To divide the number 33 by the fraction [tex]\(\frac{11}{12}\)[/tex], follow these steps:
1. Understand the Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
2. Find the Reciprocal of the Fraction: The given fraction is [tex]\(\frac{11}{12}\)[/tex]. The reciprocal of [tex]\(\frac{11}{12}\)[/tex] is [tex]\(\frac{12}{11}\)[/tex].
3. Rewrite the Division as Multiplication:
[tex]\[
33 \div \frac{11}{12} = 33 \times \frac{12}{11}
\][/tex]
4. Perform the Multiplication:
[tex]\[
33 \times \frac{12}{11} = \frac{33 \times 12}{11}
\][/tex]
5. Simplify the Expression:
- Multiply the numerators: [tex]\(33 \times 12 = 396\)[/tex].
- Keep the denominator: [tex]\(11\)[/tex].
Thus, we get:
[tex]\[
\frac{396}{11}
\][/tex]
6. Simplify the Fraction: Now, divide 396 by 11.
[tex]\[
396 \div 11 = 36
\][/tex]
Therefore, [tex]\(\frac{396}{11} = 36\)[/tex].
So, [tex]\(33 \div \frac{11}{12} = 36\)[/tex]. The final answer is:
[tex]\[
36
\][/tex]
