Answer :

To solve the fraction division problem [tex]\(\frac{13}{15} \div \frac{2}{9}\)[/tex], follow these steps:

1. Understand Division of Fractions:
When you divide by a fraction, it is the same as multiplying by its reciprocal. The reciprocal of a fraction is created by flipping its numerator and denominator.

2. Find the Reciprocal:
- The fraction you are dividing by is [tex]\(\frac{2}{9}\)[/tex].
- The reciprocal of [tex]\(\frac{2}{9}\)[/tex] is [tex]\(\frac{9}{2}\)[/tex].

3. Multiply the Fractions:
Now, multiply the first fraction [tex]\(\frac{13}{15}\)[/tex] by the reciprocal of the second fraction, [tex]\(\frac{9}{2}\)[/tex].

[tex]\[
\frac{13}{15} \times \frac{9}{2} = \frac{13 \times 9}{15 \times 2}
\][/tex]

4. Calculate the Numerator and Denominator:
- Numerator: [tex]\(13 \times 9 = 117\)[/tex]
- Denominator: [tex]\(15 \times 2 = 30\)[/tex]

So, the product is [tex]\(\frac{117}{30}\)[/tex].

5. Simplify the Fraction:
Check if [tex]\(\frac{117}{30}\)[/tex] can be simplified. Both numbers can be divided by 3:

[tex]\[
\frac{117 \div 3}{30 \div 3} = \frac{39}{10}
\][/tex]

Thus, [tex]\(\frac{39}{10}\)[/tex] is in simplest form.

6. Convert to Decimal (If Needed):
As a decimal, [tex]\(\frac{39}{10}\)[/tex] is equal to 3.9.

Therefore, the result of [tex]\(\frac{13}{15} \div \frac{2}{9}\)[/tex] is [tex]\(\frac{39}{10}\)[/tex] or 3.9 as a decimal.

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