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} ):
-
Original fractions:
- Numerator: ( 1 )
- Denominator: ( 4 )
- Divisor (the fraction to divide by): ( \frac{19}{12} )
-
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
- The factors of 12: ( 1, 2, 3, 4, 6, 12 )
- 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
Operation | Fraction | Result |
---|---|---|
Division | ( \frac{1}{4} \div \frac{19}{12} ) | ( \frac{3}{19} ) |
Reciprocal of Divisor | ( \frac{19}{12} ) | ( \frac{12}{19} ) |
Multiplication of Numerators | ( 1 \times 12 ) | ( 12 ) |
Multiplication of Denominators | ( 4 \times 19 ) | ( 76 ) |
GCD of 12 and 76 | ( 4 ) | |
Simplified Result | ( \frac{3}{19} ) |
By following these steps, you should feel more confident in tackling problems involving division of fractions! Happy calculating! 🥳