Certainly! Let's go through a detailed, step-by-step solution for adding the mixed numbers [tex]\(4 \frac{1}{5}\)[/tex] and [tex]\(2 \frac{1}{5}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- For [tex]\(4 \frac{1}{5}\)[/tex]:
- Multiply the whole number part (4) by the denominator (5): [tex]\(4 \times 5 = 20\)[/tex].
- Add the numerator (1) to the result: [tex]\(20 + 1 = 21\)[/tex].
- Thus, [tex]\(4 \frac{1}{5}\)[/tex] is equivalent to the improper fraction [tex]\(\frac{21}{5}\)[/tex].
- For [tex]\(2 \frac{1}{5}\)[/tex]:
- Multiply the whole number part (2) by the denominator (5): [tex]\(2 \times 5 = 10\)[/tex].
- Add the numerator (1) to the result: [tex]\(10 + 1 = 11\)[/tex].
- Thus, [tex]\(2 \frac{1}{5}\)[/tex] is equivalent to the improper fraction [tex]\(\frac{11}{5}\)[/tex].
2. Add the improper fractions:
- The denominators are the same (5).
- Add the numerators: [tex]\(21 + 11 = 32\)[/tex].
- Therefore, the sum of the improper fractions is [tex]\(\frac{32}{5}\)[/tex].
3. Convert the resulting improper fraction back to a mixed number:
- Divide the numerator (32) by the denominator (5): [tex]\(\frac{32}{5} = 6 \text{ remainder } 2\)[/tex].
- The whole number part is 6.
- The remainder is 2, which becomes the new numerator.
- Thus, [tex]\(\frac{32}{5}\)[/tex] can be written as the mixed number [tex]\(6 \frac{2}{5}\)[/tex].
So, the detailed solution is:
[tex]\[
4 \frac{1}{5} + 2 \frac{1}{5} = \frac{21}{5} + \frac{11}{5} = \frac{32}{5} = 6 \frac{2}{5}
\][/tex]
Therefore, the final result is [tex]\(6 \frac{2}{5}\)[/tex].
