1/2 divided by 4 in fraction
The Correct Answer and Explanation is :
The correct answer is: ( frac{1}{8} )
To divide the fraction ( \frac{1}{2} ) by 4, we first express 4 as a fraction. Since any whole number can be written as a fraction with 1 as the denominator, we write 4 as ( \frac{4}{1} ).
Now, we can rewrite the division of fractions as a multiplication problem. The rule for dividing fractions states that you multiply by the reciprocal of the second fraction. The reciprocal of ( \frac{4}{1} ) is ( \frac{1}{4} ). Therefore, we can write the equation as follows:
[
\frac{1}{2} \div 4 = \frac{1}{2} \times \frac{1}{4}
]
Next, we perform the multiplication of the two fractions:
[
\frac{1 \times 1}{2 \times 4} = \frac{1}{8}
]
Thus, ( \frac{1}{2} \div 4 = \frac{1}{8} ).
Explanation of the Process
Dividing fractions can seem tricky at first, but the process becomes clearer with practice. When dividing by a number, you are essentially determining how many times that number fits into the original fraction. In our case, when we divide ( \frac{1}{2} ) by 4, we want to find out how much of ( \frac{1}{2} ) is equivalent to one-fourth of that amount.
By converting the divisor (4) into a fraction, we can use the multiplication approach that works universally for all fractions. The reciprocal is crucial here; by flipping the second fraction, we can switch from division to multiplication, which is often easier to manage.
This method not only applies to simple fractions but is also effective with more complex numbers. When practicing these operations, it’s essential to keep in mind that the numerator (top number) and denominator (bottom number) interact independently. Ultimately, this technique allows for easier calculations and a clearer understanding of how fractions relate to one another.
In conclusion, the division of ( \frac{1}{2} ) by 4 yields ( \frac{1}{8} ), demonstrating the fundamental properties of fractions and their operations.