1/2 divided by 3/4 in simplest form

1/2 divided by 3/4 in simplest form

The Correct Answer and Explanation is :

To solve the division of fractions ( \frac{1}{2} ) divided by ( \frac{3}{4} ), we can follow these steps:

Step 1: Understand Division of Fractions

When dividing fractions, the operation can be transformed into multiplication by the reciprocal of the divisor. The reciprocal of a fraction is obtained by flipping the numerator and denominator.

Step 2: Write the Problem

The problem can be rewritten as:

[
\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3}
]

Step 3: Multiply the Fractions

Now, we multiply the numerators and denominators:

[
\frac{1 \times 4}{2 \times 3} = \frac{4}{6}
]

Step 4: Simplify the Result

Next, we need to simplify ( \frac{4}{6} ). We can do this by finding the greatest common divisor (GCD) of the numerator and denominator.

The GCD of 4 and 6 is 2. We divide both the numerator and denominator by their GCD:

[
\frac{4 \div 2}{6 \div 2} = \frac{2}{3}
]

Final Result

Thus, ( \frac{1}{2} \div \frac{3}{4} = \frac{2}{3} ) in simplest form.

Conclusion

Dividing fractions might seem challenging at first, but by using the reciprocal, we simplify the process to multiplication. This method not only streamlines calculations but also enhances understanding of how fractions interact. The importance of simplifying fractions cannot be overstated, as it aids in clarity and communication, especially in mathematics. Ultimately, mastering these foundational concepts lays the groundwork for more advanced topics, enabling better problem-solving skills in future mathematical endeavors. Thus, the final answer to ( \frac{1}{2} \div \frac{3}{4} ) is ( \frac{2}{3} ).