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If [tex]\frac{4}{3} \div \frac{1}{6} = p[/tex], then the value of [tex]p[/tex] is between which of the following pairs of numbers?
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].
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:
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