1/4 Divided by 19/12: The Math Explained

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24-10-2024

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Understanding how to divide fractions can seem tricky at first, but with the right approach, it becomes much clearer. Today, we’ll dive into the problem of dividing ( \frac{1}{4} ) by ( \frac{19}{12} ). Let’s break it down step-by-step! 🧮✨

Step 1: Understand the Division of Fractions

When we divide one fraction by another, we actually multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is simply flipping the numerator and the denominator.

So, for the problem ( \frac{1}{4} \div \frac{19}{12} ):

1. Original fractions:

   • Numerator: ( 1 )
   • Denominator: ( 4 )
   • Divisor (the fraction to divide by): ( \frac{19}{12} )

2. Reciprocal of ( \frac{19}{12} ):

   • To get the reciprocal, switch the numerator and denominator to get ( \frac{12}{19} ).

Step 2: Multiply Instead of Divide

Now we can rewrite our division as multiplication:

[ \frac{1}{4} \div \frac{19}{12} = \frac{1}{4} \times \frac{12}{19} ]

Step 3: Perform the Multiplication

To multiply two fractions, you multiply the numerators together and the denominators together:

[ \frac{1 \times 12}{4 \times 19} = \frac{12}{76} ]

Step 4: Simplify the Result

Now we need to simplify ( \frac{12}{76} ). To do this, we can find the greatest common divisor (GCD) of 12 and 76.

Finding the GCD

1. The factors of 12: ( 1, 2, 3, 4, 6, 12 )
2. The factors of 76: ( 1, 2, 4, 19, 38, 76 )

Common Factors: ( 1, 2, 4 )
GCD: ( 4 )

Now we can simplify by dividing both the numerator and denominator by their GCD:

[ \frac{12 \div 4}{76 \div 4} = \frac{3}{19} ]

Final Result

The result of ( \frac{1}{4} \div \frac{19}{12} ) is:

[ \boxed{\frac{3}{19}} 🏁 ]

Important Note:

"Always remember to simplify your fractions whenever possible to make your answers clearer!"

Summary Table

By following these steps, you should feel more confident in tackling problems involving division of fractions! Happy calculating! 🥳