To solve the division of two fractions and determine the value of [tex]\( p \)[/tex] for [tex]\(\frac{4}{3} \div \frac{1}{6}\)[/tex], follow the steps below:
1. Rewrite the division as multiplication by the reciprocal:
[tex]\[
\frac{4}{3} \div \frac{1}{6} = \frac{4}{3} \times \frac{6}{1}
\][/tex]
2. Multiply the fractions:
- Multiply the numerators:
[tex]\[
4 \times 6 = 24
\][/tex]
- Multiply the denominators:
[tex]\[
3 \times 1 = 3
\][/tex]
Hence,
[tex]\[
\frac{4}{3} \times \frac{6}{1} = \frac{24}{3}
\][/tex]
3. Simplify the resulting fraction:
[tex]\[
\frac{24}{3} = 8
\][/tex]
Therefore, the value of [tex]\( p = 8 \)[/tex].
Given this value, we need to determine which range the value of [tex]\( p \)[/tex] falls into among the provided options:
A. 3 and 4 \\
B. 5 and 6 \\
C. 6 and 7 \\
D. 7 and 9
Since [tex]\( 8 \)[/tex] is between 7 and 9, the correct answer is:
D. 7 and 9
