1/6 divided by 1/4 =
The Correct Answer and Explanation is:
To solve the problem ( \frac{1}{6} \div \frac{1}{4} ), we can follow the steps of dividing fractions, which involves multiplying by the reciprocal of the divisor. Here’s how to do it step-by-step:
- Identify the fractions: In this case, the fractions are ( \frac{1}{6} ) (the dividend) and ( \frac{1}{4} ) (the divisor).
- Reciprocal of the divisor: The reciprocal of ( \frac{1}{4} ) is ( \frac{4}{1} ) (or simply 4).
- Rewrite the division as multiplication: The division can be rewritten as:
[
\frac{1}{6} \div \frac{1}{4} = \frac{1}{6} \times \frac{4}{1}
] - Multiply the fractions: To multiply fractions, multiply the numerators together and the denominators together:
[
\frac{1 \times 4}{6 \times 1} = \frac{4}{6}
] - Simplify the result: The fraction ( \frac{4}{6} ) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[
\frac{4 \div 2}{6 \div 2} = \frac{2}{3}
]
Therefore, the answer to ( \frac{1}{6} \div \frac{1}{4} ) is ( \frac{2}{3} ).
Explanation of the Process
Dividing fractions may seem challenging at first, but it follows a straightforward procedure. The essence of division is determining how many times the divisor fits into the dividend. When dividing by a fraction, you can conceptualize it as finding out how many times that fraction fits into the whole. To make the operation easier, we multiply by the reciprocal of the fraction being divided. This switch from division to multiplication simplifies the calculations.
In this specific case, when we divided ( \frac{1}{6} ) by ( \frac{1}{4} ), we converted the operation to a multiplication problem. This technique highlights a vital mathematical principle: division by a fraction is equivalent to multiplying by its reciprocal, allowing us to maintain the relationship of the original numbers while simplifying the operation. After multiplying, we obtained ( \frac{4}{6} ), which we simplified to ( \frac{2}{3} ). This not only yields the correct answer but also illustrates the importance of understanding fraction manipulation, which is a fundamental skill in mathematics.