Dividing Fractions: 4/6 ÷ 3/5 Simplified
Table of Contents :
To understand how to divide fractions, it’s essential to grasp the fundamentals of fraction division and how simplification works. In this article, we will walk through the process of dividing the fractions ( \frac{4}{6} ) by ( \frac{3}{5} ) step by step. This topic is vital for students and anyone looking to improve their math skills. Let's dive into the world of fractions! 🧮
Understanding Fractions
Before we delve into the division of fractions, let’s ensure we understand what fractions are. A fraction represents a part of a whole. It consists of two numbers:
- The numerator (the top part), which indicates how many parts we have.
- The denominator (the bottom part), which shows how many equal parts the whole is divided into.
For example, in the fraction ( \frac{4}{6} ):
- 4 is the numerator, indicating we have 4 parts.
- 6 is the denominator, indicating the whole is divided into 6 equal parts.
Division of Fractions
When dividing fractions, the process involves a simple rule: multiply by the reciprocal. The reciprocal of a fraction is obtained by flipping its numerator and denominator.
For example, the reciprocal of ( \frac{3}{5} ) is ( \frac{5}{3} ).
Step-by-Step Division
To divide ( \frac{4}{6} ) by ( \frac{3}{5} ), follow these steps:
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Write the problem as a multiplication of ( \frac{4}{6} ) and the reciprocal of ( \frac{3}{5} ): [ \frac{4}{6} \div \frac{3}{5} = \frac{4}{6} \times \frac{5}{3} ]
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Multiply the numerators: [ 4 \times 5 = 20 ]
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Multiply the denominators: [ 6 \times 3 = 18 ]
So we have: [ \frac{4}{6} \div \frac{3}{5} = \frac{20}{18} ]
Simplifying the Result
Next, we need to simplify the fraction ( \frac{20}{18} ). Simplification involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
Finding the GCD
To simplify ( \frac{20}{18} ):
- The GCD of 20 and 18 is 2.
- Therefore, we divide both the numerator and the denominator by 2:
[ \frac{20 \div 2}{18 \div 2} = \frac{10}{9} ]
Final Answer
Thus, the simplified result of ( \frac{4}{6} \div \frac{3}{5} ) is: [ \frac{10}{9} ]
Visual Representation
Visual aids can enhance understanding of fractions and their operations. Below is a table that summarizes the steps we've taken in this division:
<table> <tr> <th>Step</th> <th>Description</th> <th>Result</th> </tr> <tr> <td>1</td> <td>Write the division as multiplication by the reciprocal</td> <td>(\frac{4}{6} \times \frac{5}{3})</td> </tr> <tr> <td>2</td> <td>Multiply the numerators</td> <td>20</td> </tr> <tr> <td>3</td> <td>Multiply the denominators</td> <td>18</td> </tr> <tr> <td>4</td> <td>Simplify the fraction</td> <td>(\frac{10}{9})</td> </tr> </table>
Important Notes
Always remember to simplify your final answer if possible! Simplifying helps in presenting fractions in their simplest form, which is often more useful in mathematical applications.
Conclusion
Dividing fractions may seem daunting at first, but with the understanding of reciprocals and simplification, it becomes a straightforward process. The example of dividing ( \frac{4}{6} ) by ( \frac{3}{5} ) to get ( \frac{10}{9} ) illustrates the principles clearly.
Remember, practice makes perfect! Try working on different examples to build your confidence in dividing fractions. Happy calculating! 🥳