To solve the problem of adding the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{4}{6}\)[/tex], let's follow a step-by-step approach:
1. Understand the Problem:
We need to add two fractions:
[tex]\[
\frac{5}{6} + \frac{4}{6}
\][/tex]
2. Add the Numerators:
Since the denominators are the same, we keep the denominator (6) and add the numerators (5 and 4):
[tex]\[
\frac{5+4}{6} = \frac{9}{6}
\][/tex]
3. Simplify the Sum:
Simplify [tex]\(\frac{9}{6}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{9 \div 3}{6 \div 3} = \frac{3}{2}
\][/tex]
4. Convert to a Mixed Number (if needed):
We can convert [tex]\(\frac{3}{2}\)[/tex] to a mixed number by dividing the numerator by the denominator:
[tex]\[
3 \div 2 = 1 \quad \text{remainder: } 1
\][/tex]
This gives us:
[tex]\[
1 \frac{1}{2}
\][/tex]
The result of [tex]\(\frac{5}{6} + \frac{4}{6}\)[/tex] is therefore:
[tex]\[
1 \frac{1}{2}
\][/tex]
Now let's compare this with the given options:
1. [tex]\(1 \frac{3}{6}\)[/tex]
2. [tex]\(1 \frac{2}{6}\)[/tex]
3. [tex]\(\frac{9}{12}\)[/tex]
4. [tex]\(\frac{1}{6}\)[/tex]
- [tex]\(1 \frac{3}{6}\)[/tex] simplifies to [tex]\(1 \frac{1}{2}\)[/tex], which matches our result.
- [tex]\(1 \frac{2}{6}\)[/tex] simplifies to [tex]\(1 \frac{1}{3}\)[/tex], which does not match.
- [tex]\(\frac{9}{12}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex], which does not match.
- [tex]\(\frac{1}{6}\)[/tex] is clearly not a match.
Hence, the correct answer is:
[tex]\[
1 \frac{3}{6}
\][/tex]
