Which expression is equivalent to 1/3 divided by 1/6
The Correct Answer and Explanation is :
To find an expression equivalent to (\frac{1}{3} \div \frac{1}{6}), we can use the rule for dividing fractions: to divide by a fraction, multiply by its reciprocal. Here’s the step-by-step solution:
- Rewrite the Division:
[
\frac{1}{3} \div \frac{1}{6}
]
becomes:
[
\frac{1}{3} \times \frac{6}{1}
] - Multiply the Fractions: Multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{1 \times 6}{3 \times 1} = \frac{6}{3}
] - Simplify the Result:
[
\frac{6}{3} = 2
]
Thus, (\frac{1}{3} \div \frac{1}{6} = 2).
Explanation (300 Words)
When dividing fractions, we use the concept of the reciprocal. The reciprocal of a fraction is simply flipping its numerator and denominator. So, the reciprocal of (\frac{1}{6}) is (\frac{6}{1}), or just 6. The division problem (\frac{1}{3} \div \frac{1}{6}) is equivalent to asking, “How many times does (\frac{1}{6}) fit into (\frac{1}{3})?” When we turn this into a multiplication problem by using the reciprocal, it becomes easier to solve.
In this case, (\frac{1}{3} \times \frac{6}{1} = \frac{6}{3}). We then simplify (\frac{6}{3}) by dividing both the numerator and the denominator by their greatest common factor, which is 3. This gives us 2.
This result makes sense because (\frac{1}{6}) is half the size of (\frac{1}{3}), so (\frac{1}{3}) contains two (\frac{1}{6}) parts. This approach applies to all fraction division problems: flipping the divisor and then multiplying makes it straightforward to determine how many times the divisor fraction fits into the dividend fraction.