To divide [tex]\(1 \frac{3}{5} \div \frac{2}{3}\)[/tex], we will follow these steps:
1. Convert the mixed number to an improper fraction:
[tex]\[
1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5}
\][/tex]
2. Set up the division problem with the fractions:
[tex]\[
\frac{8}{5} \div \frac{2}{3}
\][/tex]
3. Rewrite the division as multiplication by the reciprocal:
Division of fractions is equivalent to multiplying by the reciprocal. So:
[tex]\[
\frac{8}{5} \div \frac{2}{3} = \frac{8}{5} \times \frac{3}{2}
\][/tex]
4. Multiply the fractions:
[tex]\[
\frac{8 \times 3}{5 \times 2} = \frac{24}{10}
\][/tex]
5. Simplify the fraction:
The fraction [tex]\(\frac{24}{10}\)[/tex] can be simplified. The greatest common divisor (GCD) of 24 and 10 is 2, so divide both the numerator and the denominator by 2:
[tex]\[
\frac{24 \div 2}{10 \div 2} = \frac{12}{5}
\][/tex]
6. Convert the improper fraction back to a mixed number:
[tex]\[
\frac{12}{5} \text{ can be written as } 2 \frac{2}{5}
\][/tex]
- 12 divided by 5 gives a quotient of 2 with a remainder of 2.
- Thus, the mixed number is [tex]\(2 \frac{2}{5}\)[/tex].
Therefore, the result of [tex]\(1 \frac{3}{5} \div \frac{2}{3}\)[/tex] is [tex]\(\boxed{2 \frac{2}{5}}\)[/tex].
