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When working with fractions, understanding the concept of the 'reciprocal' is crucial. A reciprocal of a fraction simply means flipping the numerator (the top part) and the denominator (the bottom part). For instance, the reciprocal of the fraction \( \frac{1}{5} \) is \( 5 \), because you swap the 1 and the 5.

To visualize it better, consider the fraction \( \frac{a}{b} \): its reciprocal would be \( \frac{b}{a} \). This concept is quite handy when dealing with division of fractions, as converting the division of fractions problem into a multiplication one often simplifies the calculation significantly.

Remember:

• The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \).
• The reciprocal of \( \frac{7}{1} \) is simply 7.
• For a whole number \( n \), its reciprocal is \( \frac{1}{n} \).

Another critical step in solving fraction division problems is understanding the 'multiplication of fractions'. Once you've converted the division problem into a multiplication problem by using the reciprocal, you can proceed with straightforward multiplication.

For multiplying fractions, it's essential to multiply the numerators together and the denominators together. For example:

• \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \).

If either number is a whole number, you can write it as a fraction by putting it over 1. For example, 2 can be written as \( \frac{2}{1} \).

With our example in the exercise, once we’ve converted \( 2 \times 5 \) after finding the reciprocal of \( \frac{1}{5} \), we proceed to multiply:

• First, convert 2 into a fraction as \( \frac{2}{1} \).
• Multiply the fractions: \( \frac{2}{1} \times 5 = 2 \times 5 = 10 \).

Applying these steps simplifies solving fraction problems significantly!

Understanding how to work with whole numbers is fundamental when dealing with fraction problems. A whole number is any number without fractional or decimal parts, like 1, 2, 3, etc.

When a whole number is involved in operations with fractions, it's usually beneficial to first convert it into a fraction to make the calculations easier. This conversion involves writing the whole number as a numerator and using 1 as the denominator. For example:

• 2 becomes \( \frac{2}{1} \),
• 7 becomes \( \frac{7}{1} \),

This method facilitates operations such as addition, subtraction, multiplication, and division with fractions.

In our example, dividing 2 by \( \frac{1}{5} \) required us to treat 2 as \( \frac{2}{1} \), making the process of finding the reciprocal and then multiplying straightforward. Remember, converting whole numbers to fractions when necessary can simplify and clarify the operations you need to perform.