Question

Evaluate each expression. $$ \frac{\frac{5}{21}}{\frac{2}{35}} $$

   Evaluate each expression.
$$
\frac{\frac{5}{21}}{\frac{2}{35}}
$$

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 0, Problem 84

Instant Answer

Solved by Expert Victoria Karaluz

05/18/2020

Step 1

The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of $\frac{2}{35}$ is $\frac{35}{2}$. Therefore, the expression becomes: $$ \frac{5}{21} \times \frac{35}{2} $$ Show more…

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Evaluate each expression. $$ \frac{\frac{5}{21}}{\frac{2}{35}} $$

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Key Concepts

Division of Fractions

This concept involves recognizing that dividing by a fraction is equivalent to multiplying by its reciprocal. Understanding this principle is crucial because it simplifies the operation and ensures that the division of two fractions can be performed as a multiplication problem, which is generally more straightforward.

Multiplication of Fractions

When multiplying fractions, the numerators are multiplied together and the denominators are multiplied together. This concept is essential in fraction arithmetic as it provides a systematic method to combine fractions, which later allows for simplification of the result.

Simplification of Fractions

Simplification involves reducing a fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor. This process helps to present answers in a more concise and understandable form and is a key step after performing operations on fractions.

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