To add the mixed numbers [tex]\(3 \frac{1}{4}\)[/tex] and [tex]\(2 \frac{1}{6}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(3 \frac{1}{4}\)[/tex]:
[tex]\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
\][/tex]
- For [tex]\(2 \frac{1}{6}\)[/tex]:
[tex]\[
2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6}
\][/tex]
2. Find a common denominator for the fractions:
- The denominators are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12.
- Convert [tex]\(\frac{13}{4}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}
\][/tex]
- Convert [tex]\(\frac{13}{6}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}
\][/tex]
3. Add the fractions:
[tex]\[
\frac{39}{12} + \frac{26}{12} = \frac{39+26}{12} = \frac{65}{12}
\][/tex]
4. Convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator to get the whole number part:
[tex]\[
65 \div 12 = 5 \text{ with a remainder of 5}
\][/tex]
- The remainder forms the fractional part of the mixed number:
[tex]\[
\frac{65}{12} = 5 \frac{5}{12}
\][/tex]
So, the sum [tex]\(3 \frac{1}{4} + 2 \frac{1}{6}\)[/tex] in simplest form is:
[tex]\[
5 \frac{5}{12}
\][/tex]
