To solve the problem of dividing [tex]\( \frac{7}{15} \)[/tex] by [tex]\( \frac{3}{5} \)[/tex], we will follow these steps:
### Step 1: Understand the Problem
We need to divide one fraction by another. Specifically:
[tex]\[
\frac{7}{15} \div \frac{3}{5}
\][/tex]
### Step 2: Division of Fractions
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and the denominator.
So, the reciprocal of [tex]\( \frac{3}{5} \)[/tex] is [tex]\( \frac{5}{3} \)[/tex].
### Step 3: Multiply the Fractions
Now, we multiply [tex]\( \frac{7}{15} \)[/tex] by [tex]\( \frac{5}{3} \)[/tex]:
[tex]\[
\frac{7}{15} \times \frac{5}{3}
\][/tex]
### Step 4: Multiply Numerators and Denominators
Multiply the numerators together and the denominators together:
[tex]\[
\text{Numerator: } 7 \times 5 = 35
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 3 = 45
\][/tex]
So, the result of the multiplication is:
[tex]\[
\frac{35}{45}
\][/tex]
### Step 5: Simplify the Fraction
To simplify [tex]\( \frac{35}{45} \)[/tex], we need to find the greatest common divisor (GCD) of 35 and 45, which is 5. Divide both the numerator and the denominator by 5:
[tex]\[
\frac{35 \div 5}{45 \div 5} = \frac{7}{9}
\][/tex]
Thus, the simplified result of dividing [tex]\( \frac{7}{15} \)[/tex] by [tex]\( \frac{3}{5} \)[/tex] is:
[tex]\[
\frac{7}{9}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{7}{9}}
\][/tex]
So the best answer for the question is option B: [tex]\( \frac{7}{9} \)[/tex].
