How To Divide 2/5 By 3/4: Step-by-Step Guide
Table of Contents :
To divide fractions, you need to understand a few basic concepts. Dividing one fraction by another can seem tricky at first, but with a step-by-step approach, it becomes quite simple! In this guide, we will explore how to divide ( \frac{2}{5} ) by ( \frac{3}{4} ).
Understanding Fraction Division
When dividing fractions, the key is to remember the phrase "multiply by the reciprocal." The reciprocal of a fraction is obtained by swapping its numerator and denominator. Therefore, when you divide ( \frac{2}{5} ) by ( \frac{3}{4} ), you actually multiply ( \frac{2}{5} ) by the reciprocal of ( \frac{3}{4} ).
Step 1: Identify the Fractions
Let's identify the fractions we are working with:
- First Fraction: ( \frac{2}{5} )
- Second Fraction: ( \frac{3}{4} )
Step 2: Find the Reciprocal of the Second Fraction
The reciprocal of ( \frac{3}{4} ) is obtained by flipping the numerator and denominator:
[ \text{Reciprocal of } \frac{3}{4} = \frac{4}{3} ]
Step 3: Rewrite the Division as Multiplication
Now that we have the reciprocal, we can rewrite the division problem as a multiplication problem:
[ \frac{2}{5} \div \frac{3}{4} = \frac{2}{5} \times \frac{4}{3} ]
Step 4: Multiply the Fractions
To multiply two fractions, you multiply the numerators together and the denominators together:
[ \frac{2 \times 4}{5 \times 3} = \frac{8}{15} ]
Step 5: Simplify the Result (if necessary)
In this case, ( \frac{8}{15} ) is already in its simplest form since there are no common factors between 8 and 15.
Recap of the Steps
Here’s a quick recap in a tabular format:
<table> <tr> <th>Step</th> <th>Action</th> <th>Result</th> </tr> <tr> <td>1</td> <td>Identify the fractions</td> <td>(\frac{2}{5}), (\frac{3}{4})</td> </tr> <tr> <td>2</td> <td>Find the reciprocal of the second fraction</td> <td>(\frac{4}{3})</td> </tr> <tr> <td>3</td> <td>Rewrite the division as multiplication</td> <td>(\frac{2}{5} \times \frac{4}{3})</td> </tr> <tr> <td>4</td> <td>Multiply the fractions</td> <td>(\frac{8}{15})</td> </tr> <tr> <td>5</td> <td>Simplify the result (if necessary)</td> <td>(\frac{8}{15})</td> </tr> </table>
Conclusion
Dividing fractions may seem challenging at first, but following these steps makes it manageable and straightforward. By remembering to multiply by the reciprocal and carefully performing the multiplication, you can confidently divide any fractions.
Now you know how to divide ( \frac{2}{5} ) by ( \frac{3}{4} ), resulting in ( \frac{8}{15} ). Practice with other fractions to master this important math skill! 🧮✨