Simplify the fractions and add them: We start with the expression [tex]\(\left(\frac{3}{6} + \frac{1}{4}\right)\)[/tex].
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
- Now, let's find a common denominator to add [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]. The common denominator is 4.
- [tex]\(\frac{1}{2}\)[/tex] can be rewritten as [tex]\(\frac{2}{4}\)[/tex].
- Adding these fractions: [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
2. Multiply the fractions: Now let's solve [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex].
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex].
- Multiply [tex]\(\frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}\)[/tex].
3. Add both results together: Now, add the results from steps 1 and 2.
- You need a common denominator to add [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex]. The common denominator is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to a denominator of 36: [tex]\(\frac{3}{4} = \frac{27}{36}\)[/tex].
- Convert [tex]\(\frac{4}{9}\)[/tex] to a denominator of 36: [tex]\(\frac{4}{9} = \frac{16}{36}\)[/tex].
- Adding these fractions: [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
The result of the original expression [tex]\(\left(\frac{3}{6} + \frac{1}{4}\right) + \frac{6}{9} \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{43}{36}\)[/tex], which can also be expressed as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
