Answer :
Let's solve the expression step by step:
1. Simplify Fractions:
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex] because both the numerator and the denominator can be divided by 3.
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex] because both the numerator and the denominator can be divided by 3.
2. Add the First Two Fractions:
- [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex].
- To add these, we need a common denominator. The common denominator for 2 and 4 is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex].
- Now the expression is [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Multiply the Second Fraction Expression:
- [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex] simplifies to [tex]\(\frac{2}{3} \cdot \frac{2}{3}\)[/tex] since [tex]\(\frac{6}{9}\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
- Multiply the fractions: [tex]\(\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add the Results:
- Now add [tex]\(\frac{3}{4} + \frac{4}{9}\)[/tex].
- To add these, we need a common denominator. The smallest common denominator for 4 and 9 is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{27}{36}\)[/tex].
- Convert [tex]\(\frac{4}{9}\)[/tex] to [tex]\(\frac{16}{36}\)[/tex].
- Now the expression is [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Result as a Mixed Number:
- [tex]\(\frac{43}{36}\)[/tex] can be written as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
So, the final answer is [tex]\(1 \frac{7}{36}\)[/tex].
1. Simplify Fractions:
- [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex] because both the numerator and the denominator can be divided by 3.
- [tex]\(\frac{6}{9}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex] because both the numerator and the denominator can be divided by 3.
2. Add the First Two Fractions:
- [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex].
- To add these, we need a common denominator. The common denominator for 2 and 4 is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex].
- Now the expression is [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
3. Multiply the Second Fraction Expression:
- [tex]\(\frac{6}{9} \cdot \frac{2}{3}\)[/tex] simplifies to [tex]\(\frac{2}{3} \cdot \frac{2}{3}\)[/tex] since [tex]\(\frac{6}{9}\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
- Multiply the fractions: [tex]\(\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\)[/tex].
4. Add the Results:
- Now add [tex]\(\frac{3}{4} + \frac{4}{9}\)[/tex].
- To add these, we need a common denominator. The smallest common denominator for 4 and 9 is 36.
- Convert [tex]\(\frac{3}{4}\)[/tex] to [tex]\(\frac{27}{36}\)[/tex].
- Convert [tex]\(\frac{4}{9}\)[/tex] to [tex]\(\frac{16}{36}\)[/tex].
- Now the expression is [tex]\(\frac{27}{36} + \frac{16}{36} = \frac{43}{36}\)[/tex].
5. Result as a Mixed Number:
- [tex]\(\frac{43}{36}\)[/tex] can be written as the mixed number [tex]\(1 \frac{7}{36}\)[/tex].
So, the final answer is [tex]\(1 \frac{7}{36}\)[/tex].
