Answered

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?

A. 3 and 4
B. 5 and 6
C. 6 and 7
D. 7 and 9



Answer :

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