To evaluate [tex]\(\frac{6}{7} \div \frac{1}{6}\)[/tex], follow these steps:
1. Understand the Division of Fractions:
Dividing by a fraction is equivalent to multiplying by its reciprocal. In this problem, we need to divide [tex]\(\frac{6}{7}\)[/tex] by [tex]\(\frac{1}{6}\)[/tex].
2. Find the Reciprocal of the Second Fraction:
The reciprocal of [tex]\(\frac{1}{6}\)[/tex] is obtained by swapping the numerator and the denominator. So, the reciprocal of [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{6}{1}\)[/tex].
3. Multiply the First Fraction by the Reciprocal of the Second Fraction:
Now, rewrite the original division problem as a multiplication problem:
[tex]\[
\frac{6}{7} \div \frac{1}{6} = \frac{6}{7} \times \frac{6}{1}
\][/tex]
4. Multiply the Numerators and the Denominators:
Multiply the numerators together and the denominators together:
[tex]\[
\frac{6}{7} \times \frac{6}{1} = \frac{6 \times 6}{7 \times 1} = \frac{36}{7}
\][/tex]
5. Simplify the Fraction (If Necessary):
The fraction [tex]\(\frac{36}{7}\)[/tex] is already in its simplest form, but it can be expressed as a mixed number if preferred.
6. Convert to a Decimal (Optional):
For clarity, we can express [tex]\(\frac{36}{7}\)[/tex] as a decimal by performing the division [tex]\(36 \div 7\)[/tex], which gives approximately [tex]\(5.142857142857142\)[/tex].
Thus, the value of [tex]\(\frac{6}{7} \div \frac{1}{6}\)[/tex] is [tex]\(\frac{36}{7}\)[/tex] or approximately [tex]\(5.142857142857142\)[/tex].
