What is 1/8 divided by 4 in fraction form simplified?
The Correct Answer and Explanation is:
To solve the problem of dividing ( \frac{1}{8} ) by ( 4 ) in fraction form, we can follow a systematic approach.
First, we need to understand that dividing a fraction by a whole number can be simplified by converting the whole number into a fraction. The whole number ( 4 ) can be expressed as ( \frac{4}{1} ).
Now, the expression ( \frac{1}{8} \div 4 ) can be rewritten as:
[
\frac{1}{8} \div \frac{4}{1}
]
When dividing by a fraction, we multiply by its reciprocal. The reciprocal of ( \frac{4}{1} ) is ( \frac{1}{4} ). Therefore, we rewrite the division as follows:
[
\frac{1}{8} \div \frac{4}{1} = \frac{1}{8} \times \frac{1}{4}
]
Now, we can multiply the fractions. When multiplying fractions, we multiply the numerators together and the denominators together:
[
\frac{1 \times 1}{8 \times 4} = \frac{1}{32}
]
Thus, ( \frac{1}{8} \div 4 = \frac{1}{32} ).
Simplification
In this case, the fraction ( \frac{1}{32} ) is already in its simplest form. The numerator is ( 1 ), which is a prime number and has no common factors with ( 32 ). Therefore, there are no further simplifications possible.
Conclusion
The final answer to ( \frac{1}{8} \div 4 ) is ( \frac{1}{32} ). This demonstrates an important principle in fraction arithmetic: dividing fractions by whole numbers involves converting the whole number into a fraction and then using multiplication by the reciprocal to arrive at the answer. Thus, we see that ( \frac{1}{32} ) is a smaller fraction, illustrating how division by a larger whole number reduces the value of the original fraction.