To solve the division of fractions [tex]\(\frac{2}{3} \div \frac{3}{4}\)[/tex], we can follow a systematic approach. Let's go through the steps in detail:
### Step 1: Understand Division of Fractions
The division of fractions can be converted into multiplication by the reciprocal. Specifically, to divide by a fraction, you multiply by its reciprocal.
### Step 2: Find the Reciprocal of the Second Fraction
The second fraction is [tex]\(\frac{3}{4}\)[/tex]. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex].
### Step 3: Change the Division to Multiplication
Convert the division of the fractions into multiplication:
[tex]\[
\frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{4}{3}
\][/tex]
### Step 4: Multiply the Fractions
To multiply two fractions:
1. Multiply the numerators together.
2. Multiply the denominators together.
Specifically:
[tex]\[
\frac{2}{3} \times \frac{4}{3} = \frac{2 \times 4}{3 \times 3} = \frac{8}{9}
\][/tex]
### Step 5: Simplify the Fraction (if necessary)
In this case, [tex]\(\frac{8}{9}\)[/tex] is already in its simplest form because the greatest common divisor (GCD) of 8 and 9 is 1.
Thus, the result of [tex]\(\frac{2}{3} \div \frac{3}{4}\)[/tex] is:
[tex]\[
\frac{8}{9}
\][/tex]
So, the detailed solution is:
[tex]\[
\frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{4}{3} = \frac{8}{9}
\][/tex]
Therefore, the final answer is [tex]\(\frac{8}{9}\)[/tex].
