To determine [tex]\(\frac{11}{12} \div \frac{1}{3}\)[/tex], we can follow these steps:
1. Understand the Division of Fractions: Dividing one fraction by another involves multiplying by the reciprocal of the divisor. In this case, we need to divide [tex]\(\frac{11}{12}\)[/tex] by [tex]\(\frac{1}{3}\)[/tex].
2. Reciprocal: The reciprocal of [tex]\(\frac{1}{3}\)[/tex] is [tex]\(\frac{3}{1}\)[/tex] (since flipping the numerator and the denominator gives the reciprocal).
3. Multiplication by the Reciprocal:
[tex]\[
\frac{11}{12} \div \frac{1}{3} = \frac{11}{12} \times \frac{3}{1}
\][/tex]
4. Multiply the Fractions:
[tex]\[
\frac{11}{12} \times \frac{3}{1} = \frac{11 \times 3}{12 \times 1} = \frac{33}{12}
\][/tex]
5. Simplify the Fraction:
[tex]\[
\frac{33}{12} = \frac{33 \div 3}{12 \div 3} = \frac{11}{4}
\][/tex]
6. Convert the Improper Fraction to a Mixed Number:
[tex]\[
\frac{11}{4} = 2 \frac{3}{4}
\][/tex]
Therefore, [tex]\(\frac{11}{12} \div \frac{1}{3} = 2 \frac{3}{4}\)[/tex].
The numeric result of converting [tex]\(\frac{11}{4}\)[/tex] to a decimal is:
[tex]\[
\frac{11}{4} = 2.75
\][/tex]
Thus, the answer to [tex]\(\frac{11}{12} \div \frac{1}{3}\)[/tex], expressed as a mixed number, is [tex]\(2 \frac{3}{4}\)[/tex], and as a decimal, it is [tex]\(2.75\)[/tex].
