How To Divide 1/4 By 19/12: Simple Steps Explained
Table of Contents :
Dividing fractions can seem daunting, but it’s easier than you might think! Let's break down the steps to divide ( \frac{1}{4} ) by ( \frac{19}{12} ) in a clear and simple manner. Follow along as we explore each step in detail, ensuring you grasp the concept fully! 🤓
Understanding Fractions
Before diving into the division of fractions, it's essential to understand what fractions are. A fraction consists of two parts: the numerator (the top number) and the denominator (the bottom number). In our case:
- Numerator of ( \frac{1}{4} ) is 1
- Denominator of ( \frac{1}{4} ) is 4
- Numerator of ( \frac{19}{12} ) is 19
- Denominator of ( \frac{19}{12} ) is 12
When dividing fractions, we can use the rule that states:
[ \frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} ]
This means we will flip the second fraction and multiply instead of dividing. Let’s go through the steps! 📊
Step-by-Step Guide to Dividing ( \frac{1}{4} ) by ( \frac{19}{12} )
Step 1: Flip the Second Fraction
As mentioned, the first step in dividing fractions is to flip the second fraction, which is also known as taking the reciprocal.
So, flipping ( \frac{19}{12} ) gives us ( \frac{12}{19} ).
Step 2: Rewrite the Division as Multiplication
Now, we can rewrite the division of fractions as multiplication:
[ \frac{1}{4} ÷ \frac{19}{12} = \frac{1}{4} \times \frac{12}{19} ]
Step 3: Multiply the Fractions
Next, we multiply the numerators and the denominators:
[ \text{Numerator: } 1 \times 12 = 12 ] [ \text{Denominator: } 4 \times 19 = 76 ]
Now we combine these results:
[ \frac{1}{4} \times \frac{12}{19} = \frac{12}{76} ]
Step 4: Simplify the Result
To simplify ( \frac{12}{76} ), we find the greatest common divisor (GCD) of 12 and 76. Both numbers can be divided by 4.
[ 12 ÷ 4 = 3 ] [ 76 ÷ 4 = 19 ]
This gives us:
[ \frac{12}{76} = \frac{3}{19} ]
Final Answer
Thus, dividing ( \frac{1}{4} ) by ( \frac{19}{12} ) results in:
[ \frac{1}{4} ÷ \frac{19}{12} = \frac{3}{19} ]
Visualizing the Process
It might help to visualize the process with a table:
<table> <tr> <th>Step</th> <th>Operation</th> <th>Result</th> </tr> <tr> <td>1</td> <td>Flip the second fraction</td> <td> ( \frac{12}{19} ) </td> </tr> <tr> <td>2</td> <td>Rewrite as multiplication</td> <td> ( \frac{1}{4} \times \frac{12}{19} ) </td> </tr> <tr> <td>3</td> <td>Multiply numerators and denominators</td> <td> ( \frac{12}{76} ) </td> </tr> <tr> <td>4</td> <td>Simplify the result</td> <td> ( \frac{3}{19} ) </td> </tr> </table>
Key Takeaways
Dividing fractions is not as complex as it seems. Here’s a quick summary of the steps:
- Flip the second fraction to its reciprocal.
- Rewrite the operation as multiplication.
- Multiply the numerators and denominators.
- Simplify the result if possible.
Using these steps will ensure that you confidently divide fractions in the future! 🎉
Important Note
It's crucial to remember that multiplying fractions is straightforward once you get the hang of it. Always look for opportunities to simplify your fractions during the multiplication process, as it makes your calculations much easier.
Now that you've learned how to divide ( \frac{1}{4} ) by ( \frac{19}{12} ), feel free to practice with other fractions to improve your skills! 📚 Happy learning!