To divide the mixed numbers [tex]\( 5 \frac{3}{5} \)[/tex] and [tex]\( 2 \frac{4}{10} \)[/tex], we first convert each mixed number into an improper fraction.
1. Convert [tex]\( 5 \frac{3}{5} \)[/tex] to an improper fraction:
- [tex]\( 5 \frac{3}{5} \)[/tex] means [tex]\( 5 \)[/tex] whole and [tex]\( \frac{3}{5} \)[/tex].
- Converting this to an improper fraction: [tex]\( 5 + \frac{3}{5} = \frac{25}{5} + \frac{3}{5} = \frac{28}{5} \)[/tex].
2. Convert [tex]\( 2 \frac{4}{10} \)[/tex] to an improper fraction:
- [tex]\( 2 \frac{4}{10} \)[/tex] means [tex]\( 2 \)[/tex] whole and [tex]\( \frac{4}{10} \)[/tex].
- Note that [tex]\(\frac{4}{10}\)[/tex] can be simplified to [tex]\(\frac{2}{5}\)[/tex].
- Converting this to an improper fraction: [tex]\( 2 + \frac{4}{10} = \frac{20}{10} + \frac{4}{10} = \frac{24}{10} = \frac{12}{5} \)[/tex].
3. Now, we have the division problem:
[tex]\[
\frac{28}{5} \div \frac{12}{5}
\][/tex]
4. To divide by a fraction, multiply by the reciprocal of that fraction:
[tex]\[
\frac{28}{5} \div \frac{12}{5} = \frac{28}{5} \times \frac{5}{12}
\][/tex]
5. Simplify before multiplying:
- The [tex]\(5\)[/tex] in the numerator and the denominator cancel out:
[tex]\[
\frac{28}{5} \times \frac{5}{12} = \frac{28 \times 5}{5 \times 12} = \frac{28}{12}
\][/tex]
- Simplify [tex]\(\frac{28}{12}\)[/tex]:
[tex]\[
\frac{28}{12} = \frac{7}{3}
\][/tex]
6. The improper fraction [tex]\(\frac{7}{3}\)[/tex] can be converted to a mixed number:
- Divide [tex]\(7\)[/tex] by [tex]\(3\)[/tex]: The quotient is [tex]\(2\)[/tex] and the remainder is [tex]\(1\)[/tex].
- So, [tex]\(\frac{7}{3} = 2 \frac{1}{3}\)[/tex].
Thus, the division result [tex]\(5 \frac{3}{5} \div 2 \frac{4}{10}\)[/tex] equals:
[tex]\[
2 \frac{1}{3}
\][/tex]
By verifying and understanding the steps, we confirm that the final answer matches the given numerical result.
