To solve the problem [tex]\(\frac{4}{3} \div \frac{1}{6} = p\)[/tex] and determine the value of [tex]\(p\)[/tex], let's go through the steps carefully:
1. Understand Division of Fractions:
When you divide by a fraction, it is the same as multiplying by the reciprocal of that fraction. The reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is [tex]\(\frac{b}{a}\)[/tex].
2. Rewrite the Division as Multiplication by the Reciprocal:
Given [tex]\(\frac{4}{3} \div \frac{1}{6}\)[/tex], we can rewrite this as [tex]\(\frac{4}{3} \times \frac{6}{1}\)[/tex]. This is because the reciprocal of [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{6}{1}\)[/tex].
3. Perform the Multiplication:
[tex]\[
\frac{4}{3} \times \frac{6}{1} = \frac{4 \times 6}{3 \times 1} = \frac{24}{3}
\][/tex]
4. Simplify the Fraction:
Simplify [tex]\(\frac{24}{3}\)[/tex] by performing the division:
[tex]\[
\frac{24}{3} = 8
\][/tex]
So, the result is [tex]\(p = 8\)[/tex].
5. Determine the Range of [tex]\(p\)[/tex]:
We need to check the given options to see which one contains the number 8. The options are:
- A. 3 and 4
- B. 5 and 6
- C. 6 and 7
- D. 7 and 9
The correct pair of numbers that contains 8 is [tex]\(7\)[/tex] and [tex]\(9\)[/tex].
Thus, the value of [tex]\(p\)[/tex] is between 7 and 9. The correct answer is:
D. 7 and 9
