Let's add the mixed fractions [tex]\(6 \frac{1}{6}\)[/tex] and [tex]\(7 \frac{1}{2}\)[/tex].
1. Convert the mixed fractions to improper fractions:
- [tex]\(6 \frac{1}{6}\)[/tex] can be expressed as:
[tex]\[
6 + \frac{1}{6} = \frac{36}{6} + \frac{1}{6} = \frac{37}{6}
\][/tex]
- [tex]\(7 \frac{1}{2}\)[/tex] can be expressed as:
[tex]\[
7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2}
\][/tex]
2. Find a common denominator for the two fractions:
- The common denominator for [tex]\(6\)[/tex] and [tex]\(2\)[/tex] is [tex]\(6\)[/tex].
- Convert [tex]\(\frac{15}{2}\)[/tex] to a fraction with a denominator of [tex]\(6\)[/tex]:
[tex]\[
\frac{15}{2} = \frac{15 \times 3}{2 \times 3} = \frac{45}{6}
\][/tex]
3. Add the two fractions:
- Now, we have [tex]\(\frac{37}{6}\)[/tex] and [tex]\(\frac{45}{6}\)[/tex]:
[tex]\[
\frac{37}{6} + \frac{45}{6} = \frac{37 + 45}{6} = \frac{82}{6}
\][/tex]
4. Convert the improper fraction back to a mixed number:
- Divide [tex]\(82\)[/tex] by [tex]\(6\)[/tex] to find the whole number part:
[tex]\[
82 \div 6 = 13 \quad \text{(quotient is the whole number part)}
\][/tex]
- Find the remainder:
[tex]\[
82 \mod 6 = 4 \quad \text{(remainder is the numerator of the fractional part)}
\][/tex]
- The fractional part with the remainder as the numerator is:
[tex]\[
\frac{4}{6}
\][/tex]
- Simplify the fractional part:
[tex]\[
\frac{4}{6} = \frac{2}{3}
\][/tex]
5. Combine the whole number part and the simplified fractional part:
- The final answer is:
[tex]\[
13 \frac{2}{3}
\][/tex]
So, when you add [tex]\(6 \frac{1}{6}\)[/tex] and [tex]\(7 \frac{1}{2}\)[/tex], the result is [tex]\(13 \frac{2}{3}\)[/tex].
