To solve the division of two fractions, [tex]\(\frac{4}{5} \div \frac{5}{6}\)[/tex], follow these steps:
1. Understand the Concept of Dividing Fractions:
Dividing fractions is equivalent to multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
2. Reciprocal of the Second Fraction:
The reciprocal of [tex]\(\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
3. Rewrite the Division as a Multiplication:
[tex]\[
\frac{4}{5} \div \frac{5}{6} = \frac{4}{5} \times \frac{6}{5}
\][/tex]
4. Multiply the Fractions:
Multiply the numerators together and the denominators together:
[tex]\[
\frac{4 \times 6}{5 \times 5} = \frac{24}{25}
\][/tex]
5. Convert to Decimal Form (Optional):
To convert the fraction [tex]\(\frac{24}{25}\)[/tex] to its decimal form, divide the numerator by the denominator:
[tex]\[
\frac{24}{25} = 0.96
\][/tex]
Thus, the result of [tex]\(\frac{4}{5} \div \frac{5}{6}\)[/tex] is [tex]\(0.96\)[/tex].
