Sure, let's solve the problem of dividing the fractions [tex]\(\frac{7}{9}\)[/tex] by [tex]\(\frac{8}{15}\)[/tex].
### Step 1: Reciprocal of the second fraction
To divide by a fraction, multiply by its reciprocal. So, we take the reciprocal of [tex]\(\frac{8}{15}\)[/tex], which is [tex]\(\frac{15}{8}\)[/tex].
### Step 2: Multiplication
Multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{7}{9} \times \frac{15}{8}
\][/tex]
To multiply these fractions, we multiply the numerators and the denominators:
[tex]\[
\text{Numerator} = 7 \times 15 = 105
\][/tex]
[tex]\[
\text{Denominator} = 9 \times 8 = 72
\][/tex]
So, we have:
[tex]\[
\frac{7}{9} \div \frac{8}{15} = \frac{105}{72}
\][/tex]
### Step 3: Simplifying the fraction
To simplify [tex]\(\frac{105}{72}\)[/tex], we find the greatest common divisor (GCD) of 105 and 72.
The GCD of 105 and 72 is 3.
Now, we divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{105 \div 3}{72 \div 3} = \frac{35}{24}
\][/tex]
So, the simplified form of [tex]\(\frac{105}{72}\)[/tex] is [tex]\(\frac{35}{24}\)[/tex].
### Final Answer
Thus, the simplified form of [tex]\(\frac{7}{9} \div \frac{8}{15}\)[/tex] is:
[tex]\[
\frac{35}{24}
\][/tex]
