To solve the fraction [tex]\(\frac{11}{5}\)[/tex], we need to perform the division of the numerator by the denominator.
1. The fraction [tex]\(\frac{11}{5}\)[/tex] represents the division of 11 by 5.
2. When we divide 11 by 5, we start by seeing how many times 5 can fit into 11.
3. 5 fits into 11 two times because [tex]\(5 \times 2 = 10\)[/tex], which is the largest multiple of 5 less than or equal to 11.
4. After accounting for [tex]\(10\)[/tex] (the product of [tex]\(5 \times 2\)[/tex]), we subtract 10 from 11.
5. The subtraction gives us [tex]\(11 - 10 = 1\)[/tex], which is the remainder.
6. To express the division more completely, we write it as [tex]\(2 + \frac{1}{5}\)[/tex].
7. The remaining fraction [tex]\(\frac{1}{5}\)[/tex] can be expressed as a decimal.
8. [tex]\(\frac{1}{5} = 0.2\)[/tex].
9. So we add the whole number part and the decimal part together: [tex]\(2 + 0.2 = 2.2\)[/tex].
Thus, the result of dividing 11 by 5, or [tex]\(\frac{11}{5}\)[/tex], is [tex]\(2.2\)[/tex].
