What is the simplified result of dividing 3/5 by 2/9?

Study for the Pharmacy Technician Certification Board Math Exam. Prepare with flashcards and multiple choice questions, each question includes hints and explanations. Excel in your exam!

To determine the result of dividing the fraction 3/5 by the fraction 2/9, you can use the rule that dividing by a fraction is equivalent to multiplying by its reciprocal.

First, take the reciprocal of the second fraction, which means you invert the fraction 2/9 to get 9/2.

Now the operation becomes:

[

\frac{3}{5} \div \frac{2}{9} = \frac{3}{5} \times \frac{9}{2}

]

To carry out the multiplication of these fractions, multiply the numerators together and the denominators together:

Numerators:

[

3 \times 9 = 27

]

Denominators:

[

5 \times 2 = 10

]

This gives you the fraction:

[

\frac{27}{10}

]

Therefore, the simplified result of dividing 3/5 by 2/9 is 27/10. This choice reflects proper understanding of fraction division and multiplication, leading to the correct final answer.

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